On the vibrations of formic acid predicted from first principles

In this article, we review recent first principles, anharmonic studies on the molecular vibrations of gaseous formic acid in its monomer form. Transitions identified as fundamentals for both cis- and trans form reported in these studies are collected and supported by results from high-resolution experiments. Attention is given to the effect of coordinate coupling on the convergence of the computed vibrational states.

Introduction
Vibrational spectroscopies continue to be a shared interest of both theoretical and experimental approaches in chemistry, with the harmonic approximation 1 as the dominating theoretical description in practice. In contrast, methods that describe vibrations from first principles, obey to the rules of quantum mechanics and go beyond the harmonic approximation are far from routine, despite the apparent anharmonicity of many molecular vibrations. Since a clear hierarchy is not well established for these methods, investigating their performance and characteristics in a joint discussion with regard to the accuracy of the predicted vibrations of a selected molecule may be of interest in addition to the comparison to high-accuracy experimental data. Formic acid, the smallest carboxylic acid, emerges as a good candidate in this respect; it exhibits structural cistrans isomerism and it forms a hydrogen-bonded dimer at room temperature, giving rise to complex nuclear dynamics which are difficult to model accurately. 2 In a broader perspective, understanding the nuclear dynamics of carboxylic acids could also give insight into the conformation and folding mechanisms of proteins. After a brief discussion of selected concepts employed in the anharmonic and variational computation of molecular spectra, we review experimental results and discuss ab initio calculations of the anharmonic molecular vibrations of the monomer forms of formic acid in a chronological order.

Selected concepts of the variational calculation of molecular vibrations
Arguably one of the most difficult aspects of the calculation of molecular vibrations beyond the harmonic approximation is the definition of an appropriate coordinate system and the derivation of the corresponding vibrational Hamiltonian. The separation of the purely vibrational motion of the molecule requires internal coordinates, 1,3 but the conditions which define a unique and an optimal coordinate system which is appropriate for various types of nuclear motion are not known. 4 The Watson Hamiltonian which was derived for non-linear 5 and linear 6 reference configurations and defines the rovibrational motion in terms of rectilinear normal coordinates remains to be one of the most popular choices, since its definition ensures minimal rovibrational coupling and an optimal representation of molecular vibrations with small displacements from the reference geometry. 1,4 It follows, that difficulties are encountered if vibrations corresponding to e.g. torsional motions or significant displacements from the equilibrium structure are computed in this representation. Slow convergence of the computed vibrational eigenstates or inaccurate results in approximate methods are often encountered in these cases. 7 Since the Watson Hamiltonian is invariant under the unitary transformations of the normal modes, attempts for improvement have been made by optimizing [8][9][10] and localizing 11 the normal modes. The choice of the vibrational Hamiltonian also affects the ease of interpretation of the computed results. Whereas vibrations which are well described by the harmonic approximation are found to be mostly localized on the respective normal coordinate, anharmonic vibrations which are encountered e.g. in the high-energy region, can have contributions along multiple normal coordinates, leading to increasingly difficult assignments. 12 Whereas an ill-defined coordinate system can introduce artificial correlation, a well-choosen one may minimize the correlation between the different degrees of freedom. 13 The main focus of this section is not a to give a comprehensive review of available vibrational methods, for which already vast literature is available, 4,14-19 but rather to give an overview of selected concepts and methods necessary for discussing the literature on formic acid, reviewed below. We also shall not discuss the computation of intensities, but emphasize the importance of the development of e.g. accurate electronic dipole surfaces aiding the interpretation of IR spectra.
In order to present a joint discussion of variational methods and the literature reviewed below, we introduce the following notation for the vibrational coordinates q = {q 1 ,. . .,q M }. Once defined, the vibrational Hamiltonian may be separated into a kinetic and potential part, where the form of both the kinetic and potential term depends on the employed coordinate system. The potential term, the so called Potential Energy Surface (PES) V(q) can be calculated either by direct evaluation of ab initio electronic energies along the vibrational coordinates, or it may be pre-fitted to an appropriate analytic form. Most commonly, either a Taylor expansion 20 @VðqÞ @q m @q n @q l q 0 q m q n q l þ . . . ; (1) where q 0 is a reference geometry, or a many-body expansion 21 is employed, where the V m (q m ) are the so-called one-, V mn (q m ,q n ) are the two-, and V mn. . .M (q m ,q n ,. . .,q M ) are the Mbody terms, respectively, each dependent on a subset of coordinates. The sum-of product (SOP) form 22,23 VðqÞ is also commonly employed. Here, the potential is expressed as a sum with expansion coefficients c r of potential terms V r , where the latter is expressed as a product of terms dependent only on coordinate Q k , respectively. The Q k s may combine multiple coordinates of q, therefore reducing the computational effort, i.e. f o M and r = [r 1 ,. . .,r f ]. We note, that the accuracy of any vibrational structure calculation is limited by the accuracy of the PES, and therefore the electronic structure method employed for its construction.
Beyond the well-known harmonic approximation, for which the solutions can be obtained exactly due to approximating the potential as a second order Taylor expansion in normal coordinates, variational solutions 24 to the vibrational Schrödinger equation require an ansatz. In the Vibrational Self-Consistent-Field (VSCF) method, 18,25 the vibrational states are computed in the product form where the functions dependent on a single vibrational coordinate are eigenfunctions of the mean-field operator 26 where we have assumed that the kinetic energy operator can be written as a sum of independent terms, T m (q m ). n = [n 1 ,. . .,n M ] collects the available quantum numbers associated with the single-coordinate functions f nm (q m ) determined self-consistently, and % n denotes all quantum numbers but the m-th. The vibrational energies are then the expectation value of the full Hamiltonian with the VSCF wavefunction (eqn (4)) which can be obtained in a state-specific, for a chosen set of quantum numbers, or in a non state-specific fashion. The VSCF approximation has been improved by the correlation-corrected VSCF approach (CC-VSCF) developed by Gerber and co-workers 18,27,28 also known as second order vibrational Møller-Plesset (VMP2) theory. In this method, the deviation of the exact wave function from the mean-field solution is assumed to be small, such that a second order perturbation correction is applied for a correlation-corrected energy expression. The latter differs in the zeroth order problem from the well-known second order vibrational perturbation (VPT2) theory in which the harmonic approximation is corrected.
Going beyond the product form, a linear combination of configurations with expansion coefficients C n may be used. A full direct product basis can be employed as a basis in eqn (6) (e.g. products of weighted classical orthogonal polynomials, 29 harmonic oscillator basis functions 30 ), however, without further approximations, this leads to an ansatz with an exponential scaling with regard to the size of the system treated and therefore a blowup in the number of terms in the expansion. The truncation of the direct product basis according to some condition is therefore common practice. In Vibrational Configuration Interaction (VCI) 26,31,32 the configurations are usually taken from preceding VSCF calculations. The ansatz can be written as where c i (q) is the reference configuration andt l generates an excited configuration from the quantum numbers i = [i 1 ,. . .,i M ].
If the full excitation space is used, the method is called full VCI (FVCI). Similarly to CI in electronic structure theory, singles, doubles, and higher excitations are generated, and the expansion is truncated to allow for a subset of the available quantum numbers and/or excitations, therefore introducing a bound on the, in

Review PCCP
principle, infinite sum. The expansion coefficients C n of the normalized wavefunction are determined variationally as eigenvectors of the VCI matrix hc n (q)|H(q)|c l (q)i. However, the straightforward construction of the untruncated VCI matrix and computation of its eigenvectors is prohibitively expensive and in practice approximations are introduced. 33,34 By partitioning the modes into a set of active and a set of bath modes Mizukami and Tew 35 have introduced the vibrational active space self-consistent field theory (VASSCF), vibrational active space configuration interaction (VASCI) and vibrational active space second order perturbation theory (VASPT2) methods. These methods employ a product of a CI type ansatz for the active modes and a simple product ansatz for the bath modes. Whereas in their VASSCF approach all CI coefficients and all single-coordinate functions are optimized, only a subset of single-coordinate functions are optimized in their VASCI approach.
In the Multi-configurational time-dependent Hartree 22,36 (MCTDH) method a time-dependent ansatz is employed with expansion coefficients C r where f corresponds to the number of combined coordinates (particles) and the orthonormal single-particle functions f rk (Q k ,t) are determined as linear combination of primitive basis functions with time-dependent expansion coefficients, determined variationally. In practice an upper bound is introduced for the sum by limiting the number of single-particle functions. The eigenstates can be computed via the improved relaxation or block-improved relaxation method of MCTDH. 23 Since MCTDH uses time-dependent configurations, the configurational space can naturally adapt during the evolution of the wave function and can therefore be compared to the vibrational multiconfigurational self-consistent field method. 37 Generally speaking, the underlying coordinate system defines the level of coupling among the coordinates that has to be captured by the Hamiltonian and the wave function of each vibrational state. The convergence of the Hamiltonian with respect to the convergence of the computed energy levels can be tested by e.g. including higher-order terms of a Taylorexpanded PES or higher-order coupling terms in a many-body expanded PES. A systematic improvement of variational wave functions is possible through e.g. the enlargement of the underlying basis set(s) and by employing multiple configurations. Finally, SCF and dynamic methods have the advantage of adapting the single-coordinate functions to a given computed state. Besides obtaining converged states within the respective approach, the accuracy of the latter can be quantified by comparison to high-accuracy experimental frequencies, or a higher level of theory, if available. It follows, that an inaccurate PES computed at a low-level of electronic structure theory or not supportive of the relevant nuclear positions will not yield good results, as will not a single-configurational approach for a coordinate system which is inappropriate for the computed vibration (e.g. rectilinear coordinates for vibrations involving torsional motions). In addition, resonances between states cannot be captured by single-configurational approaches such that any variational or perturbative approach relying only on one configuration will fail in this respect. 35 We note, that although multi-configurational approaches can provide the most accurate results, due to their inherent scaling with system-size, they are difficult to apply to larger systems or highly-coupled motions requiring large bases. In this respect, perturbative approaches represent cost-effective alternatives beyond the harmonic approximation.
Once the vibrational states are determined, the interpretation of the computed levels presents the next challenge. In the harmonic approximation the vibrations are decoupled, such that a single quantum number is sufficient for characterizing a molecular vibration, i.e. n n 1 corresponds to the n-th solution of the harmonic oscillator in the coordinate q 1 . If n = 1 the vibration is called a fundamental and otherwise with n 4 1 an overtone vibration. As mentioned at the beginning of this section, it is advantageous to find a representation which allows each vibration to be localized along its coordinate and therefore to be decoupled from the remaining degrees of freedom. In this case, the product form is already sufficient and an unequivocal assignment in terms of a single set of quantum numbers is possible. Then, the harmonic or VSCF approximation may already present a satisfactory description of the vibrational state, and the corresponding VCI wave function is characterized by a single large CI coefficient. In the opposite case, the absence of a prevalent configuration may be regarded as the evidence of the vibrational counterpart of the concept of static correlation in electronic structure theory. As a dynamic method, in MCTDH the single-particle functions naturally adapt to the computed state, such that in principle a compact wave function can be achieved. In certain cases a singleconfigurational description completely fails, as is the case for resonances: in Fermi resonance, 38 for instance, an energy splitting, ascribed to the interaction of an overtone and a fundamental accidentally close in energy, is observed.

Formic acid
Despite its size, formic acid exhibits a rich structural complexity, which has led to an ongoing theoretical and experimental interest in its nuclear dynamics over the years. 30,35,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] In its monomer form (Fig. 1), two stable configurations of the C s point group symmetry, cis and trans have been identified via microwave 57-59 and submillimeter spectroscopy 60,61 in the gas phase. With a difference of about 1365 cm À1 in zero point energy, as measured by gas-phase microwave relative intensity measurements, 57 and 1412 cm À1 62 and 1415 cm À1 56 determined ab initio, the trans form is significantly more abundant at room temperature. This relative stability has been assumed to be due to an intramolecular hydrogen bond, 20 but this idea was discarded later on. 20,63 The gas-phase structure of the trans form was determined via electron diffraction. 64 Based on the ground-state rotational constants determined by microwave spectroscopy, approximate equilibrium structures have been derived. 65 The geometries can be connected via an internal rotation of hydrogen of the OH group around the CO axis, 66 where the earliest experiments found a barrier height of 4827 cm À1 . 57 At low temperatures, proton tunneling through the torsional barrier was found to limit the lifetime of cis-HCOOH as measured in Argon matrix by Petterson et al., 42,67 whereas the deuterium tunneling rate was found to be significanty slower. 68 The first IR absorption and Raman spectra of gaseous formic acid were measured in 1938 69 and 1940 70 by Bonner et al., and numerous experimental studies determining the vibrational transitions have been performed ever since at an increasingly high resolution. [39][40][41][42][43][44][45][46][47][50][51][52]54,[71][72][73][74][75][76][77][78][79] The signals arising due to the presence of the cis and trans monomers or the dimer have been differentiated experimentally by signal intensification via population control with thermal 54 or laser 42 excitation. Most variational theoretical methods consider purely the vibrational motion at zero temperature which can be compared to low temperature or high-resolution (e.g. FT absorption) rotationally analysed data. Two popular low temperature spectroscopic methods have emerged in this respect. In matrix isolation spectroscopy 80,81 the analyte is condensed with an inert gas, e.g. a noble gas or nitrogen at low temperature, such that the molecules are ''trapped'' with different local environments in a matrix. This results in a shift of the measured frequencies and a splitting of absorption bands. For highresolution data, the best agreement with theory is therefore achieved if the matrix-analyte interactions are also modeled in the theoretical description. As opposed to matrix isolation spectroscopy, jet-cooled spectroscopy 76 does not suffer from such effects. In this method the analyte is passed through a nozzle with a neutral carrier gas and expanded into an evacuated jet chamber at low temperatures. Population enhancement has been achieved in a jet-setup via thermal control therefore recording and spectra at different temperatures have been compared. 54 Complementary high-resolution IR and Raman spectra of partially and fully deuterated formic acid have been recorded for all isotopologues of the cis and trans monomer (DCOOH, HCOOD, DCOOD). 41,44,45,50,[82][83][84][85][86][87][88] Some spectral regions of formic acid are dense and therefore require a careful rotational analysis, hot bands and overlapping dimer signals further complicate the spectrum with the density of states generally increasing in the higher energy region. 54,82 Amongst the many experimental studies performed for trans HCOOH, 50,55,61,83,88,89 we mention the work of Freytes et al. 82 , who measured gas-phase room-temperature Fourier-transform (FT) and intracavity laser absorption spectra of trans-HCOOH. They reported band origins from 626 cm À1 to 13 284 cm À1 and performed a detailed analysis on the rotational structure of the first CH stretching vibrational overtone n 2 2 and the second OH stretch overtone n 3 1 of formic acid. Their work built on a previous study of Hurtmans et al., who presented a rovibrational analysis in the range of the first and third overtone of the OH stretching vibration n 2 1 and n 4 1 of trans-HCOOH based on FT spectroscopy and intracavity laser absorption spectroscopy measurements. 83 Room temperature Raman measurements were performed by Bertie et al. 40 in the range from 70 cm À1 to 4000 cm À1 for all isotopologues of the dimer, where the monomer signals could also be identified. Recent work of Nejad, Suhm and Meyer 54 provided gas-phase Raman-jet measurements for all four deuterated isotopologues of formic acid monomer of both the cis and trans configuration, where the spectra were recorded with a nozzle temperature of 160 1C. They detected Fermi resonance doublets for the fundamentals n 1 and n 5 of trans-HCOOH, n 3 and n 5 for trans-DCOOH, n 2 and n 5 for trans-HCOOD, and n 2 and n 3 for trans-DCOOD. A summary of available benchmark quality experimental values for the vibrational transitions of trans-HCOOH and deuterated forms up to 4000 cm À1 in the far and mid-IR region with additional Raman-jet measurements has been recently compiled by Nejad and Sibert 70 from gas-phase IR and Raman spectra reported in literature.
Vibrational data for cis-HCOOH and isotopologues is more scarce 48,66,68,[90][91][92][93][94][95] due to the experimental difficulty of populating the cis state. Matrix-isolation spectroscopy measurements in Argon have been performed for cis-HCOOH by narrowband IR pumping of the first OH stretching overtone of trans-HCOOH n 2 1 by Pettersson et al. 42 Maçôas et al. recorded near-and mid-IR spectra for HCOOH, DCOOH and HCOOD in solid argon matrix at 8 K from 400 cm À1 to 7800 cm À1 48 where the cis population was enhanced by pumping a trans to cis transition by narrowband tunable IR radiation. Raman-jet spectra for cis-HCOOH and isotopologues have been recorded recently by Meyer, Nejad and Suhm 54,87,96 via thermal excitation between 100-190 1C prior to the jet expansion. In Table 1 we summarize transition frequencies of gaseous formic acid monomer from highresolution experiments, which have been assigned as fundamentals of the cis and trans monomer, respectively. We note, that many of the fundamentals have been found to be affected by rovibrational 97 and resonance interactions, 20 of which the n 5 /n 2 9 Fermi resonance pair of trans-HCOOH has been the most prominent due to an early experimental misassignment of the more intense overtone band as the fundamental. 82 Throughout this work, the assignment of the fundamentals in terms of nuclear displacements is discussed with the valence coordinate definition of Richter and Carbonniére 56 (Fig. 2), although some of the studies reviewed below employ different coordinates. 4 Ab initio studies on the formic acid monomer

First ab initio studies
One of the first ab initio, anharmonic studies on the formic acid monomer was concerned with the overtone series of the OH stretching vibration n n 1 of trans-HCOOH. 83 Hurtmans et al. recorded rotationally resolved overtone spectra of formic acid with high-resolution gas-phase FT and intracavity laser absorption spectroscopy and performed rovibrational analysis for the first n 2 1 and third n 4 1 overtones in the same work. They constructed an effective one-dimensional Hamiltonian dependent on the normal coordinate of the OH stretching mode for the analysis of the OH stretching vibration by relaxing the remaining geometrical parameters along the coordinate. The resulting effective potential was constructed at the MP2/cc-pVTZ level, and the corresponding one-dimensional variational solutions were computed for n n 1 , n r 4 with an agreement within 50 cm À1 compared to the experimental band origins of the same work. It was found that the excitation of these n n 1 vibrations affects the HOC angle with increasing n. The induced electric dipole moment was found to be initially almost parallel to the OH bond and progressively tilted towards the CQO bond with increasing n. Based on these results Hurtmans et al. proposed a possible proton exchange mechanism promoted by the excitation of the OH overtones.
Subsequently Maçôas et al. 48 performed CC-VSCF calculations to support the assignment of the mid-and near-IR transitions measured by matrix-isolation spectroscopy in the same work. The transitions were determined at two trapping sites in solid argon for cis-and trans-HCOOH. Mid-IR spectra of trans and cis-DCOOH and near-IR spectra of trans-DCOOH and trans-HCOOD were also recorded, where the cis transitions were determined by narrowband IR pumping of the first OH overtone transition n 2 1 of the trans configuration. For cis-HCOOH about half of the expected fundamentals could be recorded and strong matrix effects, such as splitting of the recorded signals, was observed, making the assignments difficult. The CC-VSCF calculations were performed in the normal mode representation without rovibrational coupling terms and the PES was expressed with pairwise coupling terms, constructed directly at the MP2/ 6-311++G(2d,2p) level of theory for each pair of normal coordinate gridpoints. They computed all fundamentals and selected overtone and combination bands in the mid-and near-IR region for both trans-and cis-HCOOH and -DCOOH. We have included in Tables 2 and 3 the computed transitions identified as fundamentals of cis-and trans-HCOOH reported in their work. Anharmonicity was found to be strongest for the highfrequency stretching vibrations of trans and cis-HCOOH, i.e. n 1 and n 2 were found to have a downshift of up to 200 cm À1 compared to their calculated harmonic counterpart, whereas most fundamentals were found to reproduce the matrixisolation experiments reasonably well. Exceptions are fundamentals corresponding to torsional and deformation type motions, that is, n 5 and n 9 were predicted to be below the experimental values, e.g. for n 9 around 40 cm À1 and 70 cm À1 for trans-HCOOH and cis-HCOOH, respectively. In the near-IR region, the first overtones n 2 1 and n 2 2 of trans-HCOOH and cis-HCOOH were found to be reasonably accurate compared to the measured experimental values. On the other hand, most combination and overtone bands involving n 5 and n 6 were inaccurate. In addition to limitations based on e.g. the level of ab initio theory and the order of coupling in the potential, the reason for this was found to be the normal modes associated with the aforementioned fundamentals. We note, that this inaccuracy may be due to the inability of VSCF to reproduce Fermi resonances. The well-known n 5 /n 2 9 Fermi resonance was observed experimentally for trans-HCOOH and no analogous resonance was identified for cis-HCOOH. For DCOOH an n 3 /n 2 8 Fermi resonance was observed for both the trans and cis form with the involvement of the OH stretching vibration n 1 .
We also briefly mention the work of Scribano and Benoit, 101 who four years later computed the OH stretching frequency n 1 of trans-HCOOH with CC-VSCF, VCI and single-to-all (STA) CC-VSCF and STA-VCI. The STA methods were introduced in their work and rely on the idea that the modes could be partitioned into an active and a ''spectator'' set. In these calculations, the rovibrational coupling terms were neglected and the potential was expressed with up to two-body coupling terms in normal coordinates. The direct evaluation of the potential was performed at the MP2 and CCSD(T) level with TZP and polarization augmented SBK bases. The OH stretch fundamental n 1 was computed using standard VCI and STA-VCI with only one active degree of freedom. At the CCSD(T)/TZP level of theory a the STA-CC-VSCF and STA-VCI energies were found to be only 8 cm À1 worse compared to the CC-VSCF and VCI calculations for the frequency of the n 1 fundamental, where only singles and doubles excitations were included in the VCI expansion.

Advanced calculations with analytic potential energy surfaces
A more accurate description of the nuclear dynamics of formic acid has become available due to the development of analytic ab initio PESs, the availability of which leads to a significant speedup in the potential energy evaluation and therefore allows for the use of higher accuracy vibrational structure methods.  The first anharmonic ab initio force-fields of formic acid were developed for trans-HCOOH by Demaison et al. 20 at the MP2/ VTZ, MP2/aVTZ and CCSD(T)/VTZ(ae) level of theory. In addition to analytic harmonic terms, the cubic and semidiagonal quartic force constants were determined via displacements along the normal coordinates with the method of finite differences. With this force field they computed anharmonic fundamentals using vibrational perturbation theory for trans-HCOOH. In Table 2 we included transitions obtained with the CCSD(T)/ VTZ(ae) force-field. Vibration-rotation interaction constants as obtained by standard perturbation theory were also reported. The n 7 , n 9 , and n 3 fundamentals of trans-HCOOH were found to be affected by strong rovibrational interactions. They carried out an analysis of the resonances in terms of the magnitude of the force constants, where the Fermi resonant states were assumed to be connected via the cubic constants of force constants of type k ijj and Darling-Dennison type resonances 102 via the quartic constant k kkll . In contrast to the experimentally derived force constants, several calculated force constants indicating Fermi resonance (e.g. k 499 for n 4 /n 2 9 , k 677 for n 6 /n 2 7 ) differed significantly in magnitude and sign whereas the n 5 /n 2 9 Fermi resonance matched qualitatively. The resonance interactions were further analyzed by constructing a 5 Â 5 symmetric matrix representing interactions involving the n 2 9 , n 2 7 , n 6 , n 5 , n 4 states and computing the corresponding eigenstates.
In 2013, Tew and Mizukami reported their first PES for formic acid, initially fitted for the description of the trans form ref. 35 with 5873 randomly generated configurations within the energy range 0-15 000 cm À1 at the CCSD(T)(F12*)/ccpVDZ-F12 level of theory. With this preliminary surface, they performed VSCF, VMP2, VASCI, and VASPT2 calculations based on the normal-coordinate Watson Hamiltonian for the fundamentals of trans-HCOOH (see Table 2). Rovibrational coupling terms were neglected and up to three body coupling terms were included in the many-body expansion. Up to seven singlemode functions were employed for the state-specific VSCF calculations and for the VASCI calculations an active space of four modes was selected, involving the normal modes associated with the n 1 , n 5 , n 7 , and n 9 fundamentals. The authors note a good performance of VMP2 except for the fundamentals n 1 and n 5 , where the former was overestimated by 22 cm À1 compared to the rovibrational-interaction-corrected experimental value. The largest deviations of the VASPT2 calculations were found for the n 2 and n 4 fundamentals. Since the isomerisation barrier was reached already at six quanta of excitation of the singlecoordinate function along the torsional mode associated with the n 9 fundamental, only a limited excitation space was available. This led to multiple unconverged states due to the involvement of the torsional mode in multiple states. The authors concluded, that for fully converged values adopting a different coordinate system that can treat both the cis and trans minima would be necessary.
Consequently, two semiglobal PESs capable of describing the cis-trans isomerization have been developed. Tew and Mizukami published a PES in 2016 62 constructed using LASSO-based regression 62 with electronic energies obtained at the CCSD(T)(F12*)/cc-pVTZ-F12 level of theory using 17 076 random structures in the energy range 0-15 000 cm À1 relative to the trans minimum. The structures were generated by random displacements from cis and trans equilibria as well as from the transition state of the OH torsional motion and with points generated in the internal coordinate path (ICP) coordinate system which was constructed for formic acid. The latter corresponds to curvilinear path for the torsional motion and 8 normal coordinate displacements. The analytic potential fit consists of a zeroth order surface, which is a sum of Morse functions of atomatom separations, and a correction surface, which is a sum of distributed multivariate Gaussian functions which are a combination of atom-atom separations. In the same work, the authors constructed an internal-coordinate path Hamiltonian (ICPH) using their PES, where a curvilinear path was used for the torsional motion connecting the trans and cis rotamers and the remaining mutually orthogonal rectilinear modes were defined such that the rovibrational coupling constant associated with the motion along the path was minimized. Trigonometric functions were used for the expansion of the single-mode functions along the torsional path coordinate, and harmonic oscillator functions were used for the remaining coordinates. State-specific VSCF and VMP2 calculations were carried out with the ICP Hamiltonian of HCOOH, where the potential included up to four-body coupling terms, whereas in the ICPH-VCI calculations up to five-body coupling terms were included with a maximum overall excitation of up to 10 quanta in the VCI expansion. The change of the zero point energy by including, instead of four-body terms, five-body terms in the Hamiltonian was 2 cm À1 and for the fundamentals n 2 , n 3 , n 5 , n 8 n 9 it was within 1 cm À1 . For the n 1 , n 4 , n 6 , and n 7 fundamentals slower convergence with a change of up to 6 cm À1 was observed with respect to the increase in the coupling. The ICPH-VCI vibrational energies with respect to the trans-minimum were reported up to 4750 cm À1 with respect to the global trans minimum and 14 bands in the region 0-4720 cm À1 were reassigned based on the VCI coefficients compared to the assignment of Freytes et al. 82 The cis-zero point energy (ZPE) and cis states were identified from the quantum number of the torsional mode. The authors note the overestimation of the n 2 6 and n 3 6 states in their ICPH-VCI calculations compared to experiment. They also discuss the ambiguity of the assignment of some states in the high-energy region and of increasing excitation, further complicated by the high density of states in this region. They observed a coupling between the n 4 , n 5 , n 6 , and n 7 cis states and concluded that the coupling could be an artifact from the definition of the coordinate system. Due to this coupling and the associated slow convergence only states with up to two quanta of excitations relative to the cis-ZPE were reported. The highest cis-HCOOH fundamental n 1 was not reported in this work, and the n 2 4 overtone was identified to be part of a Fermi doublet with n 2 . We report only the transitions identified as fundamentals in their work in Tables 2 and 3.
The second semiglobal ab initio PES was developed by Richter and Carbonnière 56 in 2018 who fit 660 single point calculations at the CCSD(T)-F12a/aug-cc-pVTZ level of theory in the energy range 0-6000 cm À1 relative to the trans minimum. The PES was fit in terms of internal valence coordinates 1 (i.e. bond stretches, angles and torsions) with the points generated by the Adaptive Generation of Adiabatic PES (AGAPES) procedure. 103 The coordinate definition used is depicted in Fig. 2. The barrier between the two minima along the torsional coordinate t 2 was found to be 4442 cm À1 , where the barrier height was found to be affected by the bond-length r 1 and the bending angle y 2 . The barrier of this PES is 20 cm À1 higher compared to the value reported by Tew and Mizukami. 56 For the vibrational Hamiltonian, the exact analytical kinetic energy operator was constructed in the SOP form with the TANA program 104 in polyspherical coordinates, and the PES was expanded as a many-body expansion in valence coordinate displacements. The ''dead branching'' 105 option of the AGAPES procedure was used, in which only certain coordinate combinations were selected based on a remoteness measure defined by geometric mean values for the potential coupling terms. Out of the 256 possible coordinate combinations in the four-body expansion, 36, 84 and 126 were kept, for two, three and fourbody terms, respectively. A maximal number of terms was kept for the coupling between the y 3 and t 2 coordinates, associated with the n 5 and n 9 fundamentals. Below 3500 cm À1 with respect to the trans ZPE only half the period of the grid of the torsional coordinate was used (t 2 r p/2), such that no cis-trans delocalization effects were included in the computation of the trans states. Full-period calculations were performed between 3500 cm À1 -3640 cm À1 . The high-lying fundamentals associated with the CH and OH stretch vibrations (n 2 , n 1 ) were computed with the improved relaxation scheme of MCTDH, and all states below 3100 cm À1 for trans and 2700 cm À1 for cis with respect to their respective ground state were computed with the block Davidson scheme of MCTDH. We have included the transitions identified as fundamentals in Tables 2 and 3. The MCTDH reference state was found to have only a minor effect on the convergence of the states. All vibrational states below 3796 cm À1 were converged in either the cis or the trans well, as differentiated by the torsional coordinate, and the first delocalized state was found at 3796 cm À1 above trans ZPE, which was labeled as the n 6 9 overtone of cis-HCOOH. Four states could not be converged to sufficient accuracy, these were the states at (assignments of Richter Carbonnière in brackets) 3086 cm À1 (n 4 + n 3 ), 3116 cm À1 (n 2 8 + n 2 6 ) for trans-HCOOH and at 2357 cm À1 (n 9 + n 7 + n 5 ), 2479 cm À1 (n 2 7 + n 5 ) for cis-HCOOH. For most states which were previously identified in literature to be involved in Fermi resonances, a single-configurational description was found to be sufficient, except for the well known n 5 /n 2 9 Fermi resonance, where a mixing of the reference configurations was observed. The computed states of trans-HCOOH were in good agreement with the values reported by Tew and Mizukami with a root mean square deviation (RMSD) of 11 cm À1 : the RMSD of the fundamentals, two, three and four quanta excited states were 5 cm À1 , 8 cm À1 , 9 cm À1 and 25 cm À1 , respectively with maximal deviations (MAXDs) for n 3 , n 3 2 , n 5 + n 2 7 and n 2 7 + n 2 9 . The RMSDs of the cis states were about 49 cm À1 compared to the levels of Tew and Mizukami, where the RMSDs for fundamentals, two and three quanta excited states were 14 cm À1 , 49 cm À1 and 111 cm À1 , respectively, and the MAXDs were found for the n 8 , n 4 + n 8 and n 8 + n 2 9 states. This discrepancy of the cis results compared to the work of Tew and Mizukami was further investigated by the authors. 56 For cis-HCOOH the authors validated their results by performing the AGAPES construction referenced on the cis, instead of the trans geometry: the levels computed with the global PES were found to be consistent with the latter. VPT2 and MCTDH calculations were performed with both the present PES and the 2016 PES of Tew and Mizukami, for which the latter was re-fitted in the SOP form. The VPT2 fundamentals were found to compare well with each other and with the original MCTDH values such that the authors concluded that the disagreement for the cis levels stems from the ICPH-VCI calculations, rather than from the PES. For the cis levels, a mixing of the n 5 and n 6 levels was identified.

Recent developments
Fundamentals, combination bands and overtone transitions up to approximately 3000 cm À1 with respect to the global trans minimum were computed by Aerts et al. 53 in 2020 for the deuterated forms of cis and trans formic acid using the above mentioned PES of Richter and Carbonnière 56 with the blockimproved relaxation method of MCTDH. The assignment of the states was performed via visualization of the reduced densities of the computed vibrational wavefunctions. The RMSDs with respect to experimental data of the fundamental transitions were found to be 8 cm À1 , 7 cm À1 and 3 cm À1 for trans-DCOOD, trans-HCOOD and trans-DCOOH, respectively. The calculations were performed by defining modes combining r 1 and y 3 , y 1 and y 2 , and t 1 and t 2 , respectively (see Fig. 2). Aerts et al. Vibrational transition energies were computed by Nejad and Sibert 79 up to 4000 cm À1 for HCOOH and isotopologues with sixth order Canonical Van Vleck Perturbation theory (CVPT6) employing both surfaces of Tew and Mizukami and Richter and Carbonnière. 56 In their work, the PESs were represented as a Taylor expansion in terms of stretch, bend, and dihedral angles with the valence coordinate definition of Richter and Carbonnière. 56 Up to four-body coupling terms were used for the PES, and the elements of the exact kinetic energy operator were expanded up to the sixth order in the internal coordinates. The CVPT6 calculations were performed with the Hamiltonian constructed in curvilinear normal coordinates based on only one geometry. As a basis for the matrix representations, a product of harmonic oscillator functions was used where the excitation degree of each oscillator was limited. A slightly faster convergence of the trans-HCOOH states obtained with the 2016 PES of Mizukami and Tew as compared to the 2018 PES of Richter and Carbonnière was observed with regard to the order of perturbation, where fourth and sixth order corrections were found to be especially important for higher lying vibrational transitions. Slower convergence was observed for the cis-HCOOH states on the 2016 compared to the 2018 PES. It was found, that the 2016 surface generally overestimates, whereas the 2018 PES often underestimates the transition energies for all isotopologues as compared to experimental values, where increasing deviations were found for higher lying vibrational states. The CVPT6 fundamentals of trans-HCOOH compared within 2 cm À1 to ICPH-VCI and MCTDH results of the respective surface (see Table 2). For cis-HCOOH it was suggested by the authors that the ICPH-VCI results of Tew and Mizukami were not fully converged. The band assignment was performed based on the leading coefficient in the VCI expansion and in comparison to previous calculations and previously assigned IR and Raman bands reported in literature. 11 new vibrational band centers were assigned for trans-HCOOH and 53 for the deuterated isotopologues by the authors with multiple reassignments in comparison to previous assignments from theory or experiment. For trans formic acid strong coupling among the states which share the polyad quantum number N p = n 5 + n 9 /2 was found, with an involvement of the n 1 fundamental at higher energies.
Most recently, Martín Santa Daría, Avila, and Mátyus performed calculations using the 2016 PES of Tew and Mizukami with a Hamiltonian constructed using the cis-trans torsional coordinate and eight curvilinear normal coordinates defined with respect to an instantaneous reference configuration along the torsional motion. 30 The curvilinear normal coordinates were adapted to the cis-trans isomerization of formic acid by relaxing the internal coordinates such that the potential energy was at minimum along the torsional motion. In principle, the kinetic and potential energy coupling among the coordinates was reduced by employing curvilinear normal coordinates. The kinetic energy operator was constructed numerically with the kinetic and potential energy integrals evaluated over the direct product basis with the GENIUSH (general rovibrational code with numerical, internal-coordinate, user-specified Hamiltonians) code. 106 For the curvilinear normal coordinates harmonic oscillator basis functions and for the torsional degree of freedom a Fourier basis was used. A Smolyak grid was then used for the truncated direct product basis for the evaluation of the multidimensional integrals. The authors computed converged vibrational states up to ca. 4700 cm À1 with respect to the trans-ZPE, slightly above the cis-trans isomerization barrier and therefore the highest-energy cis n 1 fundamental was not computed. The convergence was evaluated by increasing the basis set size. The energy difference between calculations using the same basis set size was performed with rectilinear and relaxed curvilinear normal coordinates and the difference was found to be around 8-10 cm À1 , with an increasing difference in the higher energy region. The assignment of the cis-states was performed in terms of the contribution of the 1D torsional basis function, which in the lower energy ranges was localized in either well. A variational improvement of up to 5-10 cm À1 was reported compared to the CVPT6 results and by 10-40 cm À1 compared to the previously computed ICPH-VCI levels. Beyond 3700 cm À1 , mixed cis-trans states were reported and the ''tunneling splittings'' associated with these mixed states were computed to be below 1-5 cm À1 , almost within the convergence uncertainty of the calculations.
Beyond 3900 cm À1 , non-negligible contributions from delocalized torsional states were observed. We note, that although the results of the authors unequivocally indicate the switching of the n 5 and n 6 cis-HCOOH states as opposed to previous calculations, in Table 3 we list the labeling to be consistent with previous results.
Finally, we discuss the recent work of Aerts et al., who simulated the intramolecular vibrational redistribution (IVR) dynamics of formic acid on the 2018 PES of Richter and Carbonniére with the goal of identifying a possible laserinduced trans-cis isomerization pathway. The dynamical evolution following the excitation of an infrared-active vibration was simulated by the time-evolution of an initial vibrational wave function which was prepared by the excitation of the single particle function of the torsional mode t 2 associated with the isomerization. The probability of finding the molecule in the trans well, as defined by the value of the torsional coordinate, was followed during the evolution, and local energies were ascribed to each mode. By investigating the time-evolution of the fractional energies defined for each overtone of the local torsional vibration of trans-HCOOH, multiple mode-couplings and resonances were identified and confirmed. The n 5 /n 2 9 Fermi resonance was observed as a strong, reversible energy flow between the two fundamentals, also for states sharing the previously mentioned polyad quantum number N p = n 5 + n 9 /2. A coupling between the modes of the n 9 and n 4 fundamentals was identified. The probability to find the wavepacket in the initial trans well was found to diminish at n 6 9 at which part of the wavepacket transfered from trans to cis within 100 fs. The non-periodic probability indicated, that this transition between trans and cis is irreversible.

Summary
We have reviewed first principles, anharmonic studies on the molecular vibrations of formic acid in its monomer form and collected all reported computed transitions identified as fundamentals for both cis-and trans-HCOOH. Formic acid has been a widely explored albeit challenging system to both experiment and theory. On one hand, the spectrum is dense and complex in certain spectral ranges and requires a careful rovibrational analysis 83 and experimental differentiation of the signals arising due to its possible geometries. 107 Undistorted, high-resolution experimental data has still not been recorded for all of the available cis transitions predicted by theory. On the other hand, the higherenergy vibrations of the molecule are expected to explore trans and cis geometries or both, 30 a formidable task for vibrational methods. The minimal energy path connecting the two minima was found to be a function of the t 2 torsional coordinate, 56,57 but possible isomerization pathways involving the excitation of the n n 1 OH overtones 83 or involving n 6 and n 9 were also suggested. 2 Early on, multiple resonances affecting the vibrational levels of formic acid were identified, most notably the n 5 /n 2 9 Fermi resonance of trans-HCOOH. 48 Hurtmans et al. reported the involvment of the HOC angle in the n n 1 excitations, 83 however, the first ab initio studies employed rectilinear normal coordinates which were found to be ill-suited for torsional and deformation vibrations. 48 The first PESs were computed directly along the normal coordinates 48 or as a Taylor 20 or a local many-body expansion, 35 such that vibrations with a local trans character could be predicted. The development of analytic semiglobal PESs capable of reproducing transitions both from the cis and trans minima followed. 56,62 Transitions of cis-and trans-HCOOH were computed with a Hamiltonian constructed with normal coordinates along the curvilinear isomerisation path, and the computed high-energy cis states were found to be coupled significantly. 62 The vibrational transitions were also computed with the dynamical MCTDH method in valence coordinates, 56 and the computed cis-states differed significantly from the previously reported results. A comparison between the PESs was made with transitions computed based on a curvilinear normal coordinate Hamiltonian, where the coordinates were defined based on a single geometry. 79 The transitions of the deuterated species 53,79 and assignments up to 4000 cm À1 with respect to trans-ZPE were also described. 79 A curvilinear normal coordinate Hamiltonian adapted to the cis-trans torsional motion was constructed, 30 and vibrational states slightly above the isomerisation barrier were reported including cis-trans entangled and delocalized states. Small splittings associated with the high torsional isomerisation barrier were reported. The study of Martín Santa Daría et al. reported the lowest energy variational solutions up to now 30 with a good agreement with high-accuracy experimental values for both cis (Table 3) and trans ( Table 2) fundamentals.
Finally, we discuss the computed vibrations of formic acid which have been identified as fundamentals across the studies mentioned in this work, as compiled in Tables 2 and 3. Although such an analysis is not necessarily warranted considering that different PES and Hamiltonians are used across these approaches, it is still worth analyzing the results in terms of the employed methods. The harmonic analysis performed by many of the studies shows the worst agreement to experimental values with an RMSD ranging from approximately 80-125 cm À1 where generally a better agreement is achieved for the lower energy states. Single-configurational approaches follow with an RMSD ranging from approximately 3.4-31 cm À1 . Finally, all multi-configurational methods achieve an RMSD better than 4 cm for the trans-states and better than 8 cm À1 for the cis states, where for the latter conclusions should only be drawn with care due to the few available experimental results.
As a small molecule exhibiting large-amplitude motion, the vibrations of formic acid are comparatively difficult to model, where the computation of converged cis states and highly excited states above the delocalization barrier remains to be challenging due to the strong coupling of the coordinates in this region. We note that these difficulties are illustrative of the challenges faced for larger systems, since the nuclear dynamics of bigger molecules and clusters can become increasingly intricate but multiconfigurational methods become prohibitively expensive due to their scaling with respect to system size.

Conflicts of interest
There are no conflicts to declare.


Curcumin Is an Iconic Ligand for Detecting Environmental Pollutants

The rapid increase in industrial revolution and the consequent environmental contamination demands continuous monitoring and sensitive detection of the pollutants. Nanomaterial-based sensing system has proved to be proficient in sensing environmental pollutants. The development of novel ligands for enhancing the sensing efficiency of nanomaterials has always been a challenge. However, the amendment of nanostructure with molecular ligand increases the sensitivity, selectivity, and analytical performance of the resulting novel sensing platform. Organic ligands are capable of increasing the adsorption efficacy, optical properties, and electrochemical properties of nanomaterials by reducing or splitting of band gap. Curcumin (diferuloylmethane) is a natural organic ligand that exhibits inherent fluorescence and electrocatalytic property. Due to keto-enol tautomerism, it is capable of giving sensitive signals such as fluorescence, luminescence, ultraviolet absorption shifts, and electrochemical data. Curcumin probes were also reported to give enhanced meterological performances, such as low detection limit, repeatability, reproducibility, high selectivity, and high storage stability when used with nanosystem. Therefore, research on curcumin-modified nanomaterials in the detection of environmental pollution needs a special focus for prototype and product development to enable practical use. Hence, this article reviews the role of curcumin as a natural fluorophore in optical and electrochemical sensing of environmentally significant pollutants. This review clearly shows that curcumin is an ideal candidate for developing and validating nanomaterials-based sensors for the detection of environmental pollutants such as arsenic, lead, mercury, boron, cyanide, fluoride, nitrophenol, trinitrotoluene, and picric acid and toxic gases such as ammonia and hydrogen chloride. This review will afford references for future studies and enable researchers to translate the lab concepts into industrial products.

Introduction
e alarming situation of environmental pollution has increased the demand for novel nanomaterials for the ultrasensitive detection of pollutants. Fabrication of specific and sensitive nanoplatform for the detection of various environmental pollutants such as metal ions, anions, and explosives has become essential to solve many environmental issues and their adverse biological effects [1,2]. Ligandfunctionalised nanostructures exhibit novel behavior and enhanced functional ability. Organic ligands are capable of increasing the adsorption efficacy, optical properties, and electrochemical properties of nanomaterials by reducing or splitting of band gap [3,4]. Among many methods, fluorescent techniques have become customary due to the simplicity of operation and ability to detect trace concentrations of pollutants. erefore, several reports have been published on the application of fluorescent organic probe for the detection of metal ions and for anions, such as cyanide [5][6][7][8][9]. Advantages of fluorescent organic probes are flexibility in the synthesis protocol, and optical signals, that is, aggregation-induced enhanced emission [10,11]. Organic fluorophores can conveniently be prepared by methods like emulsification evaporation, emulsification diffusion, solvent displacement, self-assembly, and reprecipitation methods [12,13].
Curcumin (C 21 H 20 O 6 ), a natural fluorophore is an ideal organic ligand, capable of showing alterations in their optical as well as electrochemical properties in the presence of significant environmental pollutants. Such signals can be used for the effective detection of select pollutants [14,15]. Furthermore, the tautomeric form of curcumin is used as an electrochemical transducer and ion receptor. It is capable of offering potentiometric response with good linear ranges for toxic ions such as cyanide ions and mercuric ions. For example, chelation of mercury(II) ions and cyanide ions to curcumin decorated on graphene-modified glassy carbon electrodes (GCE) induces anodic shift and cathodic shift, respectively. As curcumin exists in keto form and enol form, it is capable of simultaneous detection of cationic and anionic pollutant in a given sample. Keto form is responsible for giving signals pertaining to cationic detection while the enol form gives signal corresponding to anionic detection. Curcumin probes were also reported to give enhanced meterological performances such as low detection limit, repeatability, reproducibility, high selectivity, and high storage stability when used with nanosystem [15]. Considering the merits of curcumin in generating optical and electrochemical signals, research work on surface functionalisation of nanomaterials with curcumin needs a special focus. Hence, this article reviews the role of curcumin as a natural fluorophore in optical and electrochemical sensing of environmentally significant pollutants such as heavy metal ions, nitrophenols and explosives such as trinitrotoluene (TNT). is review will probably afford references for future studies and enable researchers to translate the lab concepts into products and devices.
It is easy to identify the binding of curcumin to nanomaterials and to pollutants by spectroscopically analyzing the band of its functional groups such as keto group, enol group, phenol group, and methoxy group. e β-diketone group in the central 7-carbon chain of the curcumin has a high driving force to chelate with metal ions [36]. In alkaline pH, the enolic form of curcumin predominates so that the heptadienone chain functions as an electron rich site/electron donor [37]. is property is responsible for bonding with electron deficient analytes such as explosives and capable of sensing them with high sensitivity [20]. Nanomaterial Surface Energy Transfer (NSET) was found to be more efficient when curcumin is used as a ligand and the resultant optical signal is used to detect pollutants [20]. Zinc curcumin oxide nanoparticles, coated with chitosan (Zn(Cur)O-Chi), were found to be an excellent nanoprobe capable of giving fluorescence signal [38]. e enol band becomes more clear and prominent and broadness increases when curcumin forms a hybrid with nanomaterial/metal ions as compared to free curcumin as evidenced by Fourier Transform Infrared Spectroscopic results [17]. e hydroxyl and methoxy groups on the phenyl rings of curcumin are electron-donating systems expected to even cause stronger hydrogen bond effect. So, any weakening of these groups' electronegativity (phenyl ring and/or the existing methoxy and hydroxy groups on it) by forming bonds or conjugating with other moieties would cause the hydrogen bond strength to decrease, thus allowing the enol peak to appear more clearly [17]. Curcumin is capable of showing a red shift in the UV absorption peak after interacting with metal ions or nanostructures. is is attributed to a decrease in band gap between Π − Π * electronic transition of curcumin due to their interaction [17]. Energy gap for curcumin decreases on binding with divalent cations leading to a shift in UV absorbance peak to longer wavelength. Patra et al. have reported the role of curcumin in a fluorimetric detection system. Curcumin was encapsulated in nanoparticle-assembled microcapsules prepared from poly[diallylammonium chloride-co-(sulfur dioxide)] [26].
In addition to its role in enhancing the optical (spectroscopic, colorimetric, and fluorescence) signals, curcumin is also capable of enhancing the electrochemical signals as evidenced by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) [20,39]. e methylene radical at the central 7-carbon chain of curcumin has crucial involvement in its redox behavior due to H-shift from the methylene group [40]. Masek et al. have revealed the optical and electrochemical characteristics of curcumin that are applicable to sensing pollutant analytes [41]. Metal organic framework (MOF) exhibits electrochemical activity and it is a potential material for electrochemical sensors [42][43][44]. Dang et al. have adsorbed curcumin into nano-MOF and suggested that the conjugate can emerge as a promising sensing platform generating quality electrochemical signals [45]. Mars et al. have reported the dual functionality of curcumin as a fluorescence and electrochemical transducer in a nanoplatform formed by curcumin and graphene sheets [46]. Integration of electrochemical techniques with nanoconjugates for sensor applications results in enhanced sensitivity, better limit of detection, and robustness of the sensors [47]. Above all, curcumin is environment-friendly and can easily be biodegraded on disposal. Hence, curcumin is an ideal candidate for developing and validating nanomaterials-based sensors for the detection of environmental pollutants such as metal ions, anions such as cyanide, fluoride, explosives such as TNT, and toxic gases.

Heavy Metals
3.1. Arsenic. Natural sources of arsenic include volcanic ash, mineral crust, mineralized ground water, and atmospheric dusts. Arsenic pollution in water has become an alarming environmental issue as the US Environmental Protection Agency (EPA) has reduced the maximal contamination level (MCL) of arsenic in drinking water from 50 µg/L to 10 µg/L (0.01 ppm) [48]. Furthermore, arsenic contamination causes deleterious effects in vital organs [49][50][51] and also affects the mental development in children [52]. Curcumin establishes electron-hole recombination [53] when doped into the defects of ZnO (forming CM-ZnO). As the defects are the spots of luminescence, it could be suggested that curcumin plays a dual role of (i) quenching the visible photo luminescence (visible emission) at 560 nm and (ii) the enhancement of UV emission (at 358 nm) as compared to free ZnO. According to Moussawi and Patra, at an excitation wavelength of 425 nm, the curcumin-doped ZnO is sensitive to arsenic. e detectable concentration range is around 100 to 3000 ppb. During the sensing process, the arsenic adsorbs to the CM-ZnO by pseudo-second-order model with excellent adsorption rates as compared to ZnO [17]. e arsenic is capable of binding to the phenolic ring and/or the hydroxyl group of the curcumin to induce a change in fluorescence and hence, curcumin can also contribute to the water treatment by the removal of arsenic. Overall, CM-ZnO's higher affinity to arsenic is responsible for the sensing and water treatment efficacy. Sirawatcharin et al. have developed a method for UVvisible photometry-based detection and naked-eye detection of arsenic in water using difluoroboron-curcumin (BF2curcumin).
BF2-curcumin was prepared using borontrifluoride diethyletherate ((C2H5)2OBF3), and curcumin was an orange solution, which showed a maximum absorbance at 509 nm. In the presence of arsenic, the absorbance maxima were shifted to 632 nm. e red shift was accompanied by the change of the solution color from orange to blue with the detection limit of 25 μM. Additionally, BF2-curcumin solution was coated to resin and used as an equally effective naked-eye sensing system with the detection limit of 30 μM [54].

3.2.
Lead. According to World Health Organization (WHO), the maximum permissible level of Pb 2+ is 0.05 mg/L while excessive levels of Pb 2+ lead to environmental and biological toxicity. Biological effects include hypertension and functional impairment of vital organs such as heart, liver, brain, and kidney. To be specific, it affects mental coordination, learning abilities, and IQ in children [55][56][57][58].
Atomic absorption spectrometry, inductively coupled plasma-mass spectrometry, anodic stripping voltammetry and reversed-phase high-performance liquid chromatography, and UV-visible spectroscopy are conventional techniques used for lead detection [59][60][61][62]. However, these techniques are time-consuming and require skilled man power, and equipments. But colorimetric technique together with optically tunable nanomaterial probe is ideal, highly specific, and ultrasensitive towards the detection of lead.
Daniel et al. have developed a nanofiber-based cheap, disposable sensing strip with curcumin for the rapid detection of lead. e strip was fabricated using curcumin-loaded cellulose acetate nanofibers (approximately 100 nm) for the selective detection of lead amidst other heavy metal cations. e strips were capable of showing visible color change from yellow to orange-brown in the presence of lead ion detection. On complexing with lead ions, FTIR peaks of curcumin corresponding to OH group and carboxyl moiety were reported to be shifted, suggesting the formation of direct bonding or intermolecular hydrogen boding through OH and C�O groups [63].

Mercury.
Mercury enters into terrestrial and aquatic ecosystem from various sources like coal, metal ores, paint, electronic devices, chlor-alkali plants, and catalyst [64][65][66][67]. Environmental contamination with mercury ions leads to bioaccumulation in fishes, which are the vital components of the food chain. Human consumption of marine and shell fishes are important exposure factor [19]. erefore, mercury contamination is a main concern for humans. DNA breakage [68], carcinogenesis [69], and damage to vital organs like brain, heart, kidney, and digestive system [70,71] are the major toxic effects of mercuric ions. According to the WHO, the permissible level of Hg 2+ ions in drinking water is 0.006 µg/ml. Curcumin was adhered to a MnO 2 -graphenemodified GCE to enhance the performance of the potentiometric detection of mercury(II) ions. Anodic shift was obtained in the presence of mercuric ions with a peak potential at 0.82 V with the detection limit of 19.2 nM [15]. Chronoamperometry and differential pulse voltametry (DPV) confirms the curcumin-based detection of Hg(II) ions. Once the Hg(II) binds to curcumin-loaded nanosystem, there was a shift in anodic potential causing a new oxidation peak of curcumin-mercury complex at 0.82 V as revealed by DPV studies. e C�O group in the keto form of curcumin was thought to generate the signals on sensing mercury(II) ions. Delocalisation of electronic charge form the chelator site towards the metal center was responsible for the new anodic shift caused by the curcumin-metal complex. It should be noted that the free curcumin easily oxidizes as compared to the cation-curcumin complex [15].
Pourreza et al. have developed a nanocurcumin-based paper strip sensor for detecting mercury in water samples [72]. e sensor prepared using wax dipping technique was highly selective and portable. e color intensity was the signal produced in the sensor, which showed a linear increase with an increase in the concentration of Hg 2+ ions.
is team has optimized various parameters such as pH, buffer, ionic strength, the amount of curcumin nanoparticles, and the target ions. A linear range of 0.5-20 μg mL −1 of Hg 2+ with the limit of detection of 0.17 μg mL −1 (in absence of preconcentration). After 50 times preconcentration, the linear range was 0.01-0.4 μg mL −1 of Hg 2+ with the limit of detection of 0.003 μg mL −1 [72].
Atomic absorption spectroscopy (AAS), atomic fluorescence spectrometry (AFS), cold vapour-AFS (CV-AFS), inductively coupled plasma-mass spectroscopy (ICP-MS), ICP-isotope dilution mass spectrometric (ICP-IDMS), and microwave-induced plasma atomic emission spectroscopy (MIP-AES) are used for the detection of mercury. Nevertheless, colorimetry method is capable of generating signals detectable by naked eye and it is also cheap and feasible [73]. Functionalised gold nanoparticles are good detection candidates for colorimetric sensing of many metal ions including mercury [74,75]. We have green synthesized curcumin analog functionalized gold nanocubes and confirmed their interaction [30]. Kumar et al. [76] have synthesized curcumin-capped gold nanoparticles for the colorimetric detection of mercury in aqueous solution. e color of curcumin-capped gold nanoparticles was wine red which changed to blue in the presence of Hg 2+ ions. Mercury detection (binding of Hg to curcumin) was also accompanied by a decrease in the absorbance at around 523 nm. e detection of Hg 2+ was linear from 2 µM to 10 µM and the reported detection limit was 2 µM. e acetylacetone group of curcumin was responsible for binding to the mercury ion [76].

Boron.
Boron enters into the environment due to weathering or from consumer products, such as cosmetics and laundry products. Boron enters into food chains from the plants that absorb boron. Excessive boron absorbed by animals or humans due to the consumption of boron accumulated in plants results in reproductive toxicity. Boonkanon et al. [77] have doped curcumin nanoparticle into starch film and developed a rapid, cost effective, and ultrasensitive probe for sensing boron in waste water. As the curcumin nanoparticles were synthesized using turmeric powder and the starch was sourced from tapioca, this sensor was referred to as a green probe. e thin film of starch decorated with curcumin nanoparticles was coated onto a spoon forming a yellow color. In the presence of boron (pH 9), yellow changed to red. e sensor was reusable for 10 times and the components showed excellent biodegradability. e sensor showed a detection limit of 0.052 mg L −1 boron. e film can be used in conjunction with digital image colorimetry (DIC). is causes a green color layer in the reflected light image of the red-brown product and achieved high sensitivity. e sensor resisted storage for up to a year [77].

Sulphide.
Copper is an important environmental pollutant [78] and according to WHO, the tolerable concentrations of copper in drinking water is 2 ppm [79]. Excess levels of copper ions lead to oxidative stress, resulting in childhood cirrhosis, prion disease, Menkes disease, Parkinson's disease, and Wilson disease [80]. Similarly, the sulfide (S 2-) anions are generated due to synthesis of sulfur and sulfuric acid, dyes, and cosmetics. Toxic effects of sulfide anions include suffocation, loss of consciousness, and irritation of mucous membranes [81]. In aqueous solution, the protons interact with sulfide anions and generate HS−, which is even more toxic as it causes distress, unconsciousness, central nervous system damage, and asphyxiation [82]. Copper ions and sulfide anions compete for binding to curcumin. Hence, curcumin can be used as an "off-on" fluorescent probe for the simultaneous detection of copper ions and sulfide anions.
Curcumin nanoparticles prepared by simple precipitation method were used as an "off-on"-type fluorescence sensor for the selective detection of copper ions. e curcumin probe was responsible for the sequential recognition of cations and anions (copper and sulfide) based on the displacement approach. When the sensor detects copper ions, it leads to chelation-induced '"fluorescence quenching" while binding of sulfide ions recovers the quenched fluorescence. Job's, Hill's, and Benesi-Hildebrand plots were used to determine the stoichiometry and complexing capacity of curcumin nanoparticles with Cu 2+ . Carbonyl and hydroxyl groups of curcumin nanoclusters are regarded as molecular recognition sites and they have the ability to recognize and bind with metal ions [83].

Cyanide.
Cyanide is released into the environment and water sources due to gold extraction process, plastic production, and dye production [84][85][86][87]. According to the World Health Organization, the allowable exposure level for cyanide is 1.9 mM and the lethal dose is 2.6 mM. Hence, rapid and sensitive detection of cyanide has become important to protect the health and environment. e carbonyl moiety of curcumin and its derivative are capable of nucleophilic addition with anions such as cyanide and produce a change in FTIR signals. e change in the carbonyl peak after cyanide addition was significant [14,88]. e color of curcumin-based paper sensor changed from yellow to red in the presence of cyanide ions in water. e color intensity increased with the increase in cyanide concentration. Nucleophilic addition of cyanide to curcumin results in the deprotonation of phenolic site of the latter. is results in the conversion of benzenoid form into quinonoid form. At the same time, the cyanide solution becomes acidic (low pH) by gaining the protons generated from curcumin. Curcumin turns from yellow to red when its benzenoid form is converted into quinonoid form. Firstly, the carbonyl group of curcumin is highly susceptible to nucleophilic addition while the cyanide ions have high nucleophilicity. Secondly, cyanide functions as a base and its addition renders the curcumin enolic.
Curcumin has been used as a molecular probe for sensing cyanide in aqueous solution. A solution containing acetonitrile : water (90 : 10) was used as a medium for curcumin (yellow solution). In the presence of cyanide, curcumin solution undergoes a visual change from bright yellow to dark orange. In addition, the curcumin was capable of showing a bathochromic shift in UV spectrum in the presence of the target analyte. e absorption band was shifted from 428 nm to 520 nm. e fluorescence emission of curcumin got quenched on binding to cyanide ions. e visual change, the spectral change, and the fluorescent change were not produced by other interference monovalent ions such as fluoride, chloride, bromide, and so on. e lower detection limit was found to be 2.3 × 10 −6 M [89].
Curcumin is used for the electrochemical detection of cyanide when functionalized to a glassy carbon electrode (GCE) modified with MnO 2 -graphene complex [15]. Potentiometric signals were obtained. Cathodic shift was obtained in the presence of cyanide with a new DPV peak potential at 0.12 V (indicative of curcumin-cyanide complex) with the detection limit of 28.3 nM (ppb). At the same time, significant decrease in the oxidation current of curcumin was obtained [15]. e signal was attributed to the presence of hydroxyl group in the enolic form of curcumin, which was capable of forming hydrogen bond with the target analyte. e cathodic potential shift caused by the cyanide binding was thought to be associated with the amplification of the electron density of the redox active electrochemical transducer, curcumin [90,91].

Fluoride.
Fluoride enters into the environment (especially water) in natural forms like fluorite, fluorapatite, and cryolite, or from anthropogenic sources such as coal burning, oil refining, steel production, brick-making industries, and phosphatic fertilizer plants. Majority of fluoride accumulates in water. Excessive exposure to fluoride causes fluorosis of bone and teeth [92]. Curcumin was an integral recognition probe in an optical sensor developed using upconversion nanoparticles (UCNPs). is sensor was used for the detection of fluoride ions using fluorescence and colorimetric signals. In the presence of fluoride, the absorption peak of curcumin shows a bathochromic shift and an upconversion fluorescence quenching at 546 nm and 657 nm via inner filter effects. e linear range for fluorescence and colorimetric analysis was 25-200 μM and 5-200 μM with the detection limits as low as 25 μM (ca. 0.48 ppm) and 5 μM (ca. 0.10 ppm), respectively [93]. Wu et al. have used curcumin as a colorimetric and fluorescent chemosensing probe for the selective recognition of fluoride ion. In the presence of fluoride ion, the absorption spectra of curcumin show red shift from 418 nm to 562 nm with a concomitant color change from yellow to purple. e spectral change was attributed to the deprotonation of curcumin and the formation of anionic complex between the two hydroxyl groups of curcumin and the fluoride ions. Additionally, the fluorescence of curcumin quenches on detecting fluoride ions which was reported to be due to the photon-induced electron transfer in the presence of fluoride. Job plot curve provided evidence for 1 : 1 anionic complex formation [16].
Mejri et al. have used curcumin as an electrochemical transducer for the sensitive detection of fluoride simultaneous to cyanide and mercury(II) ions. A glassy carbon electrode (GCE) modified with MnO 2 -graphene complex was used as a working electrode. e electrode nanohybrid on the GCE surface was decorated with curcumin and the potentiometric signals were recorded. Sensing of fluoride was confirmed by a cathodic shift and a decrease in the oxidation current of curcumin by 2.11 µA, which was attributed to the hydroxyl group in the enolic form of curcumin. Sensing of fluoride was characterized by new DPV peak potential of −0.24 V (characteristic of curcumin-fluoride complex) with the detection limit of 17.2 nM [15]. e cathodic potential shift caused by the fluoride binding was thought to be associated with the amplification of the electron density of the electrochemical transducer, curcumin [90,91].

Trinitrotoluene (TNT)
. Trinitrotoluene (TNT) is a dangerous chemical weapon and an explosive material. is emphasizes the importance of homeland security, battlefield protection, and industrial and environmental security. erefore, the detection of even trace amount of TNT has become very essential and is emerging as an important area of research in the field of environmental sensors [94]. Commonly used methods like ion mobility spectrometry, mass spectrometry, and gas chromatography are laborious, show less sensitivity, and are not capable of on-site detection. Nanomaterial Surface Energy Transfer (NSET) is superior to Fluorescence Resonance Energy Transfer (FRET) in efficiently transferring the energy from a donor molecule to the surface of a nanomaterial covering a distance twice that of FRET [95,96].
Pandya et al. [20] have used nanocurcumin probe and developed an aggregation technique for detecting trinitrotoluene (TNT). is technique involves NSET between the electron-rich moiety of nanocurcumin and the electron deficient TNT. is probe was highly selective over other explosive compounds and showed remarkable sensitivity, detecting a concentration of 1 nM TNT.
e detection system showed several-fold fluorescence enhancement. In alkaline pH, the enol form of curcumin predominates so that the heptadienone chain functions as an electron rich site/ electron donor [37]. A π-donor-acceptor interaction between electron-deficient TNT and the π-electron-rich curcumin nanoparticles takes place, which is responsible for forming aggregates. As a result of aggregation, the yellow curcumin changes to orange and then to red. Color change was accompanied by a substantial bathochromic shift in the UV spectral band [37]. e degree of red shift and the intensity of the orange color and the red color of the solution depend on the size of the aggregate, which in turn is proportional to the concentration of the TNT.
Curcumin-silver nanoparticles conjugate interact with TNT via p-donor-acceptor interaction with excellent selectivity. Curcumin functionalized with PVP-capped Ag NPs can be used as an ultrasensitive optical probe for TNT detection. Curcumin-silver conjugate functions as a UV-visible spectroscopy, DLS, and Surface-Enhanced Raman spectroscopy-(SERS-) based multiple tier real-time probe. is probe showed an ultrasensitive detection of TNT up to 0.1 nM level.
is technique has an added advantage of producing visible flakes in the presence of TNT, thus enabling naked eye detection [97].

Picric Acid.
Picric acid (2,4,6-trinitrophenol) is a nitroaromatic explosive, mainly used in rocket fuel, fireworks, and matches [98,99]. It is also used in the preparation of dye and in pharmaceutical and in leather industries [100]. Hazardous industrial wastes containing picric acid are not only hazardous to environment but also deleterious to the biological systems [101]. MOFs [102], semiconductor quantum dots [103,104], and fluorophore-nanomaterial hybrids [105] are used for the detection of picric acid. ese methods, however, suffer from the demerit of interference by structural analogs and toxicity of the materials used [37]. Amolins et al. have prepared a co-polymeric microspherecurcumin hybrid by one-pot precipitation method [37]. Hexa-chlorocyclotriphosphazene (HCCP) was the polymeric microsphere that contains electron-rich nitrogen. HCCP exhibited affinity towards the proton-rich picric acid, thereby quenching the fluorescence of the curcumin. e sensor was selective over other interfering molecules such as nitrotoluene, nitrobenzene, and so on and showed a sensitivity of 85 ppb. Gogoi and Sen Sarma have developed a cost-effective detection system based on curcumin-cysteine and curcumin-tryptophan for the selective detection of picric acid in aqueous media. e amino acid conjugates of curcumin establish electrostatic bonding with the picric acid and result in aggregation. e aggregates are responsible for the fluorescence enhancement by nearly 25-fold.
is sensing system shows a detection limit of 13 nM of picric acid with low interference by other analogues. Amino acidcurcumin conjugates have the potential to sense picric acid in real environmental samples [106].
Environmentally benign greener sensing approach is very significant in perspective of health and environmental safety and homeland security. In this context, Chakravarty et al. [107] developed a new greener method for the sensing of picric acid by using the biomaterials scutellarin-hispiduloside and curcumin modified with the green solvent glycerol. e sensing was due to the fluorescence quenching, governed by the FRET between the fluorophore and the quencher. is sensing system was selective towards picric acid amidst other structurally similar nitro-aromatic compounds [107].

Nitrophenol.
Nitrophenols are regarded as important environmental pollutant as they contaminate water bodies due to improper disposal of its sources like pesticides, paints, dyes, plastics, and rubber products [108]. Musilová et al. [109] have suggested 7 × 10 −8 mol/L as the restricted concentration of nitrophenol in water. Higher concentrations of nitrophenols in water can induce headache, drowsiness, and nausea [110]. Anchoring of curcumin to chitosan film establishes a hydrogen between them. is could be due to interaction between the oxygen of hydroxyl group on the benzene ring of curcumin with either the hydroxyl or the amino group of the chitosan [111]. e resulting hybrid film was the apt sensor for ortho nitrophenol (ONP) as well as fluoride ion. Serial increase in the concentrations of curcumin resulted in an increase in the quantity of bound curcumin per gram of chitosan. But beyond a certain limit (i.e., above 20.0 × 10 −4 g/mL), there was no increase showing the saturation point. ONP interacts with the curcumin forming hydrogen bond that is not fluorescent active. Also, by using the Stern-Volmer equation, the quantitative detection of the targets is possible.
us, the fluorescence quenching of curcumin enables both qualitative and quantitative detection of the ONP and fluoride ions as well. Interestingly, the limit of detection level for ONP and fluoride ion provided by curcumin was well lower than the values given by other methods like UV spectroscopy and chromatography [106]. An electrochemical sensor was developed by modifying gold electrode with curcumin-amino acid conjugate monolayer and further functionalisation with confined copper nanospheres. is sensor showed excellent sensitivity and selectivity for the detection of p-nitrophenol. e copper nanosphere was reported to enhance electron transfer (less resistance) between the probe and electrode and contribute to sensing of the target. e sensor showed a practical feasibility for detecting the target in real environmental media. Furthermore, the sensing platform is costeffective, reproducible, and easy to fabricate [112].

Hydrazine.
Hydrazine and its derivatives are used as reducing agents in fuel cells, and in insecticides, explosives, rocket propellants, metal film manufactures, photographic chemicals, plastic blowing agents, and as oxygen scavengers in boilers [113,114]. Hydrazine easily penetrates through skin; it affects blood production and it is also carcinogenic, hepatotoxic, and nephrotoxic [115]. erefore, hydrazine detection is of utmost importance. Zheng and Song [21] have developed a curcumin-MWCNT modified glassy carbon electrode by electrode position. e electrochemical sensor was used for the amperometric detection of hydrazine. e sensing system showed an electrocatalytic activity towards the oxidation of hydrazine at a reduced overpotential accompanied by an increased peak current as compared to unmodified electrode. is sensor has the advantages of easy fabrication, speedy protocol, high sensitivity, and good reproducibility for hydrazine determination. e linear detection range was 2-44 µM, while the detection limit was 1.4 µM. e two o-methoxy phenolic groups in curcumin molecule functions as an electrocatalytic moiety for hydrazine oxidation.

Pyridine and
Pyrrole. 2-Vinyl pyridine (2-VP) is used as a precursor used in the synthesis of special polymers such as latex, styrene, butadiene, and so on. In medical field, it is used in the synthesis of veterinary anthelmintic and a pharmaceutical called axitinib. e toxic nature of 2-VP in spite of its extensive application in the laboratories emphasizes the significance of its sensitive detection. As per the Material Safety Data Sheet (MSDS), 2-VP is flammable, and it produces allergic/corrosive in skin, eyes, and respiratory system [116]. A novel composite of polyglycerol acrylate and curcumin has been used for the detection of 2-vinyl pyridine by dual mode (i.e., by fluorescence and by electrical properties). In the presence of 2-VP, the fluorescence of the composite quenches. e electrical properties such as DC current-voltage characteristics and AC impedance response change in the presence of saturated vapor of 2-VP. In the presence of the target vapor, the current density decreases up to 84.7 and 83.13% at an applied bias voltage of −5 to +5 V, respectively. e impedance hikes up to about 79% at lower frequency range [117].
Pyrrole is an intermediate chemical in the manufacture of dyes, herbicides, perfumes, drug manufacturing and a cross-linking agent for resins. Intraperitoneal, oral, and subcutaneous administration of pyrrole was reported to induce toxicity in experimental animals as well as in aquatic organisms. erefore, pyrrole is an important pollutant to be detected in the environment. Curcumin organogelator was prepared using N′1,N′6-bis(3-(1-pyrrolyl)propanoyl) hexanedihydrazide (DPH). is compound exhibited dual advantages of structural similarity with pyrrole and a remarkable enhancement in photoluminescence. Hence, the curcumin organogel was proved to be an optical sensing platform for the detection of pyrrole [118].

Toxic Gases
Amshel et al. have reviewed about ammonia toxicity [119]. Leakage of anhydrous ammonia gas or vapor of liquor ammonia from the site of production, storage, or transportation Curcumin organogelator Pyrrole Photoluminescence increases the risk for inhalational and dermal exposure [120,121]. Ammonia-based fertilizers and ammonia produced by decaying manure increase the risk for inhalational exposure [122,123]. Acute exposure to ammonia causes acute pulmonary congestion, edema, and desquamation of the bronchial epithelium [124]. Curcumin was incorporated into cellulose acetate nanofiber and used for the chromatic sensing of HCl and NH 3 . ough the color of curcumin is yellow, the color of curcuminincorporated cellulose fiber in alkaline medium was reddish brown due to the conversion of keto form into a mixed state of enol and enolate forms. Reddish brown changes to yellow in the presence of HCl which indicated the formation of keto form. Subsequent exposure to ammonia led to the recovery of reddish brown in a few seconds, indicating the reversible nature of the tautomerism. is color changing process was due to reversible change in the conjugation state of the curcumin via keto-enol tautomerism with protonation and deprotonation reactions by HCl and NH 3 vapors [125]. Environment is exposed to hypochlorite (ClO − ) and its protonated form (HClO/hypochlorous acid). For example, they are the major components of disinfectant, microbial agent, and bleaching agents [126]. However, higher concentrations of hypochlorite can cause deleterious effects such as tissue damage and diseases such as atherosclerosis, arthritis, and cancers [127,128]. Yue et al. have used curcumin for the sensitive detection of hypochlorous acid. e oxygenation of o-methoxyphenol into a quinone form by the hypochlorous acid was reported to be responsible for the detection. Quinone form resulted in a nonfluorescent derivative of curcumin, signaling the presence of hypochlorite.
is probe showed a high sensitivity for hypochlorous acid as very low detection limit 0.065 μM [129].

Conclusion
Rapid increase in the industrial revolution and automobile exhaust is environmentally hazardous. Incessant monitoring of the pollutants is essential to prevent environmental deterioration. So far, there is no review on the detection and quantification of heavy metals, toxic anions, and explosives using curcumin-based nanoprobes. erefore, we focused on reviewing curcuminbased sensors that are competent in sensing heavy metals, anions, and explosives as summarized in Table 1. We discussed about the specificity, sensitivity, and analytical performance of the detection system. is review clearly reveals that curcumin-based nanosensors are ideal and competent in sensing environmental pollutants by optical and electrochemical methods. erefore, this review will be of major interest for researchers, scientists, and industrialists in order to upgrade these sensors from lab to industrial level.

Data Availability
e data used to support the finding of this study are included within the article.

Conflicts of Interest
e authors declare no conflicts of interest concerning the publication of this article.