A newapproach is presented to improve the performance of semiempiricalquantum mechanical (SQM) methods in the description of noncovalentinteractions. To show the strategy, the PM6 Hamiltonian was selected,although, in general, the procedure can be applied to other semiempiricalHamiltonians and to different methodologies. A set of small moleculeswere selected as representative of various functional groups, andintermolecular potential energy curves (IPECs) were evaluated forthe most relevant orientations of interacting molecular pairs. Then,analytical corrections to PM6 were derived from fits to B3LYP-D3/def2-TZVPreference–PM6 interaction energy differences. IPECs providedby the B3LYP-D3/def2-TZVP combination of the electronic structuremethod and basis set were chosen as the reference because they arein excellent agreement with CCSD(T)/aug-cc-pVTZ curves for the studiedsystems. The resulting method, called PM6-FGC , significantly improves the performance of PM6 and showsthe importance of including a sufficient number of orientations ofthe interacting molecules in the reference data set in order to obtainwell-balanced descriptions. Contributions to this series of generations werealso made by Korth10 and Jensen and co-workers.11 The final version of this series of correctionsis called D3H4X, in reference to the third-generation dispersion correction,fourth-generation hydrogen-bonding correction, and halogen-bondingcorrection. In this version, the dispersion correction is the D3 proposedby Grimme et al. for density functional theory (DFT),23 but without including the 1/r8 term, which was considered to yield no significant improvement inthe case of SQM methods.9 For these methods,Řezáč and Hobza found a specific error in thedescription of interactions between hydrocarbons, namely, the overestimationof interaction energies and the underestimation of equilibrium distances.9 To solve this problem, they included a repulsiveterm for all pairs of hydrogen atoms. The function used to improvethe description of hydrogen bonding includes a polynomial functionof degree 7 in the donor–acceptor distance, which is scaledby an angular term (dependent on the acceptor-hydrogen-donor angle)and a proton transfer term that varies with the hydrogen position.If the system contains charged groups, an additional factor is includedto increase the strength of the correction. Finally, the correctionused for halogen bonding consists of an exponential term.8 The D3H4X correction and other generations ofcorrections have been implemented in the MOPAC2016 program.24Řezáč, Hobza, and their co-workers developedseveral generations of corrections for dispersion,9 First, they fitted the hydrogen-bonding correction, includingthe contribution from dispersion in the calculated energies of theconsidered hydrogen-bonded complexes. For the fittings, they performedleast-squares optimizations, minimizing the root-mean-square errorof the interaction energy when compared to reference data obtainedat the coupled cluster singles and doubles with perturbative triplescorrection/complete basis set (CCSD(T)/CBS) level of calculation.Specifically, as a benchmark set, they used the S66 database,27 which includes dissociation curves for 66 noncovalent complexesthat exhibit dispersion, hydrogen bonds, and mixed dispersion/electrostaticinteractions.The procedure adopted by Řezáčand Hobza toparameterize the D3H4 corrections was as follows:16 based on a NDDO Hamiltonian that includes polarization functionson hydrogen atoms. In addition, to improve the description of dispersioninteractions, they added the first damped dispersion term developedby Grimme.29 This dispersion correction waspreviously used by Hillier and co-workers20 inconjunction with the AM130 and the PM331 Hamiltonians. The final versions of the PMOmethod, that is, PMO215 and PMO2a,16 have been found to accurately describe polarizationeffects as well as noncovalent complexation energies. The PMO2 methodwas parametrized for all compounds containing H, C, and O atoms, andthe PMO2a version is an extension of PMO2 to new functionalities,which includes parameters for amino nitrogen groups and moleculescontaining sulfur–oxygen bonds. Parameterizations of the PMOHamiltonians were carried out using a genetic algorithm, which hasthe advantage of efficiently exploring the search space to find nearoptimal solutions when the number of fitting parameters is large.The abovementioned PMO versions have been implemented on the MOPAC5.022mn package.32Truhlar, Gao, and their co-workers developed thepolarized molecularorbital (PMO) method35 and ODMx,17 which includesignificant improvements in the semiempirical Hamiltonian, thus leading,in general, to better results in comparison with NDDO-based methodsthat make use of the modified neglect of diatomic overlap . These semiempirical Hamiltonians needed to incorporate dispersioncorrections to improve the description of noncovalent interactions.In particular, they include Grimme’s D3 dispersion correction36 with the Becke–Johnson damping function,39 as well asAxilrod–Teller–Muto three-body terms,40 which ameliorate the description of large dense systems.42 For the recent ODMx methods, several training sets were used, includingthe abovementioned S66 data set.27 Parameterization ofsemiempirical Hamiltonians and correction potentials for noncovalentinteractions is a key issue, and the procedure followed within theODMx methods is extensively discussed in the recent article by Dralet al.17The work of Thieland co-workers directed to improve the reliabilityof SQM methods also deserves some attention. They developed the orthogonalization-correctedmethods OMxThe abovementioned studiesled to remarkable improvements in SQMmethods for the evaluation of noncovalent interactions. In general,the corrections for dispersion and hydrogen bonding interactions aremodeled by potential functions based on physically sound formulas.In addition, the training sets used for parameterizations are quitelarge, which may ensure a wide range of applicability. However, andas it will be shown later in the present work, the errors in the descriptionof noncovalent interactions may be significant, depending on the relativeorientation of the interacting molecules. This can be a consequenceof possible shortcomings in popular data sets, which in general onlyinclude the most relevant configurations of interacting molecules.47 Following the strategy used to develop potentialsfor interactions of peptides with self-assembled monolayers of perfluorinatedalkanes,47 we selected small moleculesas representatives for typical functional groups and evaluated IPECsfor all possible molecular pairings. Specifically, for this proof-of-conceptstudy, we have chosen methane, formic acid, and ammonia, which givesix different pair combinations: the three dimers and the CH4/HCO2H, CH4/NH3, and NH3/HCO2H pairs of molecules. We developed empirical correctionsfor the PM6 method, which in principle can be used for interactionsbetween hydrocarbons, carboxylic acids, and amines. To assess theperformance of the method as well as the transferability of the correctionsto other systems, we applied them to evaluate interaction energiesfor several complexes of the S66,25 A24,48 and ADIM650 data sets, as wellas for a collection of different conformers of the diglycine dimerand trimer, and the dialanine dimer, obtained through automated explorationof the corresponding potential energy surfaces (PESs). The noveltyof our approach is the introduction of two important features. First,and most important, the inclusion of several orientations of the interactingmolecules in the database, which is crucial to obtain well-balancedcorrections. Second, the use of general corrections to take into accountthat SQM methods have significant limitations to accurately describenot only dispersion interactions but also electrostatics, induction,and exchange repulsion. We notice that the purpose of this paper isnot to present corrections with final parameters for universal applicability,but to show a strategy to develop corrections that can satisfactorilymodel noncovalent interactions for all orientations of interactingmolecules.In this paper, we present, as a proof-of-concept study, an alternativeway to develop analytical corrections for SQM methods to improve thedescription of noncovalent interactions. The idea is based on previouschemical dynamics studies in which pairwise intermolecular potentialswere parameterized through fittings to a series of intermolecularpotential energy curves (IPECs) that emphasize the different atom-pairpotentials exhibited by the interacting molecules.251 and the augmented correlation consistent polarized valence triple-zetabasis set aug-cc-pVTZ.52 The IPECs werealso evaluated employing DFT with the B3LYP functional,55 including the D3 dispersion correction with the Becke–Johnsondamping scheme39 and with the valence triple-zeta polarization def2-TZVPbasis set.56 The IPECs were computed usingthe supermolecular approach with frozen intramolecular geometriesand correcting the interaction energy for basis set superpositionerror (BSSE) through the counterpoise method.58 The intramolecular geometries were obtained by B3LYP-D3/def2-TZVPoptimizations. Several orientations of the interacting molecules wereselected to stress the different pair-type interactions. Specifically,for each pair of molecules, the number of orientations was at leastequal to the number of the different pair-type interactions. A properselection of orientations is crucial to obtain well-balanced corrections.These electronic structure calculations were performed with the ORCA4.0 program and the default frozen core approximation.60Intermolecular potential energycurves for the six pairs of moleculesindicated above were calculated using CCSD(T)i and j refer to atoms belonging to different interacting molecules,and rij is the interatomicdistance between atoms i and j.Parameters Aij, Bij, and Cij  as well as nij (integers) depend on the nature ofthe considered pair of atoms. fcut(rij) is a cutoff function introducedto remove the correction at very short rij distancessij is a parameterthat controls the strength of the damping forthe interaction between atoms i and j, and dij is the distanceat which the cutoff function takes the value 1/2. The nij parameters were not fixed to 6; rather,they were allowed to vary around this value. Also, the Aij and Cij parameters may be either positive or negative.We notice that 61 to work reasonably well because this potentialcan model intermolecular interactions with pretty good accuracy.The general expression of the noncovalent potential–energycorrection developed in this work for the PM6 method is written asa pairwise sum of the form24 We used aleast-squares nonlinear fitting procedure based on a genetic algorithm,as implemented in our GAFit code,62 andwith the following objective function, χ2xi, yi) representsone of the N data points, a is the collective variableformed by the total number of fitting parameters, and f  is the valueof the model function at xi .The square of the difference between yi and the corresponding model value, calculated with wi) assigned to each data point.The abovementioned parameters were obtained through fittings todifferences between the interaction energies calculated at the referencelevel and those computed with the PM6 method. As described in thenext section, the IPECs obtained by B3LYP-D3/def2-TZVP calculationsare in very good agreement with those determined at the CCSD(T)/aug-cc-pVTZlevel of theory, showing the efficiency of the combination of theB3LYP-D3 density functional and the def2-TZVP basis set in providingacceptable and inexpensive IPECs. For our approach, the use of anaccurate and inexpensive reference methodology is important because,in general, we need a thorough exploration of potential energy surfacesfor both parameterization and validation processes. For this reasonand considering that future work, for extending the method to othertypes of functional groups, will involve a large amount of calculations,we have selected the B3LYP-D3/def2-TZVP level as the reference forthe fittings. Furthermore, for the molecular systems considered inthis study, the errors of the fits are larger than the B3LYP-D3–CCSD(T)potential energy differences. The SQM calculations were carried outwith the MOPAC2016 program.25 A24,48 and ADIM650 databases. Moreover, we checked the performance of the correctionson a data set formed by a collection of different conformations ofdiglycine and dialanine complexes, obtained by an automated explorationof the PESs at the PM6-D3H4 level, using the AutoMeKin package,65 which has an interface with the MOPAC2016 program.24 Specifically, we considered the diglycine dimer and trimer,as well as the dialanine dimer. Although AutoMeKin has mainly beendesigned to discover and simulate chemical reaction mechanisms, itincludes an option for obtaining stationary points for intermolecularcomplexes.66 As for the fittings, the benchmarklevel for this validation was B3LYP-D3/def2-TZVP, correcting the interactionenergies for BSSE.To validateour model function and parameterization strategy, aswell as to explore the transferability of the corrections, we appliedthem to several complexes of the S66,33.1The formic acidmolecule has five chemically nonequivalent atoms, that is, all theatoms are nonequivalent. Therefore, for this system, there are 15different types of pairwise interactions. Consequently, for the fittings,we included 15 orientations that emphasize the distinct pairwise interactions,as well as an additional orientation corresponding to the global minimumof the formic acid dimer, which exhibits double hydrogen bonding.These 16 orientations are depicted in Figures S1–S7, the agreement between theCCSD(T) and DFT curves is excellent. To develop corrections for thePM6 method, using the functional form specified in r corresponds to the distance between attacking atoms, thatis, the two carboxylic hydrogens in orientation 1, for example. Theform of the energy difference as a function of r forthis orientation resembles a typical repulsive potential, indicatingthat PM6 has a less repulsive IPEC than that of the reference method.By contrast, for orientation 4, the form of the DFT–PM6 plotbehaves as a decaying exponential with negative amplitude /aug-cc-pVTZand B3LYP-D3/def2-TZVP levels. As shown in the Supporting Information, e Aij in 1, thus p62 and the geometries andenergy differences corresponding to the 16 orientations of the formicacid dimer, we simultaneously fitted the parameters involved in 16 and ODMx17 methods. For the formic acid dimer, becausethere are 15 different types of pairwise interactions, the total numberof parameters is 60, without including those associated with the cutofffunction given by sij parameters and different values for the dij parameters, depending onthe nature of atoms i and j. Theparameters obtained from our best fit are collected in A, B and C, we only show two decimals;the high precision parameters are included in Table S1 in the Supporting Information. Notice that we havedefined atom types in much the same way as in molecular mechanicsforce fields. The symbols chosen in this work are shown in Using GAFitFigure S8 in the Supporting Information.For comparison, we include the PM6 curves as well as those obtainedwith the PM6-D3H49 and PMO2a16 methods, which are implemented in the freelydistributed MOPAC201624 and MOPAC 5.022mn32 programs, respectively. It would be interestingto include results of calculations using the ODMx method;17 however, to our knowledge, the code in whichthis method is implemented is not freely available.67 As can be seen from S8, the PM6-FGC curves(black lines) agree well with the B3LYP-D3/def2-TZVP data (black opencircles).Supporting Information), this method shows anunphysical behavior, because the interaction energy in the repulsiveregion decreases as the distance between the attacking atoms decreases.These orientations correspond to configurations that emphasize theinteraction between oxygen atoms. Clearly, a revision of this methodis required to improve its performance. For this reason, for the remainingsystems under investigation here, we have not considered the PMO2amethod any further.The IPECs calculated with the PMO2a method (red lines)displayremarkable discrepancies with the reference curves. Strikingly, fororientations 6 and 8, as well as for orientation 13 /CBS data, so that slight deviations may be expectedbecause our IPECs were obtained with B3LYP-D3/def2-TZVP calculations,although, as already mentioned, they are in excellent agreement withthe corresponding CCSD(T)/aug-cc-pVTZ curves. As can be seen, fororientation 1, which corresponds to the attack between carboxyl hydrogens,the PM6-D3H4 method exhibits a clear minimum. This orientation ispredicted to be repulsive with both B3LYP-D3 and CCSD(T) methods.Also, for orientation 5, the PM6-D3H4 method gives a significant minimum,which contrasts with the small well depth predicted by the referencecalculations. It is also worth mentioning that, for orientations 6and 8, PM6-D3H4 and PM6 exhibit an unphysical behavior in the repulsiveregion (around 5 kJ/mol). Although the S66x8 data set3.2This dimer shows threedifferent types of pairwise interactions, and therefore, we need atleast three different orientations. In this work, we considered thefour orientations depicted in Table S1.Among the systems considered inthis study, the ammonia dimer wasthe most challenging. Actually, using our simple expression for theanalytical correction 1 and 2, 3.3Table S1,exhibit IPECs in satisfactory agreement with the reference curves.The underestimation of the dispersion interaction in the PM6 methodis clear, but the worse performance predicted with this method appearsfor orientation 1 , which showsa significant minimum at a quite short H···H distance.The IPECs evaluatedfor this dimer are displayed in 3.4Table S1. Figure S9. The most attractive orientation exhibitsa hydrogen bond between the carboxylic hydrogen and the ammonia nitrogen(orientation 2). Both the PM6-D3H4 (blue line) and the PM6-FGC (blackline) methods satisfactorily describe the interaction for this orientation.However, for several other orientations , thePM6-D3H4 method predicts minima with potential well depths largerthan those obtained through CCSD(T) and B3LYP-D3 calculations.For this complex, we considered 10 orientations,that is, the samenumber as that of the different types of pairwise interactions. Thebest fit for this system led to the parameters reported in Figure S9), the PM6-FGC method gives a satisfactory description of the noncovalentinteraction in the ammonia-formic acid complex.For orientation 1, that is, theattack between carboxylic and ammoniahydrogens, the behavior of the PM6-D3H4 curve resembles that foundfor orientation 1 in the formic acid and ammonia dimers. In thesethree cases, the reference IPECs clearly exhibit a repulsive character.The PM6-FGC curve shows a small deviation from the reference IPEC,similar to that exhibited in the ammonia dimer. For orientations 9and 10, which correspond to the attack of the carbonyl carbon to ammoniahydrogen and nitrogen, respectively, the PM6-D3H4 (and PM6) curvesalso show remarkable discrepancies with respect to the reference curves.For orientation 9, the PM6-FGC curve exhibits a small deviation fromthe benchmark IPEC. Overall , it predicts more attractive interactions. As expected,the PM6 interaction energies are very inaccurate, and for orientations1 and 3 (attacks of hydrogen atoms), the corresponding IPECs displayremarkable minima.For this complex,we considered 10 orientations, and four of themare depicted in 3.6Fourdifferent orientations were considered for this complex, and theyare displayed in 3.768 Consideringthe drastic approximations inherent to SQM methods, it is clear thatthese approaches fail in describing not only dispersion interactionsbut also electrostatic, induction, and exchange-repulsion. Our analyticalcorrection consists of a pairwise sum over interacting atoms, withfour parameters per interaction type. The form of the energy differencesbetween the interaction energies calculated at the reference leveland those obtained with the PM6 Hamiltonian, as exemplified in There are two critical issues that we need toconsider in order to validate our method: (1) the possibility of overfittingand (2) parameter transferability. Overfitting occurs when the modelfunction uses more parameters than are necessary or exhibits a morecomplex form than is needed.Tables S2 and S3), we evaluatedthe IPECs for the 16 orientations of the formic acid dimer, and theyare plotted in Figures S11 and S12, togetherwith the B3LYP-D3 curves and those determined with the parametersof To analyze the possibility of overfitting in ourapproach, let us focus on the formic acid dimer. For the fittings,we have considered that all the atoms are different, which led to60 parameters in all, and they were simultaneously fitted using IPECsfor 16 different orientations. The additional 15 parameters of thecutoff function were set, rather than fitted, after some exploratoryfittings. To investigate overfitting, we have performed two sets ofadditional fittings: (i) considering that all oxygen atoms share thesame parameters (4 atom types) and (ii) considering that, in addition,the hydrogen atoms are equivalent to each other (3 atom types). Thesesimplifications lead to 40 and 24 parameters, respectively. For thefittings, we used the same number of points and weights as for thefittings described previously for this system . The data points extended up torepulsive energies ranging from 23 to 141 kJ/mol, depending on theorientation. With the corrections obtained from the best fits  are, in general, in good agreement with the DFT curves. For orientation4, the PM6-FGC curve displays a potential well less pronounced thanthat of the reference level. The most important deviations are exhibitedby the PM6-D3H4 curves for orientations 3 and 7. Notice that, forseveral orientations, both PM6 and PM6-D3H4 curves deviate significantlyfrom the reference curves in the repulsive region. Finally, we noticethat the MAE calculated for the PM6-FGC curves, including all thepoints with interaction energies up to 100 kJ/mol, is 1.1 kJ/mol,slightly smaller than that calculated employing the FGC parametersobtained using 4 atom types (1.3 kJ/mol), thus resembling the resultsreached for the training set. From the discussion in this and theprevious paragraph, we conclude that our parameterization model doesnot exhibit overfitting, at least at a significant level.In addition to the previous analysis, we evaluated IPECs for 10random orientations of the formic acid dimer, which were not includedin the fittings. The comparison of these IPECs is shown graphicallyin 25 and compared the results with benchmark datataken from the GMTKN5550 and BEGDB69 web pages. All the benchmark interaction energiescorrespond to CCSD(T)/CBS calculations (with BSSE corrections). Table S4 specifies the complexes considered forthis comparison and gives the values of the benchmark interactionenergies as well as those calculated with the PM6, PM6-D3H4 and PM6-FGCapproaches. The corresponding absolute errors are displayed in Asa further validation of our method, and particularly to analyzethe transferability of the corrections to related systems, we calculatedthe interaction energies for 23 complexes defined in well-known databasesTable S4, systems 1–4correspond to complexes of methylamine and N-methylacetamide(denoted in BEGDB as peptide). For these systems, our results areworse than the PM6-D3H4 results. Notice that the training set usedfor the parameterization of the PM6-D3H4 method was the S66x8 database,25 which includes systems 1–14. For system6, the acetamide dimer, the performance of our method is clearly unsatisfactory.Interestingly, the PM6-FGC interaction energy calculated for the complexof pentane/acetamide (−14.8 kJ/mol), system 14 in N-methylacetamide and with aceticacid, systems 12 and 13, respectively, are also very well describedby our method. These results are in line with previous work47 wherein pairwise analytical potentials obtainedfrom fittings involving the CF4/NH3 and theCF4/HCOOH systems reproduced ab initio IPECs calculatedfor the CF4/HCONH2 complex.As shown in 3/CH4 fittings maybe transferable to model −NH2/alkane interactions,other parameters obtained with NH3 may not be transferableto amines and amides. The description of noncovalent interactionsinvolving the −NH2 group in amines and amides couldbe improved by including new representative compounds, namely, methylamineand acetamide. The water dimer is another challenging case; we didnot succeed in developing corrections as defined in The resultsdiscussed in the previous paragraph clarify an interestingfeature regarding transferability in the studied systems. Althoughparameters obtained from NH69 For the sake of comparison, the corresponding CCSD(T)/aug-cc-pVTZinteraction energies are −16.7 and −65.9 kJ/mol, respectively.These results reinforce the use of B3LYP-D3/def2-TZVP data as thebenchmark for our parameterizations.It is importantto notice that the interaction energies calculatedat the B3LYP-D3/def2-TZVP level for methylamine and acetamide dimers are in very goodagreement with the reference CCSD(T)/CBS(haTZ) values, .Table S4), our method predictsreasonably good interaction energies. There are, however, some deviationsfor complexes involving neopentane (8 and 9). Finally, for system15, which corresponds to the formaldehyde dimer, the interaction energycalculated with our method has an absolute error larger than thatobtained with PM6. This indicates that the parameters of the carbonylgroup developed from fittings on the formic acid dimer are not transferableto aldehydes and ketones, which supports the idea of using correctionsfor specific functional groups.For the hydrocarbon systemsconsidered in 2 group, it isimportant to assess the performance of the method on larger systems.Because our purpose is to derive corrections for biological systems,here, we have studied complexes of diglycine and dialanine. Specifically,we have considered the dimers of these dipeptides as well as the trimerof diglycine. In this work, conformers of these complexes were foundby automated exploration of their potential energy surfaces at thePM6-D3H4 level, using AutoMeKin,66 which has an interface with theMOPAC2016 program.24 These searches involvedchanges in both intramolecular and intermolecular conformations andled to 77 and 90 different conformers for diglycine and dialaninedimers, respectively, and 146 conformers for the diglycine trimer. Even though the present correctionscannot accurately describesome interactions involving the −NH27) that does not include sufficient orientations of the interactingmolecules.The linear correlationsevaluated for the conformers of the dialaninedimer are depicted in 70 SRPs should be developed and applied to theatoms involved in the reaction, and our corrections should not beused for these atoms.Finally, we would liketo point out that our corrections may beproblematic in the study of chemical reactions, since, in general,SQM methods do not predict accurate reaction barriers. To overcomethis problem, we recommend the use of specific reaction parameters(SRPs), following the strategy pioneered by Truhlar and co-workers.4We havepresented a new strategy, that is, the PM6-Functional GroupCorrections (PM6-FGC) method, to develop analytical corrections forsemiempirical quantum mechanical methods, aimed at improving the descriptionof noncovalent interactions. For this proof-of-concept presentation,we have selected the PM6 SQM method. Employing this Hamiltonian andthe B3LYP-D3/def2-TZVP level for benchmarking, we calculated intermolecularpotential energy curves for several orientations of pairs of smallmolecules, which are selected as representatives of different functionalgroups. Specifically, we have considered ammonia, formic acid, andmethane, which result in a total of six molecular pairings. A simplemathematical expression, which should be considered as a practicalway, without any physical meaning, is used to represent the correctionsto improve the performance of SQM methods. The parameters of the analyticalcorrections were evaluated from fits to differences between interactionenergies calculated at the reference level and those evaluated atthe SQM level.Intermolecular potential energy curves (IPECs)were also evaluatedat the CCSD(T)/aug-cc-pVTZ, including counterpoise correction forBSSE. The agreement between the B3LYP-D3 and the corresponding CCSD(T)curves was excellent. This result together with the fact that we willneed to perform extensive benchmark calculations to extend our methodto other functional groups, in order to develop a universally applicablemethod for peptides and other biological systems, led us to selectthe DFT method as the benchmark level for the parameterizations.In general, the IPECs obtained with the method parameterized inthis work, namely, PM6-FGC, are in good agreement with those determinedat the DFT level, and significantly improve those provided by successfullycorrected SQM methods. In this way, this work emphasizes the importanceof including, in the databases, sufficient orientations of the interactingmolecules; this fact is crucial to develop well-balanced corrections.2 group inamines and amides. This issue will be faced in future work. However,using the present set of parameters, we evaluated interaction energiesfor a large number of conformers of diglycine and dialanine dimers,and diglycine trimer, obtaining very good results in comparison withthose predicted by PM6 and PM6-D3H4.Even though the corrections proposed in this work are based ongeneral pairwise functions that include a significant number of parameters,several validation tests suggest that our parameterization strategyis not affected by overfitting, at least at a significant level. Acomparison of interaction energies calculated for a series of complexesof well-known data sets has revealed important warnings concerningparameter transferability. In particular, we found that the ammoniadimer is not a good representative for the parameterization of correctionsfor some interactions involving the −NH40 We are continuing with our efforts to improve and extend our correctionsto other functional groups, relevant to biological compounds, andwe intend to implement them in the MOPAC program.24 Meanwhile, a Python script to compute PM6-FGC correctionsis available upon request.Although the method describedhere involves simple pairwise functions,more accurate corrections could be developed by using or adding alternativefunctions, as well as by introducing three-body terms of the typeof the Axilrod–Teller–Muto potential.


Hearing preservation is one of the major goals in the surgical treatment of Neurofibromatosis Type 2 (NF2) associated vestibular schwannomas (VS) and hearing diagnostics are important monitoring parameters and intraoperative tools to pursue this goal. Our monocentric retrospective analysis aimed to predict postoperative hearing deterioration or loss based on preoperative audiometry and neurophysiological  findings. In this respect and according to our data evaluation in 100 NF2-associated VS of 72 patients both parameters seem to be prognostic markers, particularly BAEP findings. Large discrepancies between both audiometry and BAEPs which were identified in twenty-one cases of our cohort appear to be at high risk of significant postoperative hearing worsening.p = 0.015) and resection amount (p = 0.048) significantly influenced postoperative hearing outcome. The prediction model for postoperative hearing deterioration/loss between preoperative BAEP and AAO-HNS class showed increased risk by increasing BAEP class. Twenty-one tumors/ears were identified with large BAEP and AAO-HNS class discrepancies (≥2 points) and were associated with a high (48–100%) risk of deafness after surgery in ears with preoperative available hearing. Overall, the results were heterogeneous but the better both BAEP and audiometry class before surgery, the higher the chance of hearing maintenance afterwards. Large resection amounts  exhibit a significant (p < 0.05) higher risk compared to smaller amounts . Our results emphasized the indispensable role of both hearing monitoring in form of audiometry and neurophysiology (BAEP) in the pre-and perioperative monitoring of NF2-associated VS. Both BAEP and audiometry are good prognostic markers for the postoperative hearing outcome. The extent of resection should be strictly guided by and adjusted to the intraoperative neurophysiological monitoring.Both brainstem auditory evoked potentials (BAEP) and audiometry play a crucial role in neuro-oncological treatment decisions in Neurofibromatosis Type 2 associated (NF2) vestibular schwannoma (VS) as hearing preservation is the major goal. In this study, we investigated the risk of immediate postoperative hearing deterioration (>15 dB and/or 15% loss in pure-tone average [PTA]/ speech discrimination score [SDS] in a cohort of 100 operated VS (ears) in 72 NF2 patients by retrospective analysis of pre- and postoperative hearing data  taking into account relevant influencing factors, particularly preoperative audiometry and BAEP status and the extent of resection. Immediately after surgery, the hearing was preserved in 73% of ears and approximately ~60% of ears kept their hearing classes. Preoperative BAEP ( NF2 gene located on chromosome 22q [Neurofibromatosis type 2 (NF2) is an autosomal-dominant tumor predisposition syndrome caused by the inactivation of the some 22q ,2. The tsome 22q ,4,5. Patsome 22q ,4,5,6,7 some 22q ,9. NeverTreatment options in NF2-associated VS are currently limited to surgery ,11, chemIn the following study, we investigated the combined role of preoperative BAEP and audiometry on postoperative hearing function and evaluated the risk of postoperative hearing decline or loss in ears with large discrepancies between preoperative BAEP and audiometry.The diagnosis of NF2 was confirmed in all patients by clinical evaluation using the Baser diagnostic criteria for NF2 .A total of 72 NF2 patients and 100 tumors with complete hearing diagnostic before and after surgery were included in this retrospective analysis and who were followed-up between 2004 and 2019, at the Department of Neurosurgery and Centre of Neurofibromatosis in Tübingen. The Ethics Board of the Medical Faculty and the University Hospital of Tübingen approved this retrospective analysis . Surgery was performed at our institution via the retrosigmoid approach, by decompression of the internal auditory canal (IAC) with tumor various resection amounts, under continuous neurophysiological monitoring and only by the two senior authors, both very experienced in VS surgery .The indications for surgery were (1) hearing deterioration in brainstem auditory evoked potentials (BAEP) and/or pure-tone and/or speech audiometry regardless of tumor size  often associated with tumor growth, and (2) large tumors  on bothData in the observation course, under bevacizumab treatment, after radiation or with hearing aids were excluded. Mutation analysis was performed during routine diagnostic in 48 patients. The remaining 24 patients or their legal guardians refused genetic analysis.Data of 37 of 100) tumors were part of a prior study [0 tumors Tumor volumetry, growth rate, and resection amount were measured, classified, and calculated as previously described ,11.For the volumetric analysis, postcontrast thin-sliced (≤3 mm) T1-weighted magnetic resonance (MR) images were uploaded into the iPlan Net software  and volumes were measured by one experienced rater (I.G.) using the manual segmentation tool.The growth rate was determined using MRI data sets from at least 2-time points before and after surgery. Postoperatively, the growth rate determination was restarted from the first MRI session performed 3 months after surgery.The extent of resection was calculated as a percentage amount from pre-and postoperative volume values. For this calculation, there was a lack either of preoperative or postoperative volume values in 5 (out of 100) tumors. In addition, a categorical classification was also made analogous to our previous study .Hearing was assessed by regular determination of 4-frequency pure-tone average (PTA), speech discrimination score (SDS), and BAEP, within 4 weeks before surgery and directly or up to 3 months after surgery. Hearing data were classified using the Gardner and Robertson Scale (G–R) , the AmeImmediate postoperative functional hearing deterioration was defined as a decrease of >15 dB in PTA and/or >15% in SDS compared to preoperative values and as a downgrading of G-R, AAO-HNS, and BAEP class.TM Viking Quest system  in all patients according to a standardized protocol. Monitoring was performed with condensation, rarefaction, and alternate polarity as continuous click stimulation of 115 dB pSPL intensity, generated by an audio stimulator driven by pulses of 100µs duration. The stimuli were presented through TIP-100 tubal earphones inserted into the external auditory canal with a stimulus repetition rate of 10.3 Hz. The contralateral ear was masked by 80 dB white noise. A double measurement was derived for both sides with 1000 to 1500 sweeps and filter settings of 150–15,000 Hz. The latencies of waves I, III, and V as well as the interpeak latencies I–III, III–V, and I–V as well as the amplitude quotient of wave V/I were determined. During the examination, the patient is in a lying position, has its eyes closed, and is ideally maximally relaxed. The intraoperative multimodal neurophysiological monitoring additionally included facial electromyography and long tract sensory evoked potentials.Neurophysiological monitoring in form of BAEPs was performed with the NicoletBAEPs were categorized using the classification system by the Hannover group  which isStatistical evaluation was performed with Statistical Package for Social Sciences (SPSS)  and Matlab , version 9.5.0 (R2019b), Natick, Massachusetts: The MathWorks Inc., USA).Binomial logistic regression was performed to ascertain the effects of preoperative tumor volume, growth rate, PTA, SDS, AAO–HNS, G–R, and BAEP class as well as resection amounts and age at time of diagnosis on the likelihood that participants suffer from postoperative hearing loss.The linearity of the continuous variables with respect to the logit of the dependent variable was assessed via the Box–Tidwell procedure. Based on this assessment, all continuous independent variables were found to be linearly related to the logit of the dependent variable. There were five standardized residuals  with values of 3.384, 1.735, 3.492, −2.179, and −1.094 standard deviations, which were kept in the analysis.Risk stratification of postoperative hearing deterioration was estimated according to the preoperative AAO–HNS und BAEP scale.A Chi-square test of homogeneity was performed to investigate the relation of resection amount categories  were partially resected. 8/48 patients were ascertained to be mosaic and in 4/48 patients no mutation could be detected neither in blood nor in tumor DNA. 25 patients were treated with bevacizumab in the following course due to further hearing deterioration and/or tumor growth.n = 73/100) of ears maintained and 10% (n = 10/100) were unable to maintain their hearing (PTA and SDS) according to hearing preservation criteria. Deafness (=PTA 130 dB and 0% SDS) occurred in 17 ears (17%) after surgery.A total of 73% (Preservation of the preoperative hearing grade could be achieved in 61 (61%), 59 (59%), and 65 (65%) of hearing ears, with regards to the Gardner and Robertson Scale (G–R), American Association of Otolaryngology–Head and Neck Surgery (AAO–HNS) and the BAEP classification, respectively. An improvement in G–R Scale, AAO–HNS, and BAEP class could be observed in two, one and four ear/ears each.Overall functional hearing (AAO–HNS class I and II) could be preserved in 60 ears (60%). Scattergrams created according to recently recommended standardized formatting guidelines  for the 2(9) = 18.176, p = 0.033. The model explained 32.2% (Nagelkerke R2) of the variance in postoperative hearing loss and correctly classified 80.5% of cases. Sensitivity was 29.4%, specificity was 95.0%, positive predictive value was 62.5% and the negative predictive value was 82.6%. The area under the ROC curve was 0.829 , which is an excellent level of discrimination according to Hosmer et al. [In this model, 77 out of 100 cases were included. For the other 23 cases, no sufficient data was available. The logistic regression model statistically significantly predicted postoperative hearing deterioration χr et al. .Of the nine predictor variables, only two were statistically significant: preoperative BAEP class and resection amount (as shown in Patients with worse BAEP scores (BAEP class 3 to 5) carry a high risk of postoperative hearing deterioration or complete loss particularly in combination with a worse AAO–HNS score . The worTwenty-one unusual cases with large discrepancies (≥2 points) between BAEP and AAO–HNS class are listed and highlighted in the For the remaining 15 (of 21) ears with preoperative available hearing (AAO–HNS class 1–3) the risk of postoperative hearing loss (AAO–HNS class 4) increases by increasing discrepancy  between BAEP and AAO–HNS class.In patients with preoperative functional hearing (AAO–HNS class 1 and 2), the rate of postoperative hearing preservation was 73% in preoperative BAEP class 1, 67% in class 2, 60% in class 3, 50% in class 4, and zero % in class 5.For this model, the data of 95/100 tumors were included in the analysis . The remp < 0.001). Post hoc analysis involved pairwise comparisons using the z-test of two proportions with a Bonferroni correction. The group comparison was statistically significant (p < 0.05) between the groups 2 and 5, 3 and 5 as well as between 7 and 5.A statistically significant difference in group proportions was seen  and thin-sliced cranial MRI for volumetric measurements.After an initial period of close monitoring (every 3 to 6 months) to assess hearing and tumor dynamics within the first 12 months after initial presentation, monitoring should be continued or extended (every 6 to 12 months) based on patient age, hearing, and tumor growth dynamics as well as tumor size.Regardless of tumor size, the following patients should be monitored closely: children, adolescents, young adults, patients on bevacizumab therapy, patients with impaired/decreasing hearing, and those with rapidly growing or bilateral medium-sized tumors (T3 according to the Hannover Classification).Extended follow-up intervals may be considered for small tumors (T1 and T2) in older patients with a slow growth dynamic, associated stable and mildly affected hearing, or in deaf patients.Except for bilateral large tumors (T4) with critical brainstem compression, the decision for surgical treatment should always be based on impairment of hearing parameters.Due to their objectivity, the fact that their impairment often precedes audiometry decline, and taking their important intraoperative role into account, BAEPs play a very important and decisive but not exclusive role in the treatment decision.Their importance for intraoperative monitoring of function in vestibular schwannoma surgery is indisputable and well described ,18,25.Generally, there is a positive correlation between BAEP and pure-tone average (or inverse to speech discrimination score) as we described previously . MoreoveNevertheless, auditory function tests are not to be neglected, particularly for those cases with large (≥2 points) and unusual discrepancies in BAEP and audiometry scoring. For these cases, the risk of hearing loss with increasing discrepancy is between 48 and 100% according to our results. In general, neurophysiological and audiometric results correlate with each other, but in some patients’ large discrepancies were seen either in form of good to excellent BAEP and bad audiometry or vice versa. We observed this rarity in 21% of our investigated ears. However, for the subgroup of special cases with existing and subjectively useful audiometric hearing but pre-and/or intraoperative severely or no more derivable BAEPs, it is worthwhile to continue striving for a more defensive surgical approach in the sense of a partial and then anatomical-guided resection far from the cochlear nerve to maintain the residual chance of audiometric hearing preservation postoperatively.The mechanism leading to these large discrepancies is unknown and not yet described in the literature. Technical problems or examiner-dependent factors are possible but are unlikely in our setting due to the repeatedly confirmed results, the unchanged equipment, and strictly standard operating procedure driven investigations as well as the inter-examiner reliability.3 vs. 4.5 cm3) in the present cohort, but also poorer postoperative hearing parameters  and comparable good preoperative audiometric baseline values . Consequently, too large resection amounts have a negative impact on hearing maintenance in case of NF2-associated VS, so that a less aggressive surgical strategy is recommended with a lower extent of resection amounts.Certainly, as shown in our current and previous  analysisThe mechanisms leading to preoperative hearing deterioration or loss are certainly complex, multifactorial, and not yet fully clarified. Possible mechanisms like mechanical pressure and/or low cochlear perfusion ,28, hairOne limitation of the current study is the likely under detection of cases with postoperative hearing loss. With the presented statistical model, a high specificity but low sensitivity is achieved. This means that postoperative hearing preservation can be predicted with relative certainty based on the data, but a prognosis on postoperative hearing loss remains unreliable. In everyday clinical practice, this residual uncertainty must be discussed with the patients and their relatives.Patients with discreetly affected but still easily derivable BAEPs, such as class 1 and 2, with simultaneously good PTA and SDS values, have a good chance of direct postoperative hearing preservation in case the surgeon’s intention to treat is hearing preservation. The worse BAEPs before surgery, the higher the risk of postoperative hearing deterioration/loss even in cases with accompanying good PTA/SDS values. As a result, the BAEPs play a very sensitive role in the assessment of postoperative hearing outcomes. As a consequence, we strongly recommend early initiation of surgical therapy for already impaired but well-preserved BAEPs despite normal or slightly impaired audiometry in order to work with good intraoperative BAEPs that allow tailoring the amount of resection according to the intraoperative course of hearing function.Consequently, each case has to be interpreted and assessed individually. Surgical and neurophysiological expertise plays a very important and decisive role in those special cases with strong discrepancies between neurophysiology and audiometry. Furthermore, in such discrepant cases, unless there is no risk to the patient from a very large tumor , the results of our study imply, that we will discuss with the patient in advance a surgically rather defensive approach and would recommend tumor debulking with as little manipulation as possible far from the cochlear nerve. In such cases, alternatives such as radiosurgery , primary bevacizumab treatment (each tumor size), or total resection with a primary hearing restoration such as a cochlea implant or brainstem auditory implant can also be discussed. This is done regularly with all patients that have a bad functional hearing preoperatively where the goal of surgery could otherwise only be to preserve the residual hearing impression.Compared to our previous study  which iA study investigating the short- and long-term follow-up of hearing and tumor growth rate before and after surgery in older NF2 patients is currently undertaken, but there are still not enough valid long-term follow-up data to finish the investigation.Both preoperative BAEP and audiometry play a crucial role in decision making for treatment initiation and perioperative hearing monitoring in patients with NF2-associated VS.Better preoperative values are usually associated with better postoperative auditory outcomes and vice versa. Cases with large discrepancies between BAEP and audiometry are rare but associated with a high risk of postoperative functional hearing loss. For these cases, BAEPs appear to have a higher validity for the auditory outcome of surgery.


Contributing 11.6% of global DALYs (disability-adjusted life-years) and 16.5% of deaths from all causes, neurological disorders remain the leading cause of DALYs and the second leading cause of deaths (following cardiovascular diseases) over the world  to pass through the cell membrane and generate electrical signals for establishing the resting membrane potential  channel  can be done to further understand the phenotypic and functional consequences of SNPs in ion channels.Single nucleotide polymorphisms (SNPs) refers to DNA sequence polymorphisms caused by mutation of a single nucleotide. It is the most common form of genetic variants in humans, accounting for more than 90% of all known polymorphisms  T-type calcium channel Cav3.2 sets a low threshold for action potential firing in dorsal root ganglion (DRG) neurons and plays a key role in pain sensation  stimuli from the environment, and therefore are important sensors for perception  showed impaired hearing associated with loss of cochlear hear cells, but most TRPV3KO mice (72.3%) had normal hearing. Interestingly, compensatory upregulation of TRPV4 was observed in the TRPV3KO mice with normal hearing, suggesting that both TRPV4 and TRPV3 channels are important for maintaining normal hearing. Overall, these results offer not only novel insight into the molecular basis of hearing but also potential target for treating hearing loss.Unlike voltage-gated ion channels that sense the membrane voltage change Clapham, . TRPV chClapham, . TRPV3 iClapham, . Studies2+ ion is also a key player for spinal cord injury (SCI), a seriously debilitating event that can lead to paralysis and even death  can cause severe damage to the brain. During cerebral ischemia-reperfusion, oxidative stress occurs and a large number of inflammatory cytokines are present in the ischemic focus , the Natural Science Foundation of Tianjin of China (No. 19JCYBJC28300 to HA), and the Natural Science Foundation of Hebei Province of China (No. H2020202005 to HA). This work was also funded by Dr. Neher's Biophysics Laboratory for Innovative Drug Discovery (Grant no. 001/2020/ALC) as supported by the Macau Science and Technology Development Fund.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.