Development Environment and Countermeasures of 3D Printing Industry Base: A Chinese Case Study

In recent years, many local governments in China scramble to build 3D printing industry base, hoping to stimulate local economic development. However, the theoretical research on development environment and countermeasures of these 3D printing industry bases are very lacking. The model analyzing development environment of 3D printing industry base was designed. The development environment and countermeasures of Anshan city’s 3D printing industry base were analyzed as an example. The research results can provide valuable reference for the development and construction of 3D printing industry bases.

Introduction
3D printing, as a representative of emerging technology, is driving the third industrial revolution [1]. Many countries in the world, such as the United States, Germany, Sweden, Japan, and Belgium all take 3D printing as an important support of the future economic development [2,3]. Receiving great attention from governments and businesses, 3D printing has been included in the National 863 plan and science & technology support program in China [4]. Today, more and more local governments have learned the importance of the 3D printing in stimulating local economic development and building the regional characteristic industry. China 3D printing Technology Industry Alliance predicts that that Chinese 3D printing market will become the largest market in the world in 2016 which will expand to 10 billion Yuan RMB over the United States [5]. Thus, many regions of China, such as Nanjing, Wenzhou, Wuhan, Zhuhai, Qingdao, Chengdu, are rushing to build 3D printing bases (or Parks) [6,7] to take the lead in grasping the growth opportunities and seize the large 3D printing market. However, in spite of the fast development of 3D printing industry in China, there is less research about the development environment and countermeasure of 3D printing industry. China National Knowledge Internet (CNKI) database information shows the related scientific researches and reports on "3D printing" and "base" are totally up to 28 records. Among them, there are 22 records from China Core Newspapers Full-text Database, which are some China-related news about the 3D printing industry base. The other 6 records come from China Academic Journals Full-text Database, of which only 2 records are about how to use 3D printing to establish Lunar bases [8,9] and the other 4 records published in academic journals are some news reports on 3D printing industry base in China. Therefore, it is badly necessary to conduct research on development environment and countermeasures of 3D printing industry base according to the time when the 3D printing industry base is expanded and constructed heavily by numerous local governments in China.

Analysis Model on Development Environment of 3D Printing Industry Base
SWOT is a structure analysis method aiming at four elements (strengths, weaknesses, opportunities and threats) and a kind of situation analysis based on the internal and external competition environment and competition conditions. It can draw a series of conclusion by listing and comparing internal strengths and weaknesses with external opportunities and threats [10]. In view of this, combining the features of 3D printing industry, we build an analysis model on development environment of 3D printing industry base to benefit the 3D printing industry [11,12]. The model consists of four aspects and 10 elements, as shown in Figure 1. For internal environment, "3D printing industry base" reflects the area's core competence to develop 3D printing industry. Industry base is directly related to the development of regional 3D printing industry base. "Talents storage and research capability in 3D printing field" show the regional breakthrough ability of science and technology. 3D printing is an emerging technology. A lot of design and research work are needed during its industrializing. Therefore, the quality and quantity of regional research institutes as well as talents have much impact on long-term development potential of 3D printing industry base. Besides, "internal support policies for the development of 3D printing" are very important impetuses because better political supports will bring better development chances. "Industrial concentration of 3D printing" can reflect the regional competitiveness of 3D printing industry base. "Leading teams and core figures of 3D printing" are the key factors to lead the industry to success. "The regional economic scale" decides the long-term development potential of 3D printing industry base. Thus, these six factors can comprehensively reflect the regional inner advantages or disadvantages on building the 3D printing industry base. Also, these advantages and disadvantages sometimes can reciprocally transform into each other according to the specific situation. For external environment, "self-development trend of 3D printing industry" will has a direct influence on the development opportunity of 3D printing industry base. "External support policies", such as national policies, and industrial policies can indirectly reflect the prospect and development chance. Besides, the industry competence power between existing and emerging 3D printing industry base as well as technology bottlenecks of 3D printing can all bring both chances and threats to the 3D print industry base. Therefore, the four factors-"self-development trend of 3D printing industry", "external support policies", "industrial competitors" and "technology bottlenecks of 3D printing" are used to analyze development opportunities and threats of 3D printing industry base.

Case Selection
Our previous researches aiming at the type of 3D printing industry base show that most 3D printing industry bases are based on manufacturing industry, such as auto industry, textile industry, medical equipment or chip industry [13]. As the main city of old industrial bases in northeast China, Anshan city in Liaoning province has outstanding industrial base of manufacture and development environment. More importantly, high quality/level and innovative area is being built in Anshan. Among the 10 major projects for science and technology development in five years, four projects--laser technology, health manufacturing, iron reprocessing and equipment manufacturing industry all will be related to 3D printing industry [14]. For example, laser technology is one of relying on technologies for 3D printing with significant application in steel processing, equipment manufacturing industry and health manufacturing. And this is just what Anshan city is planning to achieve -laser machining as the growing point and expansion of laser application as the focus. To sum up, Anshan city has already possessed a better development background and primary groundwork for building 3D printing industry base. It will perfectly be used as a sample city for leading the orientation of the research on development environment and countermeasures.

Advantages
i. Solid industrial base Anshan City has a geographical advantage, located in the cross point of the old industrial base and coastal economic development zone in Liaoning province. Anshan City is an important production base of steel in China, honored as the "Steel City", which brings a good industrial base to 3D printing. Laser technology in Anshan is developing rapidly and there are many companies engaged in the laser industry, such as Anshan Hust laser Technology Company, Ming-hui medical laser Technology Company, Anshan Hongyuan laser technology company, Zhengya laser Technology Company, and Ziyu laser technology company. Besides, Anshan high-tech development zone has cooperatively set up Sci-tech Industrial park for laser in Liaoning with Huazhong University of Science and Technology, Harbin University of Technology, Northeastern University and University of Science and Technology Liaoning etc. It mainly focuses on developing R&D and test platform of laser applied technology, high power laser device, laser advanced manufacture technique etc., which provides a strong support for 3D printing industrial development in Anshan.
ii. Great scientific research strength Anshan, as a national technological innovative trial-city and the key city of Manufacturing information engineering, has 69 research institutes, 280 scientific research institutions, 60 research and development centers, 7 industrialization bases, 80 national high-tech enterprises, and various talented people up to 240,000 [11]. With a great location and profound history of development, Anshan has been a leader in science and technology, such as steel technology, coking technology etc. Anshan city has a cooperative relationship with about dozens of universities such as Tsinghua University, Peking University, Xi'an Jiaotong University, and University of science and technology of Liaoning. Anshan city also sets up a national technology transfer center with the branch of Chinese Academy of Sciences in Shenyang. The center has reached dozens of industrialization agreements about innovative technological achievements.
iii. Advantages of national high tech Zones Anshan high tech Industrial Development Zone is a national high-tech zone, and over the 20 years, it constantly has improved the environment, enhanced innovation ability and expanded the industrial scale, which leads to the emergence of a large number of high-tech enterprises. Now it has 31 national high-tech enterprises, which accounts for the proportion of the city about 40%; it owns 39 enterprise technological centers, among which are 6 national ones and 22 provincial ones. It includes Angang Steel Company Limited, Rongxin Company Limited, Senyuan Company Limited, Anzhong Company Limited and Fuan Company Limited and other listed companies. It also includes a group of well-known research institutes and R & D centers, for example, NETC, SINOSTEEL. The University of Science and Technology Liaoning, located in the core area of high-tech Zone is the subordinate university of original Metallurgical Industry and has research highlights in machinery, metallurgy, chemical and other disciplines. At the same time, management Committee in Anshan high-tech zone has signed a long-term cooperation agreement with the vocational education of Anshan city, which tends to recommend professional technicians for high-tech enterprises in the region.

Disadvantages
i. Lower concentration of industry chains There are not many equipment suppliers of raw materials and component suppliers for the localization of 3D printing in Anshan, so it can be limited by the development of the suppliers: the downstream has not formed a long-term, stable and large scale demand. Also, customer bases are widely dispersed. Taken together, due to lower concentration of the 3D printing industry chain in Anshan, the elongating chain may reduce the industrial competitiveness of 3D printing industry base in Anshan.
ii. Lack of first-class leading teams and characters. In China, first-class research teams on the study of 3D printing mainly include Yan Yongnian team in Tsinghua University, Wang Huaming team in Beihang University, Shi Yusheng team in Huazhong University of Science and Technology and Lu Bingheng team in Xi`an Jiaotong University etc. Anshan City is short of industry-leading support teams on the scientific research strength in this field, which will adversely affect the development of 3D printing industry base in Anshan.
iii. Lack of regional economic scale 3D printing industry development needs supporting by better economic development. The 3D industry in economically relatively developed areas tends to develop better, especially rapidly in those cities such as Beijing, Hangzhou, Nanjing and Guangzhou etc. By contrast, Anshan City has slightly economically backward development, which has a negative impact on the development of the 3D printing industry.

Chances
i. Global industrial spree In recent years, the 3D printing industry scale has expended rapidly. It is predicted that from 2013 to 2020 year, the compound annual growth rate of the global market for 3D printing will reach 23%, reaching 8.41 billion dollars in 2020 [16]. The research from Market research firm Researchmoz shows that early 2015 in China the total was up to about 3.7 billion Yuan. By 2016, the total market will be over 3 times, which is expected to exceed 10 billion Yuan [17]. The study of Lux Research shows that by 2018, the 3D printer market in China (excluding exports) will grow to 37800 with compound annual growth rate of 34% and the revenue of 3D printer will grow to 700 million Yuan with compound annual growth rate of 27%. Therefore, the global 3D printing market has a tremendous potential for development [18].
ii. More development opportunities from China and its Liaoning province together In 2013, at the national level, the government added 3D printing to the National High Technology Research and Development Program of China to upgrade it to a national strategy; Released in February 2015 national additive manufacturing industry development plan (2015-2016), China is going to establish a completer additive manufacturing (also known as "3D printing") industrial system in early 2016; May 2015, China released the plan made in China 2015, proposing to promote technological breakthroughs of many emerging fields, in which 3D printing is in the first place. At Liaoning provincial level, the laser industrial park's development in Anshan has got great support from Liaoning provincial government, which has become one of ten key industrial parks in Liaoning province. Liaoning province is in the process of construction of "Liaoning (Anshan) laser science and technology industrial park" with entire province to make Anshan laser industry as provincial strategic emerging industries. With above-mentioned national and Liaoning provincial measures, Anshan city has a better development opportunity for building the laser industry base.

Threats
i. Industrial competitors Moving quickly in some regions of the country exerts pressure on Anshan. Institutes of 3D printing technology industry and industry bases as well as public service platforms of the government were established in Nanjing. Also, the government is giving continuous support of policies and fund to the project related to 3D printing to promote the development of 3D printing. Wuhan was the first to set up Chinese first 3D printing factory. Dongguan added the emerging industry of 3D printing to the government work report in 2013 and it is proposed that Dongguan should have layouts in advance to early expend into the technology market of 3D printing. Harbin University of Technology established its own Engineering Center of 3D printing lab. Renze Science and Technology Development Co, Ltd in Heilongjiang has purchased Flash cast double 3D printer and cooperated with Harbin University of Technology to introduce 3D printing technology to the field on research development of mechanical equipment and large-scale construction projects. The construction and development of advanced base will become competitive threats to the construction of 3D printing industry base in Anshan City ii. Bottlenecks of technology development First of all, in terms of cost, though the cost of 3D printers is constantly decreasing, it is still relatively expensive, which has a direct influence on 3D printing's widespread use; secondly, in terms of printing material, selected materials of 3D printing are mainly about chemical polymers with weak physical properties which have unsteady hidden danger; thirdly, in terms of accuracy, speed and efficiency, the accuracy and speed of the 3D printing with consumption type are comparatively low and the efficiency of printing is not suitable for the demand for massive production; finally, in terms of intellectual property protection, it is easier to copy products resulted from 3D printing, increase risks of piracy and to some degree prevent the rapid growth of 3D printing industry.

Conclusions of Development Environment
Anshan City has developed 3D printing industry with 3D printing industry's expansion and rapid growth at home and abroad. Market requirements growing rapidly, Governments at all levels of nation, provinces and cities have gradually put forward a series of incentive measures to stimulate the development of 3D printing industry. Most importantly, Anshan has already possessed its own industrial base for developing 3D printing and it has clear development opportunities with better bases of scientific research strength and talents storage. Thus, Anshan City has greater development advantages and development opportunities. Meanwhile, Anshan has faced 5 major development disadvantages and threats existing in low industrial concentration, lack of leading teams and projects, limited regional economic scales, increasing competitors, technological bottlenecks and so on when developing 3D printing industry base. Taken together, advantages and opportunities of developing 3D printing industry base are more outstanding with better development environment in Anshan. Weaknesses and threats faced can also be overcome by taking a series of measures.

Deepen Reforms and Strengthen Advantages i. Strengthen organization and coordination
Through relevant government departments taking the lead, set up regional development-leading teams of 3D printing industry to establish working mechanisms, clear division of responsibility, and strengthen cooperation with provinces and municipalities. Establish the cooperation mechanism of local superior functional departments and strive for superior authority. Strengthen supervision and inspection to ensure the realization of planning objectives.
ii. Deepen the mechanism of talents cultivation Talents are the core resources of developing 3D industry. Introduce high-level personnel and teams at home and abroad, carry out related policies, and encourage overseas professionals to return home and start a business to promote the aggregation of resources. In addition, encourage related universities and research institutes to accelerate the process on professional training of 3D printing. List 3D printing into related subjects in universities and take cooperative teaching methods by school-enterprises to promote the cultivation on advanced talents of 3D printing. Also, push industrial association to have related training and carry out publicity and promotion of 3D printing technology in public agencies such as science& technology museums, activity centers, which will accumulate experiences for developing 3D printing industry.
iii. Increase more policy support Insert 3D printing industry into development priority among local emerging industries and further implement preferential policies and supportive measures in finance, land, tax and government procurement etc. Government should give priority aid to construction of major projects on 3D printing industry, extension of demonstration and application, industrialization on research and development of key technology, standards setting as well as the cultivation and introduction of talents. Set up local development funds of 3D printing technology and increase support on introduction and cultivation of related innovative enterprises and major projects. List 3D printing equipment into the catalogue of government procurement and increase support on research and development for 3D printing technology; encourage financial institutions to innovate financial products and take diversified investment and financing ways such as, credit, guarantees, venture capital and corporate bills to speed up the development of 3D printing technology and application industry.

Take Positive Action and Transform Weaknesses
i. Optimize industrial structures and improve the degree of industrial concentration The material, software, equipment and application services of 3D printing are key links of building 3D printing industry and each link is independent mutually and relate to each other. None of these can be excluded in building perfect industry chains of 3D printing. It is badly difficult for Anshan to achieve that every link has its own corresponding enterprises. However, the incomplete industry chain can also limit self-development. Therefore, we must consider that local industries focus on the introduction of vacant industry as well as measure its own ability when selecting incoming materials. Through combination of business and technology, perfect the structure of regional industry chains step by step. For example, through the introduction of relevant research institutions and research teams, Anshan can set up R&D sub-centers and offices, filling gaps of local industry.
ii. Enhance powers of existing corporations and create leading enterprises Actively work out cultivation projects of 3D printing enterprises and select better bases of 3D printing enterprises. Government should provide policy support to project implementation, construction of platform and talents introduction etc. Meanwhile, give support to technology-based SMEs with higher technology and better market prospects to promote the development into high-tech enterprises. Encourage enterprises to carry out standards setting and patent applications of 3D printing technology. Also, build industrial parks of 3D printing with key enterprises-oriented and bringing incubation, application, industrial undertaking and development function together. Form the superiority of industrial agglomeration and enhance the industrial influence of local industry.
iii. Improve qualities of investment enterprises and play a leading role The supporting enterprises of investment industry not only enhance the local industrial popularity but also can have the development effect of industrial agglomeration. It is widely suggested that Anshan City introduce large-scale industrial equipment manufacturing enterprises of 3 D printing, desktop civil equipment manufacturing enterprises and service enterprises of 3 D printing, etc. Strive to introduce the American, German, and other famous 3 D printing companies to set up offices in An Shan and focus on leading enterprises of 3D printing industry from Beijing, Shanxi, Hubei and other developed areas to establish branch offices in Anshan and enhance the overall industrial strength. Focus on the existing land and housing resources, especially working harder on a certain volume of domestic and foreign 3D printing projects. Take much more measures just like up-down multi-linkage, cooperation among customers and so on to obtain information and promote industrial development process.
iv. Strengthen the introduction of expert talents and teams to occupy industrial commanding heights Introduce domestic and foreign industrial experts and teams in 3D printing field through the introduction of a series of talents and increasing great support in research fund, personnel connection, tax relief, home treatment, etc. With their leadership, it will come true that Anshan City's 3D printing industry base has leapfrog development and occupies industrial commanding heights.

Gather Strength and Deal with Threats
i. Analyze opponents and make precise application strategies Compared to other regional situation on industrial development and combined with the existing location base in Anshan, it is necessary to appropriately locate development goals and reduce blind investment and risk. The development and application of industry can promote the popularity of technologies. Also, the combination of technology and industry can effectively improve industrial competitiveness. For example, the technology combined with existing industry can be classified properly into categories such as materials, design, control, information, etc. Further, financial and policy support can be given to key enterprises to encourage the technological innovation.
ii. Integrate resources and break through bottlenecks Due to the problem of "small and scattered", the comprehensive competitiveness and the capability to withstand risks are not strong enough. Therefore, at present, development-united is an effective way to solve this problem. In the process of developing the 3D printing industry, Anshan City can found regional Industrial Technology Association and integrate distributed resources to effectively promote the exchange and sharing of information resources, accelerating integration between industries. Also, it is achievable to build common technological research and development platforms relying on backbone enterprises, colleges and universities or professional R & D institutions. Concentrate on powerful research workforce to tackle technical breakthroughs and overcome technical bottlenecks of the regional industrial development.

Grasp the Opportunity and Accelerate the
Development i. Dock policies and plan development Actively dock national, provincial, city's development plans of 3D printing. Work out development plans reasonably and scientifically. Fully consider the eruptive growth situation on the industry in the future and high-tech barriers to arrange space layouts, development paths, enterprise fostering and project constructions. Perfect industrial structures of full chain and put the stress on the key talents and core technology. Increase the input of public platform construction. Keep on sensitivity of technology and urgency of fierce competitions to promote industrial agglomeration and speed up the pace.
ii. Speed up development and take the preemptive opportunities At present, many countries in the world are promoting the development of 3D printing industry, but development gap is not very great by technical bottlenecks and limits of application market. Therefore, in order to grasp the future rare opportunity, it is necessary to strengthen macro guidance, promote industrial layouts, exchange and cooperate actively with domestic and overseas developed regions. Accelerate the upgrading of Anshan City's technological and industrial advantages and seize the initiative among fierce competitions in the future.

Conclusion
In this paper, the SWOT analysis model on development environment of the 3D printing industry base has been designed, which can be as feasible analysis tools in other parts of China to build 3D printing industry base. However, the chosen analysis factors of the model are not comprehensive enough and need to be further improved. Although development strategies designed for 3D printing industry base in Anshan is not suitable to apply to all areas, the problems faced in the construction of 3D printing industry base are common. Therefore, the model is of great benefit for other associated builders and government management departments to have greatly useful reference.


extfieldsofstudy: Medicine Mathematics Physics

text:
Many-electron integrals over gaussian basis functions. I. Recurrence relations for three-electron integrals

Explicitly-correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations, and can often achieve chemical accuracy with relatively small gaussian basis sets. In most calculations, the many three- and four-electron integrals that formally appear in the theory are avoided through judicious use of resolutions of the identity (RI). However, in order not to jeopardize the intrinsic accuracy of the F12 wave function, the associated RI auxiliary basis set must be large. Here, inspired by the Head-Gordon-Pople (HGP) and PRISM algorithms for two-electron integrals, we present an algorithm to compute directly three-electron integrals over gaussian basis functions and a very general class of three-electron operators, without invoking RI approximations. A general methodology to derive vertical, transfer and horizontal recurrence relations is also presented.

Introduction
Many years ago, Kutzelnigg 1 showed that introducing the interelectronic distance r 12 = |r 1 − r 2 | into a simple wave function Ψ 0 for the helium atom, to yield where χ(r 1 , r 2 ) is expanded in a determinantal basis, dramatically improves the convergence of second-order perturbation theory, 2 coupled cluster 3 and other variational calculations. 4 This approach, which gave birth to the so-called "R12 methods", 2,5,6 is a natural extension of pioneering work by Hylleraas in the 1920s. 7,8 Kutzelnigg's idea was later generalized to more accurate correlation factors f 12 ≡ f (r 12 ). [9][10][11][12][13][14] Nowadays, a popular choice for f 12 is a Slater-type geminal 15 (STG) which is sometimes expanded as a linear combination of gaussian-type geminals 9,10 (GTG) for computational convenience. 11,13,14 The resulting "F12 methods" achieve chemical accuracy for small organic molecules with relatively small gaussian basis sets [16][17][18][19][20] and are quickly becoming the first-choice non-stochastic method for high accuracy. 19,20 They are now appearing within state-of-the-art composite procedures. 21 However, whereas a conventional (non-explicitly correlated) calculation using N gaussian oneelectron basis functions leads to an energy expression with O(N 4 ) relatively easy two-electron integrals, [22][23][24][25][26][27][28][29][30][31][32] the explicitly correlated wave function has an energy expression with O(N 6 ) threeelectron integrals and O(N 8 ) four-electron integrals. These many-electron integrals are known in closed form in a few special cases 33 but, in general, they are computationally expensive and the task of computing O(N 6 ) or O(N 8 ) of them appears overwhelming.
To render F12 methods computationally tractable and to avoid these three-and four-electron integrals without introducing unacceptable errors, Kutzelnigg and Klopper 2 proposed to insert the into the three-or four-electron operators. 17,34 In this way, three-and four-electron integrals are expanded in terms of one-and two-electron integrals that can be found efficiently using conventional quantum chemistry software.
Of course, the approximation (??) introduces chemically acceptable errors only if the auxiliary basis set {χ µ } is sufficiently large (N RI ≫ N). 1 This realization has fueled much research and there now exist very efficient RI formulations based on highly optimized auxiliary basis sets (ABS) 38 and complementary ABS (CABS). 39 However, to achieve millihartree accuracy, such bases must be approximately complete up to 3L occ , 17 where L occ is the highest angular momentum of basis functions in the orbital basis set associated with the occupied molecular orbitals. Even if this requirement can be reduced to 2L occ by density fitting, 40 it remains demanding in cases (e.g. for transition metals) where high angular momenta are needed in the orbital basis.
For two reasons, however, we believe that the RI tactic can be avoided. First, the number of significant (i.e. greater than a threshold) three-and four-electron integrals is very much smaller than O(N 6 ) and O(N 8 ), respectively. Second, the task of computing many-electron integrals over gaussian basis functions is less formidable than many believe. For example, for three-electron integrals, a reduction of the computational effort from O(N 6 ) to O(N 4 ) is already achievable by exploiting robust density fitting techniques. 41 Although there are O(N 4 ) two-electron integrals, it is well known to quantum chemistry programmers that the number of significant two-electron integrals in a large system is only if the two-electron operator is long-range [42][43][44] and O(N) if it is short-range. 45,46 Similar considerations apply to many-electron integrals and one can show that the number of significant threeand four-electron integrals is only O(N 3 ) and O(N 4 ), respectively, even for long-range operators.
(For short-range operators, there are even fewer.) Thus, if we can find good algorithms for identifying and computing the tiny fraction of many-electron integrals that are significant, large-scale calculations using F12 methods will become feasible, without the need for the RI approximation.
The present manuscript is the first of a series on many-electron integrals. Here, we present an algorithm to compute integrals over three-electron operators using recurrence relations (RRs). The second paper 47 in the series will discuss the construction of upper bounds and effective screening strategies and the third 48 will describe optimized numerical methods for the efficient generation of

Three-electron integrals
A primitive gaussian-type orbital (PGTO) is defined by its exponent α, its center A = (A x , A y , A z ), its angular momentum vector a = (a x , a y , a z ) and its total angular momentum a = a x + a y + a z .
A contracted gaussian-type orbital (CGTO) ψ A a (r) is a linear combination of K A PGTOs.
We are interested in the three-electron operator and we write the integral of six CGTOs over this as We will use square brackets if the integral is over PGTOs: and the fundamental integral (i.e. one in which all six PGTOs are s-type) is therefore where the exponents ζ i , centers Z i and prefactors S i of the gaussian product rule for the three electrons are For conciseness, we will adopt a notation in which missing indices represent s-type gaussians. For example, [a 2 a 3 ] is a shorthand for [0a 2 a 3 |000]. We will also use unbold indices, e.g. a 1 a 2 a 3 |b 1 b 2 b 3 to indicate a complete class of integrals from a shell-sextet.

Three-electron operators
We are particularly interested in two types of three-electron operators: "chain" operators of the form f 12 g 13 , and "cyclic" operators of the form f 12 g 13 h 23 . In both types, the most interesting cases arise when 2,16-18 and various combinations of these produce three-electron integrals of practical importance. We note that, by virtue of the identity r 12 ≡ r −1 12 (r 2 1 +r 2 2 −2r 1 ·r 2 ), integrals involving the anti-Coulomb operator can be reduced to linear combinations of integrals over the Coulomb operator.

Permutational symmetry
For real basis functions, it is known 55 that two-electron integrals have 8-fold permutational symmetry, meaning that the integrals are all equal. Three-electron integrals also exhibit permutational symmetry and, for computational efficiency, it is important that this be fully exploited. The degeneracy depends on the nature of the three-electron operator and the five possible cases are listed in Table 1. Three-electron chain f 12 g 13 8 f 12 f 13 16 Three-electron cyclic f 12 g 13 h 23 8 f 12 f 13 h 23 16

Algorithm
In this Section, we present a recursive algorithm for generating a class of three-electron integrals of arbitrary angular momentum from an initial set of fundamental integrals. The algorithm applies to any three-electron operator of the form f 12 g 13 h 23 and generalizes the HGP-PRISM algorithm following a OTTTCCCTTT pathway. 28,31 The algorithm is shown schematically in Fig. 1.
After selecting a significant shell-sextet, we create a set of generalized fundamental integrals [0] m (Step O). Next, we build angular momentum on center A 3 (Step T 1 ) and on center A 2 (Step T 2 ) using vertical RRs (VRRs). This choice is motivated by the fact that, for chain operators, the VRR for building momentum on A 1 is more expensive than that for building on A 2 and A 3 (see Appendix). Then, using transfer RRs (TRRs), we transfer momentum onto A 1 (Step T 3 ). The primitive [a 1 a 2 a 3 ] integrals are then contracted (Step C) and horizontal RRs (HRRs) are used to shift angular momentum from the bra centers A 3 , A 2 and A 1 onto the ket centers B 3 , B 2 and B 1 (Steps T 4 , T 5 and T 6 ). The number of terms in each of these RRs is summarized in Table 2 for cyclic and chain operators. We now describe each step in detail.

Construct shell-pairs, -quartets and -sextets
Beginning with a list of shells, a list of significant shell-pairs 32 is constructed. By pairing these shell-pairs, a list of significant shell-quartets is created and then, by pairing the significant pairs and quartets, a list of significant shell-sextets is created. This process is critical for the efficiency of the overall algorithm and depends on the use of tight upper bounds for the target integrals. Figure 1: PRISM representation 31 of a scheme for computing a three-electron integral class. In this work, we consider the (orange) OTTTCCCTTT path. Such bounds are straightforward for two-electron integrals [42][43][44][45][46] but are much more complicated for three-electron integrals and, for example, the popular Cauchy-Schwartz bound does not generalize easily. However, it is possible to construct a bound for each type of three-electron operator, depending on the short-or long-range character of f 12 , g 13 and (if it is present) h 23 . We will discuss these in detail in Part II of this series. 47

Step O. Form fundamental integrals
Having chosen a significant shell-sextet, we replace the three two-electron operators in its fundamental integral (??) by their Laplace representations  Table 3, one can also easily deduce the Laplace kernels for related functions, such as f (r 12 ) 2 , f (r 12 )/r 12 and ∇ 2 f (r 12 ). Integrating over r 1 , r 2 and r 3 then yields where w 0 (s) = π 3 ζ 1 ζ 2 ζ 3 D(s) and s = (s 1 , s 2 , s 3 ). The numerator and denominator are N(s) = κ 12 s 1 + κ 13 s 2 + κ 23 s 3 + κ 12 where is the squared length of the vector between the ith and jth gaussian product centers.
For reasons that will become clear later, it is convenient to introduce the generalized fundamental integral where To form an [a 1 a 2 a 3 |b 1 b 2 b 3 ] class with a chain operator, the ranges of m 1 , m 2 and m 4 are as in (21) is a GTG, the [0] m can be found in closed-form. 57,58 Otherwise, they can be reduced to one-or two-dimensional integrals, which can then be evaluated by various numerical techniques. This step can consume a significant fraction of the total computation time 30 and a comprehensive treatment of suitable numerical methods merits a detailed discussion which we will present in Part III of this series. 48

Step T 1 . Build momentum on center A 3
Given a set of [0] m , integrals of higher angular momentum can be obtained recursively, following Obara and Saika. 26,27 Whereas VRRs for two-electron integrals have been widely studied, VRRs for three-electron integrals have not, except for GTGs. 10,[49][50][51][52][53][54] The T 1 step generates [a 3 ] m from [0] m via the 8-term VRR (see the Appendix for a detailed derivation) where the superscript + or − denotes an increment or decrement of one unit of cartesian angular momentum. (Thus, a ± is analogous to a ± 1 1 1 i in the notation of Obara and Saika.) The value in the curly superscript indicates which component of the auxiliary index vector m is incremented.
For a chain operator, the {3} terms disappear, yielding the 6-term RR It is satisfying to note that, by setting ζ 2 = 0 in (??), we recover the Obara-Saika two-electron RR.

Step T 2 . Build momentum on center A 2
The T 2 step forms [a 2 a 3 ] from [a 3 ] m via the 10-term RR For a chain operator, the {3} terms disappear, yielding the 7-term VRR

Step T 3 . Transfer momentum to center A 1
The T 3 step generates [a 1 a 2 a 3 ] from [a 2 a 3 ]. There are two possible ways to do this. The first, which we call Step T ′ 3 , is to build angular momentum directly on A 1 using the 12-term VRR (Eq. (??)).
However, this is computationally expensive and we choose to avoid it. A second option exploits the translational invariance to derive the 6-term TRR which transfers momentum between centers that host different electrons.

Step C. Contraction
At this stage, following the HGP algorithm, 28 we contract the [a 1 a 2 a 3 |000] to form the a 1 a 2 a 3 |000 .
We can perform the contraction at this point because all of the subsequent RRs are independent of the contraction coefficients and exponents. More details about this contraction step can be found in Ref. 32.

Steps T 4 to T 6 . Shift momentum to ket centers
We shift momentum to B 3 , B 2 and B 1 from A 3 , A 2 and A 1 , respectively, using the 2-term HRRs

Concluding remarks
In this Article, we have presented a general algorithm to construct three-electron integrals over gaussian basis functions of arbitrary angular momentum from fundamental (momentumless) integrals. The algorithm is based on vertical, transfer and horizontal RRs in the spirit of the Head-Gordon-Pople algorithm. In Part II of this series, we will report detailed investigations of upper bounds on these integrals. In Part III, we will discuss efficient methods for computing the fundamental integrals. Our approach can be extended to four-electron integrals, and we will also report results on this soon.

A Derivation of VRRs
In this Appendix, we follow the Ahlrichs approach 59 to derive a VRR for the construction of [a 1 ] m integrals.
Defining the scaled gradient operatorD we can write the Boys relation 22 which connects an integral of higher momentum to an integral derivative with respect to a coordinate of A 1 .
In operator form, this can be written as Substituting the chain rule expression into (??), using the identities the commutator propertyM (where p is linear in A 1 and ρ is its derivative) and the identitieŝ one eventually obtains the 8-term RR for building on A 1 Equation (??), which builds on A 3 , can be derived similarly. However, for chain operators, the RR that builds on A 1 does not shed terms and it is therefore cheaper to build on A 3 than on A 1 .


Role of human factors in pediatric cardiac surgery

According to the Institute of Healthcare Improvement, “human factors” refers to the discipline of engineering that details the interface of people, equipment and the environment in which they work. Issues that impact human performance and increase the risk of error include factors that directly enable decision making, such as perception, attention, memory, reasoning, judgement and factors that directly enable decision execution, such as communication and the ability to carry out the intended action.

INTRODUCTION
According to the Institute of Healthcare Improvement, ''human factors'' refers to the discipline of engineering that details the interface of people, equipment and the environment in which they work. Issues that impact human performance and increase the risk of error include factors that directly enable decision making, such as perception, attention, memory, reasoning, judgement and factors that directly enable decision execution, such as communication and the ability to carry out the intended action.
Between 2008 and 2010 around 80,000 patients had surgery for congenital heart disease in North America 1 . About 25% of these patients were neonates. The overall mortality of surgical treatment of congenital heart disease is 4%. Neonates account for 50% of the total deaths following surgical treatment, emphasising the high risk nature of this group. Neonates are especially vulnerable for a variety of reasons. During intrauterine life, fetal circulation tolerates the most severe forms of congenital heart disease. Intra and extra cardiac shunts allow fetal circulatory adaptation to abnormal heart anatomy. At birth, metabolic rate and fetal oxygen consumption increases several fold. Coexisting congenital heart disease imposes additional metabolic demands on the new born baby. Duct dependent systemic or pulmonary circulations impose hemodynamic challenges. The organ systems of the new born baby are relatively less mature. Premature birth and low birth weight can impose considerable risk. So a neonate with congenital disease who needs surgical management usually has a complex cardiac defect, is transitioning from the protective environment of the fetal circulation to a highly stressful postnatal circulation, has immature organ systems, and is facing the likely spectre of cardiopulmonary bypass with its accompanying pan-systemic effects. Congenital heart surgery in the neonatal period is a high-risk undertaking with poor error tolerance and a limited ability to retrieve 2 .
Of all the deaths in congenital heart surgery 20% are from preventable causes, implying that human factors have a significant role to play in their causation 2 . These events may or may not be preventable, but the frequency of events and the relatively focused patient population makes congenital heart surgery a model for investigating complex systems and for studying human errors and their impact on patient safety across healthcare settings 3 .

DYNAMICS OF POOR OUTCOMES
Preventable adverse events may occur through technical and non-technical factors associated with decision-making 4 . Technical skills are fundamental to good outcomes but non-technical skills also markedly influence the performance of individuals and teams, therefore influence the outcomes of treatment 5 . The study of human factors principally involves understanding complex systems and the relationship between people, tasks and their ever-changing environment 6 . James Reason proposed the organisational accident model to explain the dynamics of poor outcomes in complex high technology systems like the aviation industry, nuclear power industry, and healthcare industry. According to this model, a complex system like modern healthcare has a sharp end and a blunt end. The sharp end of the system is the people at the service delivery end of the system (doctors, nurses, pilots, engineers). Failures at sharp end of the system have an immediate impact on safety and are called active failures. At the blunt end of the system are higher management in the organisation e.g., administrators, regulators, governments. Failures at the blunt end of the spectrum are called latent failures. Wrong decisions made by people at the blunt end lead to weaknesses in the defences of the organisation. In this vulnerable state when active failures happen in an organisation they combine with latent failures to overcome the defences of the system and result in an organisational accident 7 . In a pediatric cardiac surgery setup examples of active failures include poor communication between surgeons, cardiologists, anesthetists and intensivists, taking patients with incorrect diagnosis to the operating room, poor scheduling of cases, technical errors during operating. Examples of latent failures include poor organisation of staff roles, absence of policies and protocols for treatment, shortage of cardiac trained nurses, lack of investment in high technology equipment and failure to invest in staff training.

HUMAN FACTORS STUDIES IN PEDIATRIC CARDIAC SURGERY
Marc de Leval pioneered the study of human factors in pediatric cardiac surgery. In an important article published in the Lancet in 1987 he wrote ''By and large medical world has had great difficulties in dealing with error. The traditional teaching is that medical doctors are expected to function without error. This need to perform faultlessly has created a strong pressure to intellectual dishonesty, to cover up mistakes rather than admit them, and to overlook opportunities for improvement. The reality of the malpractice threat provides strong incentives against disclosure of mistakes'' 8 . As a result vital information about mistakes and opportunities to redress them are lost.
In the first ever study conducted to evaluate the role of human factors in pediatric cardiac surgery, de Leval teamed up with James Reason, the father of accident organisational theory. Using trained human factors researchers to make real-time observations during 243 arterial switch operations performed by 21 surgeons at 16 UK hospitals over an 18-month period, major and minor human failures were recorded during the course of these operations. Major failures were classified as events that were likely to have life threatening effects if left uncompensated. Minor failures were events that in isolation were not likely to have serious consequences for the patient. They concluded that minor and major events commonly occurred in pediatric cardiac surgery. The number of major events per case were strong predictors of death but proper compensation greatly reduced the risk of death. However a single uncompensated major event can lead to death.
Minor events are different because they are usually not noticed by the team members. No conscious attempt is made to compensate them. However they have a multiplicative effect, so that though in isolation they may have little impact but their multiplication has a strong relationship to negative outcomes 9 . In a subsequent analysis published by the same group they concluded that uncompensated minor events can impede a teams ability to compensate for future major events. Latent elements within the organisation predispose teams to have major events.
Paul Barach and his team studied the impact of human factors on intraoperative adverse events and compensation mechanisms in 102 patients undergoing pediatric cardiac surgery. They classified the adverse events into major and minor events. Events were further classified into compensated or uncompensated depending on whether appropriate action was taken to offset the effect of adverse event. They concluded that adverse events routinely occurred during pediatric cardiac surgery and were mostly compensated. Compensation was mostly reactionary and not preventative with possibility of prevention by improved processes.
Ninety percent of major adverse events and 90% of minor adverse events were compensated. An average of 1.2 major adverse events occurred per case, which were mostly cardiovascular events, and compensation was mostly cognitive. An average of 15.3 minor adverse events occurred per case which were mostly communication and coordination failures. The time period most vulnerable to adverse events was the period between aortic cross clamping and cross clamp release and subsequent weaning from cardiopulmonary bypass. About 45% of all adverse events occurred during this period. Case complexity and duration of surgery were predictors of major adverse events.The number of major adverse events per patient correlated with clinical outcomes 10 .

TECHNICAL PERFORMANCE AS A HUMAN FACTOR
While patient outcomes are dependent on multiple factors, technical performance by a surgeon during an operation is one of the most important variables in determining outcomes in patients with congenital heart disease. Boston Children's Hospital pioneered the development of a Technical Performance Score (TPS) to measure quality of repair after an operation. The initial study included four operations; repair of ventricular septal defect, tetralogy of Fallot, atrioventricular septal defect, and the arterial switch procedure 11 . It was later extended to assess the repair in Norwood procedure 12 .
Each of these operations was subdivided into its component sub-procedures based on the anatomic region of repair and a scoring system was developed defining three categorical variables for each sub-procedure; optimal, adequate and inadequate, based on a consensus between cardiac surgeons and cardiologists on echocardiographic assessment of each sub-procedure.
Echocardiography was used as the assessment tool because it is simple, reliable, available at the bedside and over the years has become the standard tool for assessing patients with congenital heart disease preoperatively, intraoperatively and post operatively. Optimal repair is achieved when all sub-procedures and conduction were graded as optimal and it is graded as inadequate if any component sub procedure or conduction was graded inadequate. Adequate repair figured somewhere in between the two with intact conduction as its integral component.
TPS is downgraded to match the lowest component score of the procedure. In scoring a VSD repair for example an optimal repair would include absence of a residual shunt or a shunt less than 1 mm with intact conduction, an adequate repair would include a shunt less than 3 mm with intact conduction and an in-adequate repair would include a shunt greater than 3 mm and/or a need for pacemaker or need for reintervention 13 .
Patients with inadequate TPS had significantly longer PICU and hospital stays, longer ventilation times and a higher occurrence of major postoperative complications 14 . TPS is a powerful predictor of postoperative outcome in Norwood procedure. Patients who had optimal technical scores had 1.2% hospital mortality compared to the ones with inadequate TPS whose mortality was 34.8% 11 .
In another prospective study, TPS was a strong predictor of postoperative morbidity in 166 neonates and infants who underwent a wide variety of operations for congenital heart disease with high complexity. Optimal TPS was associated with lower postoperative morbidity. Adequate TPS was associated with higher morbidity in babies with higher case complexity and lower morbidity in babies with lower case complexity. Inadequate TPS was associated with higher morbidity irrespective of case complexity 15 .
Technical performance score is emerging as an important tool to assess the quality of repair. As more and more studies emerge to show TPS as a predictor of patient outcomes in congenital heart surgery it has the potential of becoming a requirement as a quality control measurement 13 .

COMMUNICATION AS A HUMAN FACTOR
According to the Joint Commission International, 65% of sentinel events in 2009 occurred due to communication failure between various teams looking after a patient. Quite often errors result from breakdown of communication and coordination between teams 16 . Handover of a pediatric cardiac surgery patient from operation theatre to the intensive care environment is a particularly vulnerable time. This handover serves as a basis for transferring responsibility of patient care from the surgical team to the intensive care team. This vulnerability is compounded by the fact that handovers are not taught to physicians and nurses in a systematic way. Workforce constraints and limits on duty hours of physicians lead to increased handovers. Paradoxically errors in communication are more frequent in information technology-intense environments 17 .
Making handovers safe involves standardizing handovers, identifying and emphasizing key content to be handed over, monitoring handovers continuously to ensure protocol is being followed and identifying and resolving barriers to improvement of handovers 18 . Important aspects of a handover process that are essential to successful transition of patient care include limiting discussions to those related to the patient, a face-to-face sharing of patient information and discussion of plan between all care providers involved, efficient transition of equipment and limiting interruptions during the information handoff 19 .
A prospective interventional study in 79 pediatric cardiac surgery patients was undertaken to determine if implementation of standardised handover protocol from operating theatre to pediatric intensive care unit could reduce the number of errors occurring during transition of care 19 .
A single observer was responsible for data collection during all pre-intervention and post-intervention handovers using a standardized checklist. Technical errors were defined as protocol deviations involving personnel, equipment or handover process e.g. nonfunctional critical equipment at the time of patients arrival to the ICU, interruption of verbal handoff by receiving caregivers and disruption of the sterile team environment.
Information omissions were defined as failure to present protocol elements that were normally expected to be presented verbally during the handover to the receiving team e.g. procedure performed, cardiopulmonary bypass time, current inotrope infusions etc.
Technical errors reduced from 6.24 to 1.52 and critical information omissions reduced from 6.33 to 2.38 per handover after intervention (Figures 1 & 2). There was no change in duration of handover process. The study concluded that structured handover protocol for pediatric cardiac surgery patients transitioning from operating room to the intensive care unit reduces medical errors and improves team work among care givers.
Another study used Formula 1 pit stop and aviation models to improve safety and quality of health care. This was a prospective intervention study which measured the change in performance before and after implementation of a handover protocol which was developed after exhaustive discussions between the clinicians, a Formula 1 racing team, and aviation experts. They found that implementation of the new handover protocol reduced the number of technical errors, minimised information omissions, and the duration of handovers was also reduced 20 .

OTHER NON-TECHNICAL HUMAN FACTORS
Management and leadership play a crucial role in creating a culture of safety. They do this by creating conditions, resources and environment in which clinicians strive to create safe outcomes. Leaders create the climate that enables clinicians to acknowledge mistakes and encourage worker-clinicians to innovate 3 .
Databases provide a platform that enables comparison of outcomes between pediatric cardiac centers which significantly contributes to quality improvement. There are four pre-requisites that ensure that multi-institutional databases provide meaningful outcomes analysis in pediatric cardiac surgery: a common nomenclature, a uniform core data set, mechanisms of auditing and validating data for accuracy and adoption of uniform risk adjustment models to evaluate case complexity 21 . The Society for Thoracic Surgeons (STS) database is one such important database in pediatric cardiac surgery Figure 1. Frequency of technical errors observed before and after interventions, with 95% confidence intervals. ETCO2, end-tidal CO2; IVF, intravenous fluid. Reproduced with permission from [19]. Figure 2. Frequency of information observed before and after intervention, with 95% confidence intervals. Reproduced with permission from [19]. that allows comparison of outcomes between centres within North America, but is unfortunately not open to centres outside the continent.

HUMAN FACTORS IN QATAR
Achieving excellence in healthcare in general, and in pediatric cardiac surgery in particular, requires concerted efforts by leaders and clinicians to achieve ''high reliability'' i.e. delivering consistent performance at high levels of safety over long periods of time. The demographics of Qatar are different from North America and Europe and the role of human factors in health care safety therefore presents unique challenges for the following reasons: 1. A vast majority of health care personnel including physicians, nurses, technicians and healthcare administrators belong to diverse nationalities and backgrounds. Their training therefore vastly differs. Their skill and experience is molded by the society and environment they grew up in. Many healthcare personnel are unlikely to have received formal instruction in perception, assessment and mitigation of risk and error. Their perception of risk and error in context of the patient care is therefore likely to differ as well. 2. Verbal communication between healthcare providers poses a particularly important challenge in providing safe healthcare to patients. In Qatar, English is the unifying language for healthcare workers who speak more than seventy different mother tongues. English language is therefore spoken with many different accents and colloquialisms. This creates a risk wherein vital information can get miscomprehended or lost in translation at routine handovers or in acute situations such as coordinating management of patients in life threatening situations. Reluctance to ask a colleague to repeat him-or herself for fear of offending them can leave large gaps in information. This problem becomes even more difficult when information is exchanged on the telephone.
Dealing with these unique challenges is vital to the development of safe healthcare in Qatar. There is a strong need to develop a culture of safety within this diverse group of healthcare providers fostered by a supportive leadership. One of the most important challenges is how to develop a culture that supports the changes that are required to enable learning.
In that regard, establishment of Hamad Healthcare Quality Institute by the Hamad Medical Corporation is a big step in the right direction. Establishment of Hamad Healthcare Quality Institute will enable our organisation to understand our current healthcare safety culture and review how teams can work together to improve the quality of health care we provide . It will design and develop evidence based practical solutions for patients and promote access to high quality safe healthcare services across Qatar 22 .

CONCLUSION
Pediatric cardiac surgery has become a model for the delivery of complex multidisciplinary care. For optimal outcomes pediatric cardiac surgery relies on an organisational structure that allows early identification of deficiencies through extreme vigilance and eliminates deficiencies through use of process improvement. In other words the specialty of pediatric cardiac surgery in its ideal form exists within a ''culture of safety''. To quote Marc de Leval ''safety is not a commodity, but a value that requires continuous reinforcement and investment'' 23 .