 Research article
 Open Access
 Published:
Evolution of DFT studies in view of a scientometric perspective
Journal of Cheminformaticsvolume 8, Article number: 52 (2016)
Abstract
Background
This bibliometric study aims to analyze the publications in which density functional theory (DFT) plays a major role. The bibliometric analysis is performed on the full publication volume of 114,138 publications as well as subsets defined in terms of six different types of compounds and nine different research topics. Also, a compound analysis is presented that shows how many compounds with specific elements are known to be calculated with DFT. This analysis is done for each element from hydrogen to nobelium.
Results
We find that hydrogen, carbon, nitrogen, and oxygen occur most often in compounds calculated with DFT in terms of absolute numbers, but a relative perspective shows that DFT calculations were performed rather often in comparison with experiments for rare gas elements, many actinides, some transition metals, and polonium.
Conclusions
The annual publication volume of DFT literature continues to grow steadily. The number of publications doubles approximately every 5–6 years while a doubling of publication volume every 11 years is observed for the CAplus database (14 years if patents are excluded). Calculations of the structure and energy of compounds dominate the DFT literature.
Background
Many methods have been developed to solve the Schrödinger [1, 2] and Dirac [3–5] equations approximately. Density functional theory (DFT) has emerged as the most popular one in the past decades. The very first density functional approximation (DFA) was proposed by Thomas [6] and Fermi [7] without mentioning the term. Slater’s [8] simplification of the Hartree–Fock [9, 10] method, the theorems by Hohenberg and Kohn [11], and the orbitalbased Kohn–Sham [12] equations mark the beginning of practical DFT calculations. Kohn–Shambased DFT calculates the energy of a noninteracting reference system and approximates the difference to the real system using the exchange and correlation functionals. The first exchange and correlation functionals depend only on the electron density itself [13]. More accurate calculations became possible with the development of exchange and correlation functionals that also included the gradient (GGA functionals) [14–17] and second derivatives (metaGGA functionals) [18–20] of the electron density. These provide increased accuracy at negligible additional computational expense. The development of hybrid functionals [21–26] marked the point where the accuracy and popularity of DFT increased dramatically. At first, some amount of Hartree–Fock exchange was admixed with the exchange functional. Higher accuracy for atoms and molecules as well as applicability of hybrid functionals to solids and surfaces was achieved by rangeseparation [27–34]. The development of local hybrids [35–41] increased the accuracy of DFT calculations further. The concepts of local hybrids and rangeseparation were then combined [42–44] yielding even more accurate results. As hybrid functionals became popular, correlation from wave function methods (MP2 [45, 46], RPA [47–50], coupledcluster [51–53]) was also admixed with the correlation functional [54, 55].
Individual researchers in the field of DFT do have a qualitative overview about publications related to DFT and compounds computed with DFT, but a quantitative overview can only be obtained using bibliometric methods. Although there is considerable interest in the evolution of the annual publication volume in the field of DFT [56, 57], no detailed bibliometric study was published about DFT publications so far. We intend to fill the gap with this study.
Bibliometrics or the broader term, scientometrics—both terms are often used synonymously—can be characterized as the discipline that treats science quantitatively [58, 59]. Publication and citation numbers are the most important items that have become the basis of bibliometric indicators for research evaluation purposes. In many disciplines, particularly in chemistry, physics, and materials science, chemical compounds (substances) play a major role. In a previous paper [60], we have extended the bibliometric method and defined compoundbased (chemical) bibliometrics as a new research field. The method can be applied to analyze large numbers of publications and compounds in combination with the corresponding chemical concepts: We can establish the time evolution of the publications dealing with concepts or methods and reveal the related compounds or compound classes. Furthermore, the mapping of method related compounds by establishing elementbased landscapes has some potential to illustrate the compound basis of research topics.
Reference Publication Year Spectroscopy (RPYS) is a bibliometric method which can be used to locate seminal papers which are cited most frequently in a certain publication set [61]. The method is based on the analysis of cited references (i.e. the number of times a specific reference is included the reference lists) in published papers of certain scientific fields. Researchers in the field can answer the question about seminal papers only subjectively. RYPS can answer this question in an objective way by asking all researchers in the field (via the cited references in their publications) with subsequent quantitative analysis. Therefore, RPYS results often provide a different perspective or complement the individual expert’s perspective on the field.
Methods
Our analysis is based on the search and retrieval functions of the databases offered by Chemical Abstracts Service (CAS), a division of the American Chemical Society (ACS). The CAS literature database (Chemical Abstracts Plus, CAplus^{SM}) covers scientific publications and patents since around 1900 (including the references cited therein since the publication year 1996). The CAS compound database (Registry^{SM}) contains all chemical species mentioned within the publications in chemistry and related fields, identified and registered by the CAS Registry system. All compound records are associated with a unique CAS Registry number. These items (publications and compounds) are called documents or records. We used both databases via the new platform of the Scientific and Technical Information Network (STN^{®}) International. Both databases are connected to each other via Registry numbers^{®} (RNs). The content of both databases is also accessible with SciFinder^{®}. However, the STN platform provides more detailed search and analysis possibilities.
The CAplus publication records contain index terms (ITs, keywords carefully selected and assigned by the database producer CAS). We searched for the terms “DFT”, “density functional theory”, “d functional theory”, and “TDDFT” in the IT fields of the CAplus database. Occurrences of “TDDFT” and “timedependent density functional theory” are also found by our aforementioned search terms. The search term “d functional theory” is not used by scientists using DFT but it is used by CAS indexers. In total, we found 114,138 documents published before the end of the year 2014 (at the date of searching the year 2015 was not completely covered by the database). Throughout this paper, we will refer to this set of 114,138 documents as “all DFT publications”. Although indexing takes some time, we can expect that the publication years until 2014 are nearly complete. 102,880 documents (90.1 %) have at least one connection to a Registry compound record. Throughout this paper, we will refer to this set of 102,880 documents as “substancerelated DFT publications”. The compounds with at least one connection from a Registry to a CAplus record will be referred to as “DFTrelated compounds”. The remaining 9.9 % of the documents are either concerned with methodological developments or the calculated substances are not a major concern of the document.
We used the relationship between CAplus and Registry mainly to elucidate how often which elements are present in the corresponding compounds connected to DFT calculations. An example of the CAplus IT fields is shown in Table 1 using the document in Ref. [62].
For example, the first index term (IT1) shown in Table 1 contains the relevant compounds in the form of their RNs together with the controlled term “Properties (PRP)” in combination with the corresponding abbreviated author vocabulary (“Dewar–Chatt–Duncanson model reversed and bonding anal. of Ni, Pd, and Pt complexes [(PMe_{3})_{2}MEX_{3}] with Group IIIA element E halide ligands EX_{3} from DFTBP86 calcns.”). This indicates that properties were calculated for the substances that correspond to the itemized RNs and are described by the abbreviated author vocabulary. The other IT fields contain additional combinations of controlled terms with abbreviated author vocabulary.
We use controlled terms supplied by the indexer (e.g., “Molecular structure”, “Conformation”, “Bond”) to define subfields or topics within the corpus of DFT literature. The topics together with carefully selected index terms are presented in Table 2.
We also analyze the DFT publications with respect to seminal papers on which the DFT publications are based. Such seminal papers can be located using a bibliometric method called “Reference Publication Year Spectroscopy” (RPYS) [61] in combination with a recently developed tool named CRExplorer (http://www.crexplorer.net) [63]. The analysis of the publication years of the references cited by all the papers in a specific research field shows that (earlier) publication years are not equally represented. Some years occur particularly frequently among the references. The years appear as pronounced peaks in the distribution of the reference publication years (i.e. the RPYS spectrum). The peaks are frequently based on single early publications, which are highly cited compared to other early publications. The highly cited papers are usually of specific significance to the research field in question (here: DFT).
In a first step, the publication set is imported into the CRExplorer and all cited references are extracted. In a second step, equivalent references are clustered and merged. References below a threshold (here: 100 cited references) are removed to reduce the background noise and to sharpen the resulting spectrum. In the third and final step, the reference publication years are analyzed for frequently cited publications. We analyze the reference publication years (RPYs) between 1950 and 1990. It is very problematic to analyze younger RPYs than 1990, and 1950 is a reasonable choice as the oldest RPY for the topic DFT. Furthermore, older RPYs require a slightly different methodology, i.e., lower threshold of the number of cited references.
Results
Overall growth and growth in terms of topics
The overall annual publication volume since 1980 that is concerned with DFT is shown in Fig. 1. Note that 13 DFT relevant publications (11 substancerelated DFT publications) were published prior to 1980.
According to Fig. 1, the annual publication volume shows a strong increase since 1995. The curve of all DFT publications (blue line) is nearly parallel to the curve of DFT publications with a connection to a RN (substancerelated DFT publications, red line) until 2012. Probably, the indexing of the recent years still needs some time to be completed so the years 2013 and 2014 should be looked at with caution. The annual volume of DFT publications shows a doubling within 5–6 years, which is much faster than the overall growth of the CAplus literature. The total volume of publications covered by CAplus between 1968 (first publication with DFTrelated index term) and 2013 doubled approximately only every 11 years (14 years when patents are excluded). The growth rate of DFT literature is, for example, comparable to the growth rate of literature for a hot topic like climate change [64].
Figure 2 shows the growth of DFT publications in terms of research topics since 1980. Note that there is of course some overlap between the research topics.
Nearly all the topic curves in Fig. 2 show a decline or slowed growth rate in the years 2013 and 2014, just as the red curve showed in Fig. 1. This effect is probably also attributable to the delayed indexing for the recent years. The topics “Structure” and “Energy” start to increase before the other topics. As Fig. 2 indicates, index terms related to the topic “Energy” are only included in the record if the determination of the energy plays an essential role in the publication. The index terms related to the topic “Energy” are not included in the record if the energy calculation is only necessary to obtain properties of substances. In order to calculate the structure of a substance, obviously, one has to calculate the energy first. In such instances, the index terms related to the topic “Energy” are not added to the list of index terms. “Relativity” and “Magnetism” increase at a much slower rate than the other topics. The nine topics comprise 86.5 % of all DFT publications and 95.6 % of the substancerelated DFT publications.
Substancerelated analysis of DFT literature
For the substancerelated analysis, we extracted all Registry numbers from the publication set of all DFT papers (n = 114,138) and transferred them to the compound database Registry. The records of the compound database include various compound specific information, in particular the chemical names, molecular formulas, and structure diagrams. The search for the number of compounds indexed in DFT literature and containing specific elements was based on the molecular formula field. We determined how many compounds containing a specific element have been indexed within the DFT publication set. Figure 3 shows a periodic table where instead of the element symbols the absolute number of compounds within the DFT literature is given. It is important to note that numbers in the table may overlap, e.g. between C (467,192) and O (274,893).
By far the most frequently occurring elements in compoundspecific publications dealing with DFT calculations are hydrogen and carbon. Oxygen and nitrogen also occur very often in substancerelated DFT calculations. The lanthanides and actinides occur about as often in compoundspecific DFT calculations as the rare gas elements, with one exception: uranium occurs significantly more often than the other actinides.
Figure 4 shows the percentage of compounds that have DFTrelated publications registered relative to all registrations for each specific element. Although the absolute numbers in Fig. 3 are rather low, the percentages of DFTrelated compounds are quite high for the rare gases, many actinides, and polonium. Also, some transition metals (e.g., gold, platinum, palladium, rhodium, ruthenium, and osmium) show rather high relative occurrences. Figure 3 shows very high absolute numbers for hydrogen, carbon, nitrogen, and oxygen whereas Fig. 4 shows that their relative share of DFTrelated compounds is rather low.
In total, 558.619 DFTrelated compounds were found. Figure 5 shows the share of each element relative to the total of 558.619 DFTrelated compounds. The colorcoding is essentially the same as in Fig. 3.
Figure 6 shows the annual publication volume of DFT studies that investigate compounds containing certain elements centered on carboncontaining compounds. Only the elements shown are allowed to occur in the sum formula (e.g. in the case of C no elements other than carbon are allowed in the sum formula, CH indicates pure hydrocarbons, etc.). Organics is the superset of CH, CHN, CHO, and CHNO. Of course, there are more organic compounds, but this analysis concentrates on pure organic compounds and excludes compounds with less common heteroatoms. For comparison, also the total curve of all substancerelated DFT publications is included in the Figure. The first substance indexed with these element restrictions was a carbon modification published in 1982.
Most of the compounds contributing to the C curve are fullerenes. Additionally, different oxidation states and isotopes of the carbon atom are registered as different compounds. The curves of CHN, CHO, and CHNO are very similar. Probably, the reason is that O and NH are isoelectronic. Therefore, most CHO compounds can also be calculated when oxygen is substituted by an NH group. The curve “Organics” (according to our definition) covers 37.2 % (n = 38,277 papers) of the substancerelated DFT literature. Again, the decline or slowed growth rate in the years 2013 and 2014 is probably caused by the delayed indexing for the recent publication years.
Figure 7 shows the annual publication volume of DFT studies that investigate specific compound groups: inorganic metals, organometallic compounds, transition metal compounds, lanthanides, and actinides. Here, organometallic compounds are defined as a compound with at least one metal, carbon, and hydrogen atom. There is no restriction on additional elements. For comparison, also the total curve of all substancerelated DFT publications is included in the Figure. The compound paper curves in Figs. 5 and 6 cover 81.6 % of the total set of all substancerelated DFT publications.
The largest compounds calculated with DFT in terms of number of atoms are: C_{6000} [65], C_{5120} [66], and C_{4860} [65]. All three compounds are fullerenes with icosahedral symmetry. Unfortunately, the Registry database does not have point groups as additional information for the registered molecules, so one cannot search for the largest asymmetric molecule calculated with DFT. Also, the information about employed basis sets and specific density functionals is often missing in the CAplus database. Therefore, it is not possible using our search strategy to find the computationally most demanding molecule calculated with DFT.
Analysis of seminal DFT papers
Figure 8 shows the result of the RPYS performed with the CRExplorer. The figure presents the distribution of the number of cited references across their publication years within the time period 1950–1990. Nine distinct peaks (1951, 1955, 1964/1965, 1970, 1972/1973, 1976, 1980, 1986, and 1988) can be located in the spectrum. The publications which are mainly responsible for these peaks are listed in Table 3. The red line in Fig. 8 visualizes the number of cited references per reference publication year. In order to identify those publication years with significantly more cited references than other years, the (absolute) deviation of the number of cited references in each year from the median of the number of cited references in the two previous, the current, and the two following years (t − 2; t − 1; t; t + 1; t + 2) is also visualized (blue line). This deviation from the 5year median provides a curve smoother than the one in terms of absolute numbers. We used both curves for the identification of the peaks. Table 3 contains the seminal papers which are mainly responsible for the peaks. This is a highly selective method and many other seminal papers relevant to DFT are not mentioned in Table 3. However, such papers can be identified via the reference table alongside the spectrum in the CRExplorer.
The cited references CR1, CR4, CR5, and CR11–CR14 of Table 3 were mentioned in the Background Section of this study. Four of them (CR11–CR14) propose new density functional approximations or improvements to existing ones. The cited references CR4 and CR5 are the foundational publications for modern DFT by Hohenberg and Kohn (CR4) and Kohn and Sham (CR5). The cited reference CR1 is Slater’s approximation to Hartree–Fock exchange. The seven other cited references in Table 3 are not specific about DFT. They are of a more general interest in theoretical and computational chemistry and physics.
In cited reference CR2 Roothaan proposes to construct molecular orbitals as a linear combination of atomic orbitals (LCAO). This proposal was made for Hartree–Fock theory but is used in virtually every widespread program package for postHartree–Fock and DFT calculations. In cited reference CR3 Mulliken proposed an electronic population analysis based on Roothaan’s LCAO method. Using this methodology, it became possible to calculate partial charges and dipole moments.
Boys and Bernardi proposed in cited reference CR6 a new direct difference method for the computation of molecular interaction energies with reduced errors. Hehre, Ditchfield, and Pople presented new basis sets for the LCAO method in reference CR7. The 631G basis set, which became very popular, is among those basis sets presented in this cited reference. The relevance of polarization functions was pointed out by Hariharan and Pople in cited reference CR8, and the popular 631G* and 631G** basis sets were proposed. Baerends, Ellis, and Roos presented in cited reference CR9 a computational Hartree–Fock scheme using Slater’s approximation and Roothaans LCAO ansatz where Slatertype atomic orbitals do not increase the computational demand compared to Gaussiantype orbitals. Cited reference CR10 by Monkhorst and Pack is the only cited reference in Table 3 concerned specifically with the solid state. They propose a method for generating sets of special points in the Brillouin zone. This method provides a more efficient algorithm to integrate periodic functions of the wave vector in solid state calculations.
Discussion
Most DFT literature is substancerelated. Therefore, the publication volumes of the general DFT literature are very similar to the publication volumes of the substancerelated DFT literature. In terms of absolute numbers, most compounds calculated by DFT contain hydrogen, carbon, nitrogen, or oxygen. Also, 37.2 % of the substancerelated DFT literature is concerned with compounds build from these four elements. 81.6 % of the substancerelated DFT literature is covered when broader compound groups (inorganic metals, organometallic compounds, transition metal compounds, lanthanides, and actinides) are considered additionally. However, a relative perspective shows that DFT calculations were performed rather often in comparison with experiments for rare gas elements, many actinides, and polonium as well as some transition metals. Probably, we see rather high activity of DFT research for many actinides and polonium because of industrial interest in combination with interest in their radioactive decay. The interest in platinum, palladium, rhodium, ruthenium, and osmium might be due to their catalytic activity. The highly selective RPYS analysis shows the 14 most influential publications with relevance to DFT published between 1950 and 1990. Seven of these 14 publications were cited in the Background section of this manuscript. The other DFT publications cited in the Background section of this manuscript are newer or older.
We have to mention here the limitations of our study. Our retrieval strategy, based only on index terms, can be seen as a limitation as we obtain fewer publications this way than by a search in title, keywords, and abstract for DFTrelated keywords. This strategy is a compromise to gather the publications where DFT plays a major role. Another search strategy would yield too many false positives, i.e. publications where DFT plays only a minor role although DFTrelated keywords are mentioned in title, keywords, or abstract. In contrast to previous chemical bibliometric studies, we did not use only hit RNs but all RNs in the records. This is necessary because control tests showed that too few RNs were supplemented with DFTrelated terms. However, we can assume that these limitations do not change the picture.
The RPYS analysis has certain additional limitations. There are also seminal DFT papers published before 1950 and after 1990. However, reference publication years younger than 1990 require a different technical treatment because of the exponential increase of the number of publications and cited references. Seminal papers before 1950 comprise the historical roots of DFT and are an interesting subject for another analysis. We chose to be highly selective in the identification of seminal papers in the DFT literature. A less selective procedure would result in many more seminal papers. Such a detailed analysis is possible but is beyond the scope of our current analysis.
Of course, our search and analysis strategy is not limited to the topic DFT. Similar bibliometric analyses can be performed for other topics where a connection between publications and chemical substances is important.
Conclusions
In conclusion, we have presented an overview of the total and compoundrelated DFT literature. The total DFT literature was analyzed in terms of research topics while the compoundrelated DFT literature was analyzed in terms of chemical elements and combinations of elements. DFTrelated literature experienced an exponential growth during the 1990s. Since 2000 the growth of DFTrelated publications has become linear. Currently, the DFT publication volume doubles every 5–6 years. Finally, we have identified and discussed 14 seminal papers of the DFT literature.
Abbreviations
 TDDFT:

timedependent density functional theory
 DFT:

density functional theory
 CAS:

Chemical Abstracts Service
 CAplus^{SM} :

Chemical Abstracts Plus
 ACS:

American Chemical Society
 STN:

Scientific and Technical Information Network
 RNs:

Registry numbers
References
 1.
Schrodinger E (1926) Quantisation as an eigen value problem. Ann Phys 79:U361–U368
 2.
Schrodinger E (1926) An undulatory theory of the mechanics of atoms and molecules. Phys Rev 28:1049–1070. doi:10.1103/PhysRev.28.1049
 3.
Dirac PAM (1928) The quantum theory of the electron. Proc R Soc Lond Ser A Contain Pap Math Phys Character 117:610–624. doi:10.1098/rspa.1928.0023
 4.
Dirac PAM (1928) The quantum theory of the electron—part II. Proc R Soc Lond Ser A Contain Pap Math Phys Character 118:351–361. doi:10.1098/rspa.1928.0056
 5.
Dirac PAM (1928) On the quantum theory of electrons. Physikalische Zeitschrift 29:561–563
 6.
Thomas LH (1927) The calculation of atomic fields. Proc Camb Philos Soc 23:542–548
 7.
Fermi E (1928) A statistical method for determining some properties of the atoms and its application to the theory of the periodic table of elements. Z Angew Phys 48:73–79. doi:10.1007/bf01351576
 8.
Slater JC (1951) A simplification of the Hartree–Fock method. Phys Rev 81:385–390. doi:10.1103/PhysRev.81.385
 9.
Hartree DR, Hartree FRS, Hartree W (1935) Selfconsistent field, with exchange, for beryllium. Proce R Soc Lond Ser Math Phys Sci 150:0009–0033. doi:10.1098/rspa.1935.0085
 10.
Fock V (1930) Approximation method for the solution of the quantum mechanical multibody problems. Z Angew Phys 61:126–148. doi:10.1007/bf01340294
 11.
Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:B864. doi:10.1103/PhysRev.136.B864
 12.
Kohn W, Sham LJ (1965) Selfconsistent equations including exchange and correlation effects. Phys Rev 140:1133
 13.
Vosko SH, Wilk L, Nusair M (1980) Accurate spindependent electron liquid correlation energies for local spindensity calculations—a critical analysis. Can J Phys 58:1200–1211
 14.
Perdew JP (1986) Densityfunctional approximation for the correlationenergy of the inhomogeneous electrongas. Phys Rev B 33:8822–8824. doi:10.1103/PhysRevB.33.8822
 15.
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. doi:10.1103/PhysRevLett.77.3865
 16.
Becke AD (1988) Densityfunctional exchangeenergy approximation with correct asymptoticbehavior. Phys Rev A 38:3098–3100. doi:10.1103/PhysRevA.38.3098
 17.
Lee CT, Yang WT, Parr RG (1988) Development of the Colle–Salvetti correlationenergy formula into a functional of the electrondensity. Phys Rev B 37:785–789. doi:10.1103/PhysRevB.37.785
 18.
Tao JM, Perdew JP, Staroverov VN, Scuseria GE (2003) Climbing the density functional ladder: nonempirical metageneralized gradient approximation designed for molecules and solids. Phys Rev Lett. doi:10.1103/PhysRevLett.91.146401
 19.
Perdew JP, Kurth S, Zupan A, Blaha P (1999) Accurate density functional with correct formal properties: a step beyond the generalized gradient approximation. Phys Rev Lett 82:2544–2547. doi:10.1103/PhysRevLett.82.2544
 20.
Zhao Y, Truhlar DG (2006) A new local density functional for maingroup thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J Chem Phys 125:18. doi:10.1063/1.2370993
 21.
Becke AD (1993) Densityfunctional thermochemistry. 3. The role of exact exchange. J Chem Phys 98:5648–5652. doi:10.1063/1.464913
 22.
Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. J Chem Phys 110:6158–6170. doi:10.1063/1.478522
 23.
Zhao Y, Schultz NE, Truhlar DG (2005) Exchangecorrelation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions. J Chem Phys 123:4. doi:10.1063/1.2126975
 24.
Zhao Y, Schultz NE, Truhlar DG (2006) Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. J Chem Theory Comput 2:364–382. doi:10.1021/ct0502763
 25.
Becke AD (1993) A new mixing of Hartree–Fock and local densityfunctional theories. J Chem Phys 98:1372–1377. doi:10.1063/1.464304
 26.
Perdew JP, Emzerhof M, Burke K (1996) Rationale for mixing exact exchange with density functional approximations. J Chem Phys 105:9982–9985. doi:10.1063/1.472933
 27.
Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118:8207–8215. doi:10.1063/1.1564060
 28.
Heyd J, Scuseria GE, Ernzerhof M (2006) Hybrid functionals based on a screened Coulomb potential (vol 118, pg 8207, 2003). J Chem Phys. doi:10.1063/1.2204597
 29.
Yanai T, Tew DP, Handy NC (2004) A new hybrid exchangecorrelation functional using the Coulombattenuating method (CAMB3LYP). Chem Phys Lett 393:51–57. doi:10.1016/j.cplett.2004.06.011
 30.
Peverati R, Truhlar DG (2011) Improving the accuracy of hybrid metaGGA density functionals by range separation. J Phys Chem Lett 2:2810–2817. doi:10.1021/jz201170d
 31.
Chai JD, HeadGordon M (2008) Systematic optimization of longrange corrected hybrid density functionals. J Chem Phys 128:15. doi:10.1063/1.2834918
 32.
Iikura H, Tsuneda T, Yanai T, Hirao K (2001) A longrange correction scheme for generalizedgradientapproximation exchange functionals. J Chem Phys 115:3540–3544. doi:10.1063/1.1383587
 33.
Song JW, Watson MA, Hirao K (2009) An improved longrange corrected hybrid functional with vanishing Hartree–Fock exchange at zero interelectronic distance, LC2gauBOP. J Chem Phys 131:9. doi:10.1063/1.3243819
 34.
Vydrov OA, Scuseria GE (2006) Assessment of a longrange corrected hybrid functional. J Chem Phys. doi:10.1063/1.2409292
 35.
Jaramillo J, Scuseria GE, Ernzerhof M (2003) Local hybrid functionals. J Chem Phys 118:1068–1073. doi:10.1063/1.1528936
 36.
Arbuznikov AV, Kaupp M (2008) What can we learn from the adiabatic connection formalism about local hybrid functionals? J Chem Phys. doi:10.1063/1.2920196
 37.
Bahmann H, Rodenberg A, Arbuznikov AV, Kaupp M (2007) A thermochemically competitive local hybrid functional without gradient corrections. J Chem Phys. doi:10.1063/1.2429058
 38.
Haunschild R, Janesko BG, Scuseria GE (2009) Local hybrids as a perturbation to global hybrid functionals. J Chem Phys. doi:10.1063/1.3247288
 39.
Janesko BG, Scuseria GE (2007) Local hybrid functionals based on density matrix products. J Chem Phys. doi:10.1063/1.2784406
 40.
Janesko BG, Scuseria GE (2008) Parameterized local hybrid functionals from densitymatrix similarity metrics. J Chem Phys. doi:10.1063/1.2831556
 41.
Johnson ER (2014) Localhybrid functional based on the correlation length. J Chem Phys. doi:10.1063/1.4896302
 42.
Haunschild R, Scuseria GE (2010) Rangeseparated local hybrids. J Chem Phys. doi:10.1063/1.3451078
 43.
Henderson TM, Janesko BG, Scuseria GE, Savin A (2009) Locally rangeseparated hybrids as linear combinations of rangeseparated local hybrids. Int J Quantum Chem 109:2023–2032. doi:10.1002/qua.22049
 44.
Arbuznikov AV, Kaupp M (2012) Importance of the correlation contribution for local hybrid functionals: range separation and selfinteraction corrections. J Chem Phys 136:13. doi:10.1063/1.3672080
 45.
Grimme S (2006) Semiempirical hybrid density functional with perturbative secondorder correlation. J Chem Phys. doi:10.1063/1.2148954
 46.
Hedegard ED, Heiden F, Knecht S, Fromager E, Jensen HJA (2013) Assessment of chargetransfer excitations with timedependent, rangeseparated density functional theory based on longrange MP2 and multiconfigurational selfconsistent field wave functions. J Chem Phys 139:13. doi:10.1063/1.4826533
 47.
Janesko BG, Henderson TM, Scuseria GE (2009) Longrangecorrected hybrids including random phase approximation correlation. J Chem Phys. doi:10.1063/1.3090814
 48.
Furche F (2008) Developing the random phase approximation into a practical postKohnSham correlation model. J Chem Phys. doi:10.1063/1.2977789
 49.
Furche F, Van Voorhis T (2005) Fluctuationdissipation theorem densityfunctional theory. J Chem Phys 122:10. doi:10.1063/1.1884112
 50.
Eshuis H, Furche F (2011) A parameterfree density functional that works for noncovalent interactions. J Phys Chem Lett 2:983–989. doi:10.1021/jz200238f
 51.
Goll E, Werner HJ, Stoll H (2005) A shortrange gradientcorrected density functional in longrange coupledcluster calculations for rare gas dimers. Phys Chem Chem Phys 7:3917–3923. doi:10.1039/b509242f
 52.
Goll E, Werner HJ, Stoll H, Leininger T, GoriGiorgi P, Savin A (2006) A shortrange gradientcorrected spin density functional in combination with longrange coupledcluster methods: application to alkalimetal raregas dimers. Chem Phys 329:276–282. doi:10.1016/j.chemphys.2006.05.020
 53.
Garza AJ, Bulik IW, Henderson TM, Scuseria GE (2015) Range separated hybrids of pair coupled cluster doubles and density functionals. Phys Chem Chem Phys 17:22412–22422. doi:10.1039/c5cp02773j
 54.
Goerigk L, Grimme S (2014) Doublehybrid density functionals. Wiley Interdiscip Rev Comput Mol Sci 4:576–600. doi:10.1002/wcms.1193
 55.
Chai JD, HeadGordon M (2009) Longrange corrected doublehybrid density functionals. J Chem Phys 131:13. doi:10.1063/1.3244209
 56.
Burke K (2012) Perspective on density functional theory. J Chem Phys. doi:10.1063/1.4704546
 57.
PribramJones A, Gross DA, Burke K (2015) DFT: a theory full of holes? In: Johnson MA, Martinez TJ (eds) Ann Rev Phys Chem 66:283–304. doi:10.1146/annurevphyschem040214121420
 58.
Abbott A, Cyranoski D, Jones N, Maher B, Schiermeier Q, Van Noorden R (2010) Do metrics matter? Nature 465:860–862. doi:10.1038/465860a
 59.
Van Noorden R (2010) A profusion of measures. Nature 465:864–866. doi:10.1038/465864a
 60.
Barth A, Marx W (2012) Stimulation of Ideas through compoundbased bibliometrics: counting and mapping chemical compounds for analyzing research topics in chemistry, physics, and materials science. Chemistryopen 1:276–283. doi:10.1002/open.201200029
 61.
Marx W, Bornmann L, Barth A, Leydesdorff L (2014) Detecting the historical roots of research fields by reference publication year spectroscopy (RPYS). J Assoc Inf Sci Technol 65:751–764. doi:10.1002/asi.23089
 62.
Goedecke C, Hillebrecht P, Uhlemann T, Haunschild R, Frenking G (2009) The Dewar–Chatt–Duncanson model reversed  Bonding analysis of group10 complexes (PMe3)(2)MEX3 (M = Ni, Pd, Pt; E = B, Al, Ga, In, Tl; X = H, F, Cl, Br, I). Can J Chem Rev Can Chim 87:1470–1479. doi:10.1139/v09099
 63.
Thor A, Marx W, Leydesdorff L, Bornmann L (2016) Introducing CitedReferencesExplorer (CRExplorer): a program for reference publication year spectroscopy with cited references disambiguation. http://arxiv.org/abs/1601.01199. Accessed 1 Oct 2016
 64.
Haunschild R, Bornmann L, Marx W (2016) Climate change research in view of bibliometrics. PLoS ONE 11(7):e0160393. doi:10.1371/journal.pone.0160393
 65.
Noel Y, De La Pierre M, ZicovichWilson CM, Orlando R, Dovesi R (2014) Structural, electronic and energetic properties of giant icosahedral fullerenes up to C6000: insights from an ab initio hybrid DFT study. Phys Chem Chem Phys 16:13390–13401. doi:10.1039/c4cp01442a
 66.
Holec D, Hartmann MA, Fischer FD, Rammerstorfer FG, Mayrhofer PH, Paris O (2010) Curvatureinduced excess surface energy of fullerenes: density functional theory and Monte Carlo simulations. Phys Rev B. doi:10.1103/PhysRevB.81.235403
Authors’ contributions
All three authors have conceived and designed the analysis. RH and AB collected the data. RH performed the analysis. All three authors contributed in writing the manuscript. All authors read and approved the final manuscript.
Acknowledgements
The authors thank Bernard T. French for help with extended data retrieval for the RPYS analysis. The RPYS was performed during a research stay of RH in the CAS Innovation group (Columbus, Ohio). RH thanks CAS for financial support during his stay.
Competing interests
The authors declare that they have no competing interests.
Author information
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
About this article
Received
Accepted
Published
DOI
Keywords
 DFT
 Chemical bibliometrics
 Compound bibliometrics
 Publication analysis
 RPYS