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Are the vertical ionization energies from a bound electronic system, initially in its ground state, equal to minus the corresponding exact Kohn–Sham orbital energies of density functional theory (DFT)? This is known to be true for the first or lowest vertical ionization energy. We show that the correction from time-dependent DFT arises from the continuum and need not vanish. Recent work compared the experimental photoemission thresholds of the molecules Cu2O–, CuO–, CuO2–, and CuO3–with minus the corresponding orbital energies from a generalized gradient approximation (GGA) and its global and range-separated hybrids with exact exchange, finding striking differences which were attributed to self-interaction error, strong correlation, or both. Here, we extend that work to include the local spin density approximation (LSDA), its Perdew–Zunger self-interaction correction with Fermi–Löwdin localized orbitals (LSDA-SIC), a quasi-self-consistent locally scaled-down version of LSDA-SIC (QLSIC), and the Quantum Theory Project QTP02 range-separated hybrid functional, all but LSDA implemented in a generalized Kohn–Sham approach. QTP02 impressively yields a near equality for many sp-bonded molecules. However, for the copper oxide anions studied here, none of the tested methods reproduces the experimental photoemission thresholds.

We analyzed various possibilities to improve upon the SCAN meta-generalized gradient approximation density functional obeying all known properties of the exact functional that can be satisfied at this level of approximation. We examined the necessity of locally satisfying a strongly tightened lower bound for the exchange energy density in single-orbital regions, the nature of the error cancellation between the exchange and correlation parts in two-electron regions, and the effect of the fourth-order term in the gradient expansion of the correlation energy density. We have concluded that the functional can be modified to separately reproduce the exchange and correlation energies of the helium atom by locally releasing the strongly tightened lower bound for the exchange energy density in single-orbital regions, but this leads to an unbalanced improvement in the single-orbital electron densities. Therefore, we decided to keep the FX≤ 1.174 exact condition for any single-orbital density, where FXis the exchange enhancement factor. However, we observed a general improvement in the single-orbital electron densities by revising the correlation functional form to follow the second-order gradient expansion in a wider range. Our new revSCAN functional provides more-accurate atomization energies for the systems with multireference character, compared to the SCAN functional. The nonlocal VV10 dispersion-corrected revSCAN functional yields more-accurate noncovalent interaction energies than the VV10-corrected SCAN functional. Furthermore, its global hybrid version with 25% of exact exchange, called revSCAN0, generally performs better than the similar SCAN0 for reaction barrier heights. Here, we also analyzed the possibility of the construction of a local hybrid from the SCAN exchange and a specific locally bounded nonconventional exact exchange energy density. We predict compatibility problems since this nonconventional exact exchange energy density does not really obey the strongly tightened lower bound for the exchange energy density in single-orbital regions.

Since its formal introduction, density functional theory has achieved many successes in the fields of molecular and solid-state chemistry. According to its central theorems, the ground state of a many-electron system is fully described by its electron density, and the exact functional minimizes the energy at the exact electron density. For many years of density functional development, it was assumed that the improvements in the energy are accompanied by the improvements in the density, and the approximations approach the exact functional. In a recent analysis (Medvedev et al. Science2017, 355, 49−52.), it has been pointed out for 14 first row (Be–Ne) atoms and cations with 2, 4, or 10 electrons that the nowadays popular flexible but physically less rigorous approximate density functionals may provide large errors in the calculated electron densities despite the accurate energies. Although far-reaching conclusions have been drawn in this work, the methodology used by the authors may need improvements. Most importantly, their benchmark set was biased toward small atomic cations with compressed, high electron densities. In our paper, we construct a molecular test set with chemically relevant densities and analyze the performance of several density functional approximations including the less-investigated double hybrids. We apply an intensive error measure for the density, its gradient, and its Laplacian and examine how the errors in the density propagate into the semilocal exchange-correlation energy. While we have confirmed the broad conclusions of Medvedev et al., our different way of analyzing the data has led to conclusions that differ in detail. Finally, seeking for a rationale behind the global hybrid or double hybrid methods from the density’s point of view, we also analyze the role of the exact exchange and second-order perturbative correlation mixing in PBE-based global hybrid and double hybrid functional forms.

Recently, we have constructed a dual-hybrid direct random phase approximation method, called dRPA75, and demonstrated its good performance on reaction energies, barrier heights, and noncovalent interactions of main-group elements. However, this method has also shown significant but quite systematic errors in the computed atomization energies. In this paper, we suggest a constrained spin-component scaling formalism for the dRPA75 method (SCS-dRPA75) in order to overcome the large error in the computed atomization energies, preserving the good performance of this method on spin-unpolarized systems at the same time. The SCS-dRPA75 method with the aug-cc-pVTZ basis set results in an average error lower than 1.5 kcal mol–1for the entire n-homodesmotic hierarchy of hydrocarbon reactions (RC0–RC5 test sets). The overall performance of this method is better than the related direct random phase approximation-based double-hybrid PWRB95 method on open-shell systems of main-group elements (from the GMTKN30 database) and comparable to the best O(N4)-scaling opposite-spin second-order perturbation theory-based double-hybrid methods like PWPB95-D3 and to the O(N5)-scaling RPAX2@PBEx method, which also includes exchange interactions. Furthermore, it gives well-balanced performance on many types of barrier heights similarly to the best O(N5)-scaling second-order perturbation theory-based or spin-component scaled second-order perturbation theory-based double-hybrid methods such as XYG3 or DSD-PBEhB95. Finally, we show that the SCS-dRPA75 method has reduced self-interaction and delocalization errors compared to the parent dRPA75 method and a slightly smaller static correlation error than the related PWRB95 method.

In water clusters, there is a delicate balance of van der Waals interactions and hydrogen bonds. Although semilocal and nonlocal density functional approximations have been recently routinely applied to water in various phases, the accurate description of hydrogen bonds remains a challenge. The most popular density functional approaches fail to predict the correct ordering of the energies of water clusters. To illustrate the required accuracy, the CCSD(T) complete basis set extrapolated dissociation energy difference between the two lowest energy hexamer structures is 0.06 kcal mol–1per monomer. In this work, we assessed interaction energies in neutral and ionic water clusters with various density functionals with or without van der Waals correction. Generally, van der Waals approximations play a significant role in clusters with increasing size, while hybrid functionals improve the description of hydrogen bonds. Despite these general trends, none of the tested density functional approximations with or without van der Waals correction and exact exchange mixing can lead to a uniform performance for neutral and ionic water clusters. The recently constructed dual-hybrid dRPA75 approximation is a successful combination of exact and semilocal exchange, and nonlocal correlation in its energy, while utilizing a high fraction of exact exchange. We have shown that the dRPA75 method has a systematic error, which can be efficiently compensated for by the aug-cc-pVTZ basis set for small- and medium-sized water clusters.

The direct random phase approximation (dRPA) combined with Kohn–Sham reference orbitals is among the most promising tools in computational chemistry and applicable in many areas of chemistry and physics. The reason for this is that it scales as N4with the system size, which is a considerable advantage over the accurate ab initio wave function methods like standard coupled-cluster. dRPA also yields a considerably more accurate description of thermodynamic and electronic properties than standard density-functional theory methods. It is also able to describe strong static electron correlation effects even in large systems with a small or vanishing band gap missed by common single-reference methods. However, dRPA has several flaws due to its self-correlation error. In order to obtain accurate and precise reaction energies, barriers and noncovalent intra- and intermolecular interactions, we construct a new dual-hybrid dRPA (hybridization of exact and semilocal exchange in both the energy and the orbitals) and test the performance of this new functional on isogyric, isodesmic, hypohomodesmotic, homodesmotic, and hyperhomodesmotic reaction classes. We also use a test set of 14 Diels–Alder reactions, six atomization energies (AE6), 38 hydrocarbon atomization energies, and 100 reaction barrier heights (DBH24, HT-BH38, and NHT-BH38). For noncovalent complexes, we use the NCCE31 and S22 test sets. To test the intramolecular interactions, we use a set of alkane, cysteine, phenylalanine-glycine-glycine tripeptide, and monosaccharide conformers. We also discuss the delocalization and static correlation errors. We show that a universally accurate description of chemical properties can be provided by a large, 75% exact exchange mixing both in the calculation of the reference orbitals and the final energy.

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning’s correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number Xcontrols the size of the basis set, and we use X= 3–6 in this study. It is known that even the very expensive X= 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH4to C6H6. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use X= 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate X= 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules.

We assess the performance of the semilocal PBE functional; its global hybrid variants; the highly parametrized empirical M06-2X and M08-SO; the range separated rCAM-B3LYP and MCY3; the atom-pairwise or nonlocal dispersion corrected semilocal PBE and TPSS; the dispersion corrected range-separated ωB97X-D; the dispersion corrected double hybrids such as PWPB95-D3; the direct random phase approximation, dRPA, with Hartree–Fock, Perdew–Burke–Ernzerhof, and Perdew–Burke–Ernzerhof hybrid reference orbitals and the RPAX2 method based on a Perdew–Burke–Ernzerhof exchange reference orbitals for the Diels–Alder, DARC; and self-interaction error sensitive, SIE11, reaction energy test sets with large, augmented correlation consistent valence basis sets. The dRPA energies for the DARC test set are extrapolated to the complete basis set limit. CCSD(T)/CBS energies were used as a reference. The standard global hybrid functionals show general improvements over the typical endothermic energy error of semilocal functionals, but despite the increased accuracy the precision of the methods increases only slightly, and thus all reaction energies are simply shifted into the exothermic direction. Dispersion corrections give mixed results for the DARC test set. Vydrov–Van Voorhis 10 correction to the reaction energies gives superior quality results compared to the too-small D3 correction. Functionals parametrized for energies of noncovalent interactions like M08-SO give reasonable results without any dispersion correction. The dRPA method that seamlessly and theoretically correctly includes noncovalent interaction energies gives excellent results with properly chosen reference orbitals. As the results for the SIE11 test set and H2+dissociation show that the dRPA methods suffer from delocalization error, good reaction energies for the DARC test set from a given method do not prove that the method is free from delocalization error. The RPAX2 method shows good performance for the DARC, the SIE11 test sets, and for the H2+and H2potential energy curves showing no one-electron self-interaction error and reduced static correlation errors at the same time. We also suggest simplified DARC6 and SIE9 test sets for future benchmarking.

A correct description of the anion−π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion−π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π–anion−π′ sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values. We give a detailed explanation of the origin of anion−π interactions, using the permanent quadrupole moments, static dipole polarizabilities, and electrostatic potential maps. We use symmetry-adapted perturbation theory (SAPT) to calculate the components of the anion−π interaction energies. We examine the performance of the direct random phase approximation (dRPA), the second-order screened exchange (SOSEX), local-pair natural-orbital (LPNO) coupled electron pair approximation (CEPA), and several dispersion-corrected density functionals (including generalized gradient approximation (GGA), meta-GGA, and double hybrid density functional). The LPNO-CEPA/1 results show the best agreement with the reference results. The dRPA method is only slightly less accurate and precise than the LPNO-CEPA/1, but it is considerably more efficient (6–17 times faster) for the binary complexes studied in this paper. For 30 ternary π–anion−π′ sandwich complexes, we give dRPA interaction energies as reference values. The double hybrid functionals are much more efficient but less accurate and precise than dRPA. The dispersion-corrected double hybrid PWPB95–D3(BJ) and B2PLYP–D3(BJ) functionals perform better than the GGA and meta-GGA functionals for the present test set.

Among the computationally efficient semilocal density functionals for the exchange-correlation energy, meta-generalized-gradient approximations (meta-GGAs) are potentially the most accurate. Here, we assess the performance of three new meta-GGAs (revised Tao–Perdew–Staroverov–Scuseria or revTPSS, regularized revTPSS or regTPSS, and meta-GGA made simple or MGGA_MS), within and beyond their “comfort zones,” on Grimme’s big test set of main-group molecular energetics (thermochemistry, kinetics, and noncovalent interactions). We compare them against the standard Perdew–Burke–Ernzerhof (PBE) GGA, TPSS, and Minnesota M06L meta-GGAs, and Becke-3-Lee–Yang–Parr (B3LYP) hybrid of GGA with exact exchange. The overall performance of these three new meta-GGA functionals is similar. However, dramatic differences occur for different test sets. For example, M06L and MGGA_MS perform best for the test sets that contain noncovalent interactions. For the 14 Diels–Alder reaction energies in the “difficult” DARC subset, the mean absolute error ranges from 3 kcal mol–1(MGGA_MS) to 15 kcal mol–1(B3LYP), while for some other reaction subsets the order of accuracy is reversed; more generally, the tested new semilocal functionals outperform the standard B3LYP for ring reactions. Some overall improvement is found from long-range dispersion corrections for revTPSS and regTPSS but not for MGGA_MS. Formal and universality criteria for the functionals are also discussed.

We have improved the revised Tao–Perdew–Staroverov–Scuseria (revTPSS) meta-generalized gradient approximation (GGA) in order to remove the order of limits anomaly in its exchange energy. The revTPSS meta-GGA recovers the second-order gradient expansion for a wide range of densities and therefore provides excellent atomization energies and lattice constants. For other properties of materials, however, even the revTPSS does not give the desired accuracy. The revTPSS does not perform as well as expected for the energy differences between different geometries for the same molecular formula and for the related nonbarrier height chemical reaction energies. The same order of limits problem might lead to inaccurate energy differences between different crystal structures and to inaccurate cohesive energies of insulating solids. Here we show a possible way to remove the order of limits anomaly with a weighted difference of the revTPSS exchange between the slowly varying and iso-orbitals (one- or two-electron) limits. We show that the new regularized (regTPSS) gives atomization energies comparable to revTPSS and preserves the accurate lattice constants as well. For other properties, the regTPSS gives at least the same performance as the revTPSS or TPSS meta-GGAs.

Correlated ab initio wave function calculations have been performed, using nonrelativistic frozen core MP2 complete basis set extrapolation model chemistry. The calculations have been made for three test sets of gas-phase saccharide conformations to provide reference values for their relative energies. The remaining correlation effects are estimated from frozen core coupled-cluster singles and doubles [CCSD(T)] calculations. The test sets consist of 15 conformers of α- and β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-d-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol. These benchmark quality relative conformational energies are used to re-evaluate the performance of the best density functional methods for conformational analyses of saccharides. Our results show that the B3PW91 and PBE0 relative energies are systematically better than the B3LYP and M05-2X results. Overall, the functionals based on the exact constraints perform better for the relative energies of monosaccharide conformers than the empirically fitted functionals.

Global hybrids, which add a typically modest fraction of the exact exchange energy to a complement of semilocal exchange−correlation energy, are among the most widely used density functionals in chemistry and condensed matter physics. Here we briefly review the formal and practical advantages and disadvantages of global hybrids. We point out that empiricism seems unavoidable in the construction of global hybrids, as it is not for most other kinds of density functional. Then we use one to three parameters to hybridize many semilocal functionals (including recently developed nonempirical generalized gradient approximations or GGA’s and meta-GGA’s). We study the performance of these global hybrids for many properties of sp-bonded molecules composed from the lighter atoms of the periodic table: atomization energies, barrier heights, reaction energies, enthalpies of formation, total energies, ionization potentials, electron affinities, proton affinities, and equilibrium bond lengths. We find several new global hybrids that perform better in these tests than standard ones, and we correct some errors in literature assessments. We also discuss the representativity of small fitting sets and the adequacy of various Gaussian basis sets.

There is current interest in the random phase approximation (RPA), a “fifth-rung” density functional for the exchange−correlation energy. RPA has full exact exchange and constructs the correlation with the help of the unoccupied Kohn−Sham orbitals. In many cases (uniform electron gas, jellium surface, and free atom), the correction to RPA is a short-ranged effect that is captured by a local spin density approximation (LSDA) or a generalized gradient approximation (GGA). Nonempirical density functionals for the correction to RPA were constructed earlier at the LSDA and GGA levels (RPA+), but they are constructed here at the fully nonlocal level (RPA++), using the van der Waals density functional (vdW-DF) of Langreth, Lundqvist, and collaborators. While they make important and helpful corrections to RPA total and ionization energies of free atoms, they correct the RPA atomization energies of molecules by only about 1 kcal/mol. Thus, it is puzzling that RPA atomization energies are, on average, about 10 kcal/mol lower than those of accurate values from experiment. We find here that a hybrid of 50% Perdew−Burke−Ernzerhof GGA with 50% RPA+ yields atomization energies much more accurate than either one does alone. This suggests a solution to the puzzle: While the proper correction to RPA is short-ranged in some systems, its contribution to the correlation hole can spread out in a molecule with multiple atomic centers, canceling part of the spread of the exact exchange hole (more so than in RPA or RPA+), making the true exchange−correlation hole more localized than in RPA or RPA+. This effect is not captured even by the vdW-DF nonlocality, but it requires the different kind of full nonlocality present in a hybrid functional.

Density functionals fail to provide a consistent description of weak intra- (i.e., short-range) and inter- (i.e., long-range) molecular interactions arising from nonoverlapping electron densities. An efficient way to correct the long-range errors is to add an empirical atom pair wise interaction-correction, inspired by the Lennard-Jones potential (R−6dependence). We show that the universal damping function of Tang and Toennies (TT) that includes higher-order correction terms (R−8and R−10dependent) reduces the intramolecular errors more efficiently, without altering the long-range correction. For general applicability, the TT damping function is augmented by a Fermi damping to prevent corrections at covalent distances. The performance of the new dD10 correction was tested in combination with three nonempirical GGAs (PBE, PBEsol, RGE2) on 64 illustrative reaction energies featuring both intra- and intermolecular interactions. With only two empirical parameters, PBE-dD10 outperforms the computationally more demanding and most recent functionals such as M06-2X or B2PLYP-D (MAD = 3.78 and 1.95 kcal mol−1, respectively). At the cc-pVTZ level, PBE-dD10 (MAD = 1.24 kcal mol−1) considerably reduces common DFT errors successfully balancing intra- (short-range) and inter- (long-range) molecular interactions. While REG2-dD10 performs closely to PBE-dD10 (MAD = 1.48 kcal mol−1), the overall MAD of PBEsol-dD10 is again slightly higher (MAD = 1.76 kcal mol−1).

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg−Kohn and Kohn−Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations. (4) “Spin contamination” of the determinant of Kohn−Sham orbitals for an open-shell system is not wrong but right. (5) Only to the extent that symmetries of the interacting wave function are reflected in the spin densities should those symmetries be respected by the Kohn−Sham noninteracting or determinantal wave function. Functionals below the highest level of approximations should however sometimes break even those symmetries, for good physical reasons. (6) Simple and commonly used semilocal (lower-level) approximations for the exchange-correlation energy as a functional of the density can be accurate for closed systems near equilibrium and yet fail for open systems of fluctuating electron number. (7) The exact Kohn−Sham noninteracting state need not be a single determinant, but common approximations can fail when it is not. (8) Over an open system of fluctuating electron number, connected to another such system by stretched bonds, semilocal approximations make the exchange-correlation energy and hole-density sum rule too negative. (9) The gap in the exact Kohn−Sham band structure of a crystal underestimates the real fundamental gap but may approximate the first exciton energy in the large-gap limit. (10) Density functional theory is not really a mean-field theory, although it looks like one. The exact functional includes strong correlation, and semilocal approximations often overestimatethe strength of static correlation through their semilocal exchange contributions. (11) Only under rare conditions can excited states arise directly from a ground-state theory.

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of α- and β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-d-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol. Results obtained with the Hartree−Fock method, with pure density functional approximations (DFAs) like LSDA, PBEsol, PBE, and TPSS and with hybrid DFAs like B3PW91, B3LYP, PBEh, and M05-2X, were then compared to the reference and local MP2 relative energies. Basis sets included 6−31G*, 6−31G**, 6−31+G*, 6−31+G**, 6−311+G**, 6−311++G**, cc-pVTZ(-f), cc-pVTZ, and aug-cc-pVTZ(-f). The smallest basis set that gives good DFA relative energies is 6−31+G**, and more converged results can be obtained with 6−311+G**. The optimized geometries obtained from a smaller basis set, 6−31+G*, were useful for subsequent single point energy calculations with larger basis sets. The best agreement with MP2 was shown by M05-2X, but only when using a dense DFT grid. The popular B3LYP functional is not the best for saccharide conformational studies. The B3PW91 functional gives systematically better results, but other hybrid functionals like PBEh or TPSSh are even better. Overall, the nonempirical PBE GGA and TPSS meta-GGA functionals also performed better than B3LYP.

A new, regularized gradient expansion (RGE) approximation density functional (i.e., a generalized gradient approximation or GGA that recovers the second-order gradient expansion for exchange in the slowly varying limit) was designed in an attempt to obtain good solid-state and molecular properties at the same time from a single GGA. We assess the performance of this functional for molecular atomization energies, solid lattice constants, and jellium surface energies. We compare the performance of this functional to the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA.

Serious and systematic errors with popular density functionals occur for isodesmic stabilization energies of n-alkanes, isomerization, and dimerization energies of hydrocarbons and geometries of sterically overcrowded aromatic systems. These functionals are too biased toward the correct description of free atoms. Changing two parameters within the Perdew-Burke-Ernzerhof approximation leads to a new nonempirical functional, PBEsol, that improves the description of large organic systems.

Relative stabilities of rotamers of the N‐acetyl‐O‐(2‐acetamido‐2‐deoxy‐α‐D‐galactopyranosyl)‐l‐seryl‐N′‐methyl amide (1) and eleven analogous molecules containing β‐galactose, α‐ and β‐mannose, α‐ and β‐glucose, and l‐threonine were calculated to learn whether they could explain the natural preference for 1in linkages between the carbohydrate and protein in glycoproteins. The lowest energy rotamers of four O‐glycoside models of serine diamide were identified with a Monte Carlo search coupled with molecular mechanics (MM2*). These rotamers were further optimized with an ab initio level of theory (HF/6‐31G(d)). Subsequently, B3LYP/6‐31+G(d) single point energies were calculated for the most stable HF structures. The most favorable interactions are present in 1and its glucose analogue. The monosaccharide for the carbohydrate antenna is anchored to the serine residue with an AcNH⋅⋅⋅OC‐NHMe hydrogen bond in the most stable rotamers. The mannose analogue and the β‐anomers are considerably less stable according to the MM2* and especially to the ab inito energy values. The three analogues have HF/6‐31G(d) energies which are 4–6 kcal mol−1higher; the single point B3LYP/6‐31+G(d)//HF/6‐31G(d) calculations yield preferences of 3–5 kcal mol−1for 1. The most stable l‐threonine analogues show a behaviour very similarly to the corresponding serine analogues. The ZPE and thermal correction components of the calculated ΔH298and ΔG298values are relatively small (<0.4 kcal mol−1). However, the TΔS298term can be as large as 2.6 kcal mol−1. The entropy terms stabilize the α‐anomers relative to β‐anomers, and ManNAc relative to GalNAc. The largest stabilization effect is observed for one of the rotamers of the α‐anomer of ManNAc.

Abstract.: Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92?kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27?kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set.

Abstract.: Gaussian-3 ground-state total electronic energies have been approximated using single point 6-31G(d) basis set Harteee–Fock self-consistent-field (HF-SCF) total energies and partial charges based on our earlier rapid estimation of correlation energy from partial charges method. Sixty-five closed-shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2/97 thermochemistry database were selected for the present study. The main feature in this work is that the␣basis set error has been treated by the least squares fit of rapid estimation of basis set error and correlation energy from partial charges (REBECEP) atomic parameters. With these parameters a rather accurate closed-shell ground-state electronic total energy can be obtained from a small basis set HF-SCF calculation in the vicinity of stationary points. The average absolute deviation of the best REBECEP enthalpies of formation from the experimental enthalpies of formation is 1.39 kcal/mol for the test set of 65 enthalpies of neutral molecules.

The accuracy of the RECEP method [Chem Phys 1997, 224, 33 and Chem Phys Lett 1999, 307, 469] has been increased considerably by the use of fitted atomic correlation parameters. This method allows an extremely rapid, practically prompt calculation of the correlation energy of molecules after an HF‐SCF calculation. The G2 level correlation energy and HF‐SCF charge distribution of 41 closed‐shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2 thermochemistry database were used to obtain the fitted RECEP atomic correlation parameters. Four different mathematical definitions of partial charges, as a multiple choice, were used to calculate the molecular correlation energies. The best results were obtained using the natural population analysis, although the other three are also recommended for use. For the 41 molecules, the G2 results were approached within a 1.8 kcal/mol standard deviation (the mean absolute difference was 1.5 kcal/mol). The RECEP atomic correlation parameters were also tested on a different, nonoverlapping set of other 24 molecules from the G2 thermochemistry database. The G2 results of these 24 molecules were approached within a 2.3 kcal/mol standard deviation (the mean absolute difference was 1.9 kcal/mol). This method is recommended to estimate total correlation energies of closed shell ground‐state neutral molecules at stationary (minimums and transition states) points on the potential surface. Extension of the work for charged molecules, radicals, and molecules containing other atoms is straightforward. Numerical example as a recipe is also provided. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 241–254, 2001

The self‐consistent Madelung potential (SCMP) approach for calculating molecular wave functions for a subunit embedded in a symmetrical environment constituted by the copies of the subunit is implemented with semiempirical NDDO model Hamiltonians and supplemented with empirically parameterized dispersion–repulsion interaction potentials. This model yields sublimation enthalpies in good agreement with available experimental data for a series of molecular crystals, including imidazol, benzimidazole, urea, urethane, dicyaneamide, formamide, uracil, cytosine, maleic anhydride, succinic anhydride, and 1,3,5‐triamino‐2,4,6‐trinitro‐benzene. The SCMP‐NDDO method, which avoids difficulties concerning the parametrization of charges in the molecular mechanics force fields, is proposed mainly for the treatment of molecular crystals with large unit cells. It might be particularly useful where important charge reorganization is expected under the effect of the crystal field. Charge distributions, obtained by the SCMP and the simple dielectric cavity self‐consistent reaction field models, are compared and analyzed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 38–50, 1998

He(I) and He(II) photoelectron spectra of phenylphosphine and phenylarsine have been investigated and assigned. The rotational barrier of the phosphino group has been investigated at the MP2/6-31G(d,p)//MP2/6-31G(d,p) and HF/6-31G(d,p)//HF/6-31G(d,p) levels of theory, and that of the arsino group at the HF/6-31G(d,p)//6-31G(d,p) levels of theory. The rotational barrier of the two molecules is nearly the same. The energy difference between the two possible conformers of the molecules is low (1.5 kJ/mol at the MP2/6-31G(d,p) level of theory), allowing nearly free rotation about the P-C bond. The photoelectron spectrum cannot be interpreted by considering the most stable rotamer, but all possible conformers should be taken into account. The present interpretation is consistent with the smallnp- π interaction concluded from other investigations. The rotational barrier ofo-phosphinophenol is significantly larger than for phenylphosphine, and the photoelectron spectrum of this compound can be interpreted by considering a single conformer, and no appreciable interaction between the π-system of the ring and the phosphorus lone pair.

Vibrational analysis of tellurium tetrachloride, TeCl4, was performed with Hartree–Fock (HF), MP2, and generalized gradient approximation density functional theory (DFT) methods supplemented with polarized double-zeta split valence (DZVP) basis sets and relativistic effective core potentials (RECP) of Hay and Wadt. The molecular geometry is best reproduced at the HF and MP2/RECP+DZVP [polarized Hay and Wadt RECP for Te and 6–31G(d) basis set for Cl] levels of theory. The DFT methods gave rise to poorer results, especially those using Becke's 1988 exchange functional. Generally, the vibrational frequencies calculated by the MP2 and B3-type DFT methods with the all electron and RECP+DZVP basis sets as well as at the HF/RECP level were in satisfactory accord with the experimental data. The agreement was good enough to assist the assignment of the measured vibrational spectra. The best agreement with the experimental vibrational frequencies was achieved with the scaled HF/RECP force field. Consistent results were obtained for the unobserved A2 (ν4) fundamental, where the results of the best methods were within 4 cm⁻¹. The best force fields were obtained with the following methods: Becke3–Lee–Yang–Parr and Becke3–Perdew/all electron basis, MP2 and Becke3-Perdew/RECP+DZVP, and HF/RECP. The methods using RECPs are advantageous for large-scale computations. The RECP basis set effectively compensates the errors of the HF method for TeCl4; however, it provides poor results with correlated methods. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 308–318, 1998

Vibrational analysis of tellurium tetrachloride, TeCl4, was performed with Hartree–Fock (HF), MP2, and generalized gradient approximation density functional theory (DFT) methods supplemented with polarized double‐zeta split valence (DZVP) basis sets and relativistic effective core potentials (RECP) of Hay and Wadt. The molecular geometry is best reproduced at the HF and MP2/RECP+DZVP [polarized Hay and Wadt RECP for Te and 6–31G(d) basis set for Cl] levels of theory. The DFT methods gave rise to poorer results, especially those using Becke's 1988 exchange functional. Generally, the vibrational frequencies calculated by the MP2 and B3‐type DFT methods with the all electron and RECP+DZVP basis sets as well as at the HF/RECP level were in satisfactory accord with the experimental data. The agreement was good enough to assist the assignment of the measured vibrational spectra. The best agreement with the experimental vibrational frequencies was achieved with the scaled HF/RECP force field. Consistent results were obtained for the unobserved A2(ν4) fundamental, where the results of the best methods were within 4 cm−1. The best force fields were obtained with the following methods: Becke3–Lee–Yang–Parr and Becke3–Perdew/all electron basis, MP2 and Becke3‐Perdew/RECP+DZVP, and HF/RECP. The methods using RECPs are advantageous for large‐scale computations. The RECP basis set effectively compensates the errors of the HF method for TeCl4; however, it provides poor results with correlated methods. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 308–318, 1998

The performance of the currently used generalized gradient approximation density functionals is analyzed using several simple, yet critical requirements. We analyze the effects of the self‐interaction error, the inclusion of the exact exchange, and the parameter settings used in the popular three‐parameter hybrid density functionals. The results show that the elimination of the self‐interaction error from the current density functionals lead to very poor results for H2. The inclusion of the exact exchange does not significantly influence the self‐interaction corrected results. The variation of the A, B, and Cparameters of a hybrid DFT method influences the H(SINGLE BOND)H equilibrium bond length through a very simple linear equation, and it is possible to reproduce the experimental H(SINGLE BOND)H distance with appropriate selection of these parameters, although an infinite number of solutions exists. Similar results were obtained for the total energy and the electron density along the internuclear axis. The analysis of the exact KS potential at the bond critical point of the dissociating H2molecule shows that, for this property, the second order Moller–Plesset perturbation theory yields a better potential than the density functionals studied in this article. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 1534–1545, 1997

The geometry and vibrational spectrum of TeCl4 was calculated with various quantum chemical methods [Hartree–Fock, second-order Møller-Plesset (MP2) and generalized gradient approximation density functional theory (GGA-DFT)]. Five different basis-set combinations were tested: the relativistic effective core potentials with double-zeta split valence basis (RECP) of Hay & Wadt (HW) and Stevens et al. (CEP); the above RECP basis sets extended with polarization functions for Te and using a 6-31G* basis for Cl (HW* and CEP*); a medium-size all-electron basis set (ALL). The quality of the calculated data was assessed by comparison with recent experimental results. The Hartree-Fock method combined with the HW and CEP basis sets provided a very good approximation of the experimental vibrational spectra. The quality of the results is comparable to those of the best methods (MP2, B3-P, B3-PW with HW* and CEP* and B3-LYP, B3-P, B3-PW with the ALL basis set). However, the HW and CEP basis sets provided very poor geometry and vibrational frequencies when they were used in combination with any correlated method in this work. Similarly, the DFT methods using Becke's 1988 exchange functional (B-LYP, B-P, B-PW) without the inclusion of the exact exchange let to very poor results with the basis sets used in this study. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 817–826, 1997