A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Performance of DFT hybrid functionals in the theoretical treatment of H‐bonds: Analysis term‐by‐term

The performance of DFT to reproduce noncovalent interactions like H‐bonds was assessed. Three DFT hybrid functionals (B3LYP, BHandHLYP from Jaguar5.5, and BHandHLYP from G03) were used to calculate the interaction energies and H‐bond distances of several host–guest complexes theoretically designed. Two reference systems (whose experimental data were available) were also calculated at the same levels of theory. In all the cases B3LYP and BHandHLYP from G03 gave rather the same results of interaction energy and distances, whereas the functional BHandHLYP from Jaguar5.5 overestimated the interaction energies and underestimated the H‐bond distances. Considering the construction of each functional, the terms responsible for such differences are the gradient correction to the exchange functional (Becke88) and the correlation functional (VWN, LYP) and not the Hartree–Fock contribution. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A comparative study of DFT and traditional ab initio methodologies on the OsO4 molecule

The performance of different conventional ab initio methodologies and density functional procedures is compared through its application to the theoretical calculation of the bond distance and harmonic vibrational frequencies of the OsO₄ molecule. The problem of the basis set is first considered, with up to nine different basis sets being tested in calculations using the hybrid Becke3LYP density functional, and the most appropriate basis set is used in the comparison of Hartree–Fock, post‐Hartree–Fock, and density functional methods. The post‐Hartree–Fock methods analyzed are MP2, CISD, and CCSD(T), and the density functionals tested are SVWN, BLYP, BPW91, and Becke3LYP. The results show that for this particular system density functional methods perform better than do HF‐based methods with the exception of CCSD(T), which gives the best overall results. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 544–551, 2000     

A comparative quantum mechanical study of bond separation energies as a measure of cyclic conjugation

Restricted Hartree-Fock (RHF), second-order Møller-Plesset (MP2), and density functional calculations [using the Becke/Lee-Yang-Parr (B-LYP) exchange/correlation gradient-corrected functionals] employing the 6-311G(d, p) and 6-311 + + G(d, p) basis sets have been carried out to calculate isodesmic bond separation energies for reactions involving a number of representative five- and six-membered ring organic compounds. The MP2 and density functional approaches yield reasonably good energies; the density functional method agrees particularly well with experiment, exhibiting a root-mean-square error of only 2.5 kcal/mol. Ring geometries are calculated satisfactorily in all approaches but are given particularly accurately by the MP2 approach. A comparison of the B-LYP bond separation energies with several other definitions of resonance energy shows that these different approaches correlate with each other in a reasonable fashion. © 1995 John Wiley & Sons, Inc.     

Electron correlation and relativistic effects in xenon tetrafluoride

Ab initio all-electron fully relativistic Dirac–Fock self-consistent field and Dirac–Fock–Breit calculations are reported for the XeF₄ molecule at various internuclear distances assuming the experimental D_4h geometry with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₄ at various internuclear distances. The calculated relativistic correction to the total energy of molecule at the Dirac–Fock level is ～ ?5856 eV, whereas the magnetic part of the Breit correction to the electron-electron interaction is calculated as ～ 177 eV. The electron correlation effects were included in the nonrelativistic Hartree–Fock calculations using the second-order Møller-Plesset (MP 2) theory, and the calculated correlation energy for XeF₄ is ?71 eV. The basis-set superposition error (BSSE ) was estimated by using the counterpoise method for Xe and F. The inclusion of both the relativistic and electron correlation effects in the calculated total energies of F, Xe, and XeF₄ predicts the Xe—F bond length and dissociation energy of XeF₄ as 1.952 Å and 5.59 eV, respectively, which are in excellent agreement with the experimental values of 1.953 Å and 5.69 eV, respectively, for XeF₄. The contribution of the electron correlation and relativistic effects to the dissociation energy of XeF₄ is 8.11 and 0.05 eV, respectively. The Breit interaction, however, contributes only 0.02 eV to the dissociation energy of XeF₄. Electron correlation is most significant for the prediction of an accurate value of dissociation energy, whereas relativistic effects are very important for the prediction of spin-orbital splitting as well as the energies of the orbitals, especially the inner orbitals of XeF₄. © 1995 John Wiley & Sons, Inc.     

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

Proton transfer in small model systems: A density functional study

The structures, interaction energies, and proton-transfer features of some representative intermolecular complexes are determined by using a density functional which incorporates gradient corrections and, as recently suggested by Becke, some Hartree–Fock exchange. The results are compared with those obtained by high-order many-body perturbation theory and by a number of more conventional density functionals. Hydrogen-bond strengths and interatomic distances between heavy atoms are well reproduced by several density functionals. However, inclusion of some Hartree–Fock exchange is mandatory to improve XH bond lengths, and, especially, energy barriers governing proton transfer. Use of the new functional significantly improves the agreement with experimental and post-Hartree–Fock results. This paves the route for a detailed theoretical study of proton-transfer processes in large, biologically significant systems. © 1995 John Wiley & Sons, Inc.     

On Ethylene Polymerisation with Aluminium and Scandium Complexes: DFT and Post‐HF Calculations

Summary: The performance of Density Functional Theory (DFT) methods in predicting ethylene polymerisation and/or oligomerisation activity in selected aluminium and scandium based complexes was studied using both DFT and post‐Hartree‐Fock CCSD(T) calculations. Whereas previous reports have drawn attention to the underestimation of the barrier for the β‐hydrogen termination process for a few aluminium based species, we found that the same holds for the corresponding scandium complexes. New, however, is the observation that apart from underestimating the energy barrier connected to β‐hydrogen termination, the insertion of ethylene is also severely underestimated by the DFT methods applied compared to post‐Hartree‐Fock calculations up to the CCSD(T) level.

Structure of the diketiminate complex referred to in the text.     

Coulomb-Hole–Hartree–Fock functional

We have extended to molecules a density functional previously parametrized for atomic computations. The Coulomb-hole–Hartree–Fock functional, introduced by Clementi in 1963, estimates the dynamical correlation energy by the computations of a Hartree–Fock-type single-determinant wave function, where the Hartree–Fock potential was augmented with an effective potential term, related to a hard Coulomb hole enclosing each electron. The method was later revisited by S. Chakravorty and E. Clementi [Phys. Rev. A 39 , 2290 (1989)], where a Yukawa-type soft Coulomb hole replaced the previous hard hole; atomic correlation energies, computed for atoms with Z = 2 to Z = 54 as well as for a number of excited states, validated the method. In this article, we parametrized a function, which controls the width of the soft Coulomb hole, by fitting the first and second atomic ionization potentials of the atoms with 1 ? Z ? 18. The parametrization has been preliminarily validated by computing the dissociation energy for a number of molecules. A few-determinant version of the Coulomb-hole–Hartree–Fock method, necessary to account for the nondynamic correlation corrections, is briefly discussed. © 1994 John Wiley & Sons, Inc.     

Theoretical study of the internal elimination reactions of xanthate precursors

The gas‐phase internal elimination (E_i) reaction of ethyl xanthate (CH₃‐CH₂‐S‐CS‐O‐CH₃) has been investigated by means of Hartree–Fock, second‐order Møller–Plesset, and density functional theory (DFT) using the Becke three‐parameter Lee–Yang–Parr (B3LYP) functional and the modified Perdew–Wang one‐parameter model for kinetics (MPW1K). Considerable differences between the ground‐ and transition‐state geometries and the calculated activation energies are observed from one approach to the other, which justifies first a careful calibration of the methods against the results of benchmark CCSD(T) calculations. Compared with these, DFT calculations along with the MPW1K functional are found to be an appropriate choice for describing the E_i reaction of xanthate precursors. The precursor conformation and the transition states involved in the internal conversion of xanthate precursors of cyano derivatives of ethylene, and of cis‐ and trans‐stilbene, are then characterized in detail by means of this functional. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 2023–2031, 2003     

A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97)

We applied an improved long‐range correction scheme including a short‐range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau‐B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long‐range portion of Hartree‐Fock (HF) exchange to excitation energies of large molecules (Chai and Head‐Gordon, J Chem Phys 2008, 128, 084106) and additional short‐range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short‐range to mid‐range (0.5–3 Å) to ground state properties achieved high performances of LCgau‐B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x‐family. We also found that while a small μ value (～0.2) in LC‐DFT is appropriate to the local excitation and intramolecular charge‐transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation‐energy calculations. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Explicitly correlated configuration interaction studies using spherical Gaussians. II. Exploratory studies on LiH

Ab initio self-consistent-field and configuration interaction studies have been carried out on the ground state of the LiH molecule at its equilibrium distance. Floating spherical Gaussian basis orbitals (FSGO ) were employed, along with spherical Gaussian correlation factors, using the procedure described in the preceding paper. A near-Hartree–Fock function was found using only 13 FSGO . Exploratory configuration interaction studies recovered approximately 73% of the inner shell correlation energy and approximately 56% of the total correlation energy with five configurations plus the Hartree–Fock configuration. These studies indicate that, by using spherical Gaussian correlation factors, direct introduction of interelectronic coordinates into trial wave functions can be accomplished for molecular systems. It was also shown that correlating configurations need not utilize the full Hartree–Fock basis, but may use substantially smaller bases and still recover correlation energy effectively. Finally, the results indicate that, in spite of their improper cusp behavior, FSGOS and spherical Gaussian correlation factors can be used for construction of high accuracy wave functions.     

Examination of several density functionals in numerical Kohn–Sham calculations for atoms

We studied several exchange‐only and exchange–correlation energy density functionals in numerical, i.e., basis‐set‐free, nonrelativistic Kohn–Sham calculations for closed‐shell ¹S states of atoms and atomic ions with N electrons, where 2≤N≤120. Accurate total energies are presented to serve as reference data for algebraic approaches, as do the numerical Hartree–Fock results, which are also provided. Gradient‐corrected exchange‐only functionals considerably improve the total energies obtained from the usual local density approximation, when compared to the Hartree–Fock results. Such an improvement due to gradient corrections is not seen in general for highest orbital energies, neither for exchange‐only results (to be compared with Hartree–Fock results), nor for exchange–correlation results (to be compared with experimental ionization energies). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 227–241, 2001     

On the stability of the hydrogen chloride complexes with ethylene and acetylene. A high resolution gas phase and ab initio study

The temperature dependencies of the intensities of the HCl stretching bands of the hydrogen chloride complexes with acetylene and ethylene have been used to obtain estimates of the dissociation enthalpies of the two complexes. Quantum chemical calculations on the Hartree Fock and DFT/B3LYP levels of theory have been combined with experimental data to give estimates of the intensities of the HCl stretching vibration in the two complexes.     

Theoretical study of 1,3-dipolar cycloadditions of nitrone and fulminic acid with substituted ethylenes

Molecular orbital calculations were performed to examine the electronic effects involved in the regioselectivity in the 1,3-dipolar cycloaddition reaction of nitrone and fulminic acid. The substituted ethylene dipolarophiles were selected to represent a range of electron-donating/withdrawing abilities: amino, methyl, carbaldehyde (both in the s-cis and the s-trans conformations), and nitrile. The reactions were all asynchronous, with early transition sites. The regioselectivity was correlated with the ability of the substituent to donate or withdraw electrons. With electron-donating substituents, the substituent was directed preferentially to the oxygen end of the dipole and this shifted toward the other regioisomer as the electron-withdrawing ability of the substitutent increased. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1795–1804, 1998     

Investigation of the use of density functionals in second‐ and third‐row transition metal dimer calculations

We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second‐row transition metals, platinum, and gold. The outermost s–d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second‐ and third‐row transition metal atoms. Compared with the first‐row transition metal dimer calculations (J Chem Phys 2000, 112, 545–553), the binding energies calculated using the combination of the Becke 1988 exchange and the one‐parameter progressive correlation (BOP) functional and Becke's three‐parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high‐angular‐momentum open‐shell orbitals. Analysis of the s–d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long‐range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree–Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1995–2009, 2001     

Ab initio study of organic mixed valency

A series of six radical cations of the type (D L D)⁺ was investigated at the ab initio unrestricted Hartree–Fock level. One localized and one delocalized conformation were systematically searched by full geometry optimization. At both nuclear arrangements, mostly found as being minima in the symmetry‐restrained Hartree–Fock framework, excitation energies were calculated through the expansion of the wave function on single electronic excitations of the Hartree–Fock fundamental determinant and at the unrestricted Hartree–Fock or at the multiconfigurational self consistent field levels. Few calculations were also performed by taking into account some part of the electronic correlation. Except for N,N,N′,N′‐tetramethyl p‐phenylenediamine, all the studied compounds are localized stable cations, at the symmetry‐restrained Hartree–Fock level. However, the reoptimization of their wave function changes this observation since only three of them seem to conserve a localized stable conformation. Most of the studied systems are characterized by one or two excited electronic states very close to the fundamental one and should thus present an unresolved broadened first absorption band in the near‐infrared region. These features are in agreement with the available experimental data. Strong Hartree–Fock instabilities are found for the delocalized structure and put in relation with the existence of the large nonadiabatic coupling in this conformational region. The solvent influence is discussed in the Onsager dipolar reaction field framework. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 552–573, 2000     

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998     

Perturbation treatment of the Hartree–Fock equations of 1s2p3s 4Pθ state of the lithium isoelectronic sequence

The first order Hartree–Fock equations of the 1s2p3s ⁴P⁰ state of the three-electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree–Fock energy up to third order with high accuracy. The third order Hartree–Fock energies for Li to Ne⁷⁺ are compared with those derived from experiment and other theoretical calculations.     

Quantum chemical prediction of the adsorption conformations and dynamics at HCOOH‐covered ZnO(1010) surfaces

Results from ab initio Hartree–Fock and gradient‐corrected density functional theory calculations of formic acid interactions with ZnO (101 0) surfaces are reported. Surface relaxation is found to affect equilibrium geometries and adsorption energies significantly. Large variations in adsorption energy with coverage and ordering of the adsorbates are revealed and explained in terms of strong and highly anisotropic electrostatic adsorbate–adsorbate interactions. The results are compared to published experimental and theoretical results, and differences in suggested binding geometries from the different studies are discussed. Dynamic properties of the adsorption, surface mobility, and surface reactivity are inferred from key elements of the potential energy surface obtained from the quantum chemical computations and supported by ab initio molecular dynamics simulations. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002