The inclusion of correlation in the calculation of phosphorus NMR chemical shieldings

The effects of including correlation in the calculation of phosphorus nuclear magnetic resonance (NMR) chemical shielding has been investigated for a variety of molecules in the Hartree-Fock, second-order Møller-Plesset (MP2), and estimated infinite-order Møller-Plesset theory ab initio approaches in the gauge including atomic orbital (GIAO) scheme. The inclusion of correlation in the shielding calculations often leads to significant changes from the Hartree-Fock theory and provides results that are in improved agreement with experiment. © 1996 John Wiley & Sons, Inc.     

Ab initio calculations on the barrier height for the hydrogen addition to ethylene and formaldehyde. The importance of spin projection

Heats of reaction and barrier heights have been computed for H + CH₂CH₂ → C₂H₅, H + CH₂O → CH₃O, and H + CH₂O → CH₂OH using unrestricted Hartree-Fock and Møller–Plesset perturbation theory up to fourth order (with and without spin annihilation), using single-reference configuration interaction, and using multiconfiguration self-consistent field methods with 3-21G, 6-31G(d), 6-31G(d,p), and 6-311G(d,p) basis sets. The barrier height in all three reactions appears to be relatively insensitive to the basis sets, but the heats of reaction are affected by p-type polarization functions on hydrogen. Computation of the harmonic vibrational frequencies and infrared intensities with two sets of polarization functions on heavy atoms [6-31G(2d)] improves the agreement with experiment. The experimental barrier height for H + C₂H₄ (2.04 ± 0.08 kcal/mol) is overestimated by 7?9 kcal/mol at the MP2, MP3, and MP4 levels. MCSCF and CISD calculations lower the barrier height by approximately 4 kcal/mol relative to the MP4 calculations but are still almost 4 kcal/mol too high compared to experiment. Annihilation of the largest spin contaminant lowers the MP4SDTQ computed barrier height by 8?9 kcal/mol. For the hydrogen addition to formaldehyde, the same trends are observed. The overestimation of the barrier height with Møller-Plesset perdicted barrier heights for H + C₂H₄ → C₂H₅, H + CH₂O → CH₃O, and H + CH₂O → CH₂OH at the MP4SDTQ /6-31G(d) after spin annihilation are respectively 1.8, 4.6, and 10.5 kcal/mol.     

Localized orbitals for the description of molecular interaction

The intermolecular interaction between the molecules CH₂O and NH₃ was investigated by the supermolecule method. The interaction energies were first calculated at the ab initio SCF level, and the electron correlation was included via second-order Møller-Plesset perturbation theory (MP 2). The basis set superposition error (BSSE ) was taken into account by the counter-poise (CP ) method. The occupied and the virtual canonical molecular orbitals (CMOS ) of the supermolecule were separately localized by the Boys' procedure. The correlation correction was calculated by the many-body perturbation theory (MBPT ) in the localized representation. Contributions of the third- and fourth-order localized diagrams were added to those of the second-order canonical diagram. This procedure gives a correction nearly equivalent to that of MP 2. The possibility to separate LMO contributions responsible for the dispersion interaction was investigated.     

Crystal and molecular structure of 1,1-quasigermatranediol-1,1-dihydroxy-2,8-dioxa-5-azagermocane

By X-ray diffraction the crystal and molecular structure of quasigermatranediol (HO)₂Ge(OCH₂CH₂)₂NH at 155 K is determined. By quantum chemical method using second-order Møller-Plesset perturbation theory (MP2) and a split-valence 6-311++G(d,p) basis set with polarization and diffuse functions for all types of atoms, the structural parameters of this molecule are calculated. In the crystal, the quasigermatranediol molecules are arranged in columns due to O-H...O and N-H...O hydrogen bonds of medium strength. The columns are linked together via weak O-H...O and N-H...O hydrogen bonds. By calorimetry, the phase transition in a crystal of quasigermatranediol at 150–145 K is revealed.     

Ab initio studies of the ground-state potential energy surface of formamide

Ab initio calculations employing a standard double-zeta basis set augmented with various polarization functions have been used to investigate the lowest energy region of the ground-state potential energy surface of the formamide molecule. Hartree-Fock calculations with only d polarization functions on the nonhydrogen atoms located two stable minima, that with geometry distorted from planarity having slightly lower energy; only one stable minimum with planar structure is found when p polarization functions on the hydrogens are included. In contrast optimizations, which account approximately for the correlation energy using second-order Møller-Plesset perturbation theory consistently favor a single slightly nonplanar minimum energy geometry.     

Peculiarities of the effects of trifluoromethyl and alkoxycarbonyl groups on the structure and reactivity of acrylates

Ab initio quantum-chemical calculations of molecules of CF₃-substituted acrylates and their non-fluorinated analogs were carried out by the restricted Hartree-Fock (RHF) method and at the second-order Møller-Plesset (MP2) level of perturbation theory using the 6–31G^* basis set with full geometry optimization. Peculiarities of their molecular and electronic structure were revealed and the dipole moments, the polarizability and first molecular hyperpolarizability tensors, harmonic vibrational frequencies, electrostatic potentials, and local electron densities in the vicinity of the carbon atoms of the C=C bond were calculated. It was shown that CF₃-substituted acrylates are conjugated systems similar to their nonfluorinated analogs. Peculiarities of the structure and properties of CF₃-substituted acrylates are explained by p-π-interaction between the CF₃ group and the conjugated system.     

Basis set and correlation effects on computed proton affinities of some oxygen and nitrogen bases

Basis set expansion and correlation effects on the computed proton affinities of the oxygen and nitrogen bases CH₃OH, H₂CO, CO, CH₃NH₂, CH₂NH, and HCN have been evaluated. Basis set enhancements lead to systematic changes in computed proton affinities. These effects appear to be additive, and are greater for correlated proton affinities than for Hartree-Fock energies. Inclusion of correlation decreases proton affinities, with fourth-order Møller-Plesset energies bracketed by second and third order energies.     

The additivity of polarization function and electron correlation effects in ab initio molecular-orbital calculations

Several examples are preseted to show that estimated third-order Møller-Plesset (MP3) relative energies obtained from schemes which assume additivity of correlation and polarization function effects are likely to provide the most reliable energy comparisons in cases where full MP3 calculations with polarization basis sets are not feasible.     

Basis set and correlation effects on computed lithium ion affinities of some oxygen and nitrogen bases

Basis set expansion and correlation effects on computed lithium cation affinities have been evaluated for the oxygen and nitrogen bases CH₃OH, H₂CO, CO, CH₃NH₂, CH₂NH, and HCN. The presence of diffuse functions on nonhydrogen atoms is found to be the most important single enhancement of double- and triple-split valence plus polarization basis sets. With the triple-split basis, enhancement effects are nearly additive. Correlation usually decreases computed lithium ion affinities, with the second order Møller-Plesset correlation term being the dominant term.     

The use of the hybrid density functional theory (DFT) approach for calculation of vibrational spectra: nitromethane

The molecular geometry of nitromethane was optimized and its force field and vibrational spectrum were calculated by the BECKE3LYP method. The accuracy of optimization of the geometry of MeNO₂ obtained by this method using the 6–311G(d,p) and 6–311++G(d,p) basis sets is not poorer than that obtained at the second-order Møller-Plesset level of perturbation theory (MP2). The vibrational frequencies of nitromethane and its d₁, d₂, and d₃ isotopomers obtained by the BECKE3LYP method are in much better agreement with the experimental data than those calculated at the MP2 level using the same basis set. The average absolute error of calculations performed without the use of any scaling factors is ～2% for frequencies; the maximum deviation is ～4%.     

Use of molecular symmetry in two-electron integral transformation An MP2 program compatible with HONDO 5

A computer program is described which evaluates the second-order Møller-Plesset energy using the integral list formed by HONDO 5. In this program use may be made of full molecular symmetry for most common point groups, even if they contain two-dimensional representations. The algorithm for the integral transformation may also be applied to other methods beyond Hartree-Fock. Some numerical results and timings are presented.     

Bond alternation in infinite polyene: Peierls distortion reduced by electron correlation

The formation of the bond-alternating structure in polyene is investigated both within the one-particle (Hartree-Fock) picture and including electron correlation effects by perturbation theory. An off-diagonal charge-density wave of the equi-distant structure is identified at the Hartree-Fock level as precursor of the bond-alternate state which is found by subsequent lattice optimization. The valence-shell correlation energy is calculated by using second-order Møller-Plesset perturbation theory. It is found to be finite also in the metallic one-dimensional chain and a comparison with results obtained for the acetylene unit shows that this method recovers ~-70–75% of the total valence-shell correlation. Correlation effects are shown to reduce the Peierls distortion and the corresponding energy barrier but the bond alternation persists also if the results are extrapolated to the case of full correlation.     

Sixth-order many-body perturbation theory. I. Basic theory and derivation of the energy formula

The general expression for the sixth-order Møller-Plesset (MP6) energy, E(MP6), has been dissected in the principal part A and the renormalization part R. Since R contains unlinked diagram contributions, which are canceled by corresponding terms of the principal part A, E(MP6) has been derived solely from the linked diagram terms of the principal part A. These have been identified by a simple procedure that starts by separating A into connected and disconnected cluster operator diagrams and adding terms associated with the former fully to the correlation energy. After closing all open disconnected cluster operator diagrams, one can again distinguish between connected and disconnected energy diagrams, of which only the former lead to linked diagram representations and, therefore, contributions to E(MP6). The connected diagram parts of A have been collected in four energy terms E(MP6)₁, E(MP6)₂, E(MP6)₃, and E(MP6)₄. The sum of these terms has led to an appropriate energy formula for E(MP6) in terms of first- and second-order cluster operators. © 1996 John Wiley & Sons, Inc.     

An MP2 study on pre-reactive complexes (CH_2)_2O … XY (X,Y = H,F,Cl,Br,I)

The structures, energies, atomic chaiges and IR spectra of complexes (CH2)2O…XY (X, Y = H, F, Cl, Br, and I) have been examined by means of ab initio molecular orbital theory at the second-order level of Moller-Plesset perturbation correction. It is found that the hydrogen bond O…H-X is non-linear. The attraction between X and the H atoms in oxirane ring causes O…H-X bond bending. The hydrogen bond slighdy weakens the bond strength of C-O, and leads the bending and stretching mode of IR to shift to the red. The calculation results show that there is no evidence of a significant extent of proton transfer to give (CH2)2OH …X- in the isolated complexes.     

Internal rotation study of some sixfold barrier molecules

Molecular orbital calculations of sixfold barriers in nitromethane, methyl boron difluoride, and trifluoronitromethane were performed by various Hartree-Fock and electron correlation methods. In those calculations, staggered and eclipsed conformations are of primary concern. These results indicated that for CH₃NO₂ and CH₃BF₂ the staggered conformations are more stable, while CF₃NO₂ has a more stable conformation in an eclipsed form. Both conformations do not differ significantly, which may account for the low internal rotational barrier of each molecule. Values of the barrier calculated by the Møller-Plesset perturbation and the quadratic configuration interaction methods did not match the experimental results. However, better internal rotational barrier values of each molecule were observed when the improved better basis sets and the Hartree-Fock method were selected. © 1997 John Wiley & Sons, Inc.     

The ene reaction: Comparison of results of Hartree-Fock,Møller-Plesset,CASSCF, and DFT calculations

Structural and energetic aspects of the ene reaction were investigated using a variety of computational methods incorporating different ways of accounting for electron correlation. Compared to the noncorrelated Hartree-Fock method, opposing trends were observed in the geometry of the transition state when using the Complete Active Space-Self Consistent Field (CASSCF) method versus Møller-Plesset and density functional theory (DFT) methods. For reproducing experimental results, both Møller-Plesset and DFT methods appear to be successful, while the CASSCF method failed to reproduce the experimental energy changes. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 509–514, 1997     

The effect of electron correlation on the topological and atomic properties of the electron density distributions of molecules

The topological properties of the electron density and the properties of an atom in a molecule are calculated by means of second-order Møller-Plesset perturbation theory (MP2) and compared with the results of configuration interaction calculations (C12) which include all single and double substitutions from the Hartree-Fock reference configuration. A software package for analyzing the effects of electron correlation on the topological properties of the electron density of molecules is described. H₂CO is used to provide a numerical example and to indicate that the number of bond critical points is unaffected by the inclusion of electron correlation. Correlation leads to only a small shift in the positions of bond critical points and a small change in the electron density at bond critical points. It is further shown that the energy of an atom in a molecule can be calculated to an accuracy of 1 kcal/mol and the electron population of an atom to about 0.001e. A statistical method is used to show that the deviation of the MP2 correlation correction relative to the CI2 correlation correction for a variety of atomic properties is about 25%.     

Simplified reference wave functions for multireference perturbation theory

A number of simplifications in defining the reference wave functions used in multireference second-order M?ller-Plesset perturbation theory (MRMP2) calculations are studied. The usual multiconfigurational orbital optimization is avoided by using Hartree-Fock or Kohn-Sham orbitals; the complete configuration expansion in the active-space orbitals is replaced by a severely truncated expansion, and the spin-component-scaling idea is applied to the multireference perturbation expansion. We assess these approximations to the full procedure by calculating the barrier heights for 15 processes taken from the Zhao-Gonzalez-Garcia-Truhlar database. Our results suggest that reliable and relatively cheap reference wave functions for MRMP2 calculations can be obtained from the simplifications introduced here. We hope that this will enable the application of the MRMP2 method to a larger range of chemical systems.     

On the high accuracy of mp2-optimised geometmes and harmonic frequencies with large basis sets

An efficient procedure for the calculation of second derivatives of the energy at the closed-shell second-order Móller-Plesset (MP2) level of accuracy is described. The method is applied to H₂O, NH₃, H₂CO and HCN using large (TZ+2P or better) basis sets. For this set of molecules the accuracy of the optimised geometries is for single bonds ±0.002 Å, multiple bonds ±0.01 Å, angles ±0.2° and the mean error of the harmonic frequencies is 1.5%.