Intermolecular potential energy surface and second virial coefficients for the water-CO2 dimer

A five-dimensional potential energy surface is calculated for the interaction of water and CO(2), using second-order M?ller-Plesset perturbation theory and coupled-cluster theory with single, double, and perturbative triple excitations. The correlation energy component of the potential energy surface is corrected for basis set incompleteness. In agreement with previous studies, the most negative interaction energy is calculated for a structure with C(2v) symmetry, where the oxygen atom of water is close to the carbon atom of CO(2). Second virial coefficients for the water-CO(2) pair are calculated for a range of temperatures, and their uncertainties are estimated. The virial coefficients are shown to be in close agreement with the available experimental data.     

Perturbation expansion theory corrected from basis set superposition error II. Charge transfer,pair correlationand dispersion terms

The second-order perturbation theory based on the locally projected molecular orbitals is developed. A few test calculations with cc-pVDZ and aug-cc-pVDZ basis sets are carried out for the dimers, (H₂O)₂ and (HF)₂. The charge transfer terms remove the deficiency of the locally projected self-consistent field method for molecular interaction (LP SCF MO MI), and the potential energy curves calculated with aug-cc-pVDZ are very close to the corresponding curves of the counterpoise-corrected SCF energy. Only after adding the spin-exchanged dispersion type to the dispersion and intra-molecular pair correlation terms, the calculated potential energy curves become close to those of the counterpoise-corrected second-order Møller–Plesset (MP2). Pragmatic approaches for reducing the influence of the basis set superposition error are proposed.     

Application of many-body perturbation methods in a discrete orbital basis

The many-body perturbation theory techniques used by Kelly to calculate “pair correlation energies” have been implemented in a discrete orbital basis using a set of coupled non-linear equations. The methodology differs from the usual “independent pair” methods in that the pairs are coupled by “rearrangement” effects. Some numerical results on BH are given to illustrate the utility of the method.     

Perturbation calculation of the interaction energy using orthogonalized orbitals

The diagrammatic Rayleigh-Schr?dinger perturbation theory for the interaction of two closed-shell systems is developed up to the third order of pertur-bation using orthogonalized orbitals. The interaction energy is expressed by the Rayleigh-Schr?dinger perturbation expansion. A simple approach for the estimation of basis set superposition error is introduced. The preliminary calculations of the intermolecular interactions for the He dimer within the augmented cc-pVTZ basis set are compared with the supermolecular approach, perturbation calculation in biorthogonal basis sets and symmetry adapted perturbation theory results. Received: 17 December 1996 / Accepted: 5 November 1997     

Perturbative ab initio calculations of intermolecular energies. III. The water dimer

The interaction energy between two water molecules A and B is calculated by the method described in Paper I [1], previously applied for the interaction between two helium atoms (Paper II) [2]. This interaction energy is obtained as the difference between the energies of the complex (A + B) and the monomers (A) and (B), obtained by a perturbation method. The results obtained with the perturbation developed up to the second order in a minimal atomic basis set are decomposed into classical contributions and contributions linked to the exchange possibility. Charge transfer contributions are important and the localized character of the hydrogen bond is examined. It is pointed out that the definition of the set of excited configurations for the calculation of the energies of the isolated monomers is important, especially when one tries to use a small atomic basis set. A similar effect in SCF -type calculations is evaluated. The contribution of higher orders is evaluated by the CIPSI method.     

Application of Gaussian-type geminals in local second-order Møller-Plesset perturbation theory

In this work Gaussian-type Geminals (GTGs) are applied in local second-order Moller-Plesset perturbation theory to improve the basis set convergence. Our implementation is based on the weak orthogonality functional of Szalewicz et al., [Chem. Phys. Lett. 91, 169 (1982); J. Chem. Phys. 78, 1420 (1983)] and a newly developed program for calculating the necessary many-electron integrals. The local approximations together with GTGs in the treatment of the correlation energy are introduced and tested. First results for correlation energies of H(2)O, CH(4), CO, C(2)H(2), C(2)H(4), H(2)CO, and N(2)H(4) as well as some reaction and activation energies are presented. More than 97% of the valence-shell correlation energy is recovered using aug-cc-pVDZ basis sets and six GTGs per electron pair. The results are compared with conventional calculations using correlation-consistent basis sets as well as with MP2-R12 results.     

Comparison of the intermolecular energy surfaces of amino acids: orientation-dependent chiral discrimination

In the present work, we compare the intermolecular energy surfaces of the alanine molecule in its neutral and zwitterionic state using ab initio theory (HF/6-311++G) as a function of mutual orientation. Starting from the optimized structures of the nonbonded homochiral (l-l) and heterochiral (d-l) pairs of molecules, the energy surfaces are studied with rigid geometry by varying the distance and orientation. The potential energy surfaces of the l-l and d-l pairs are found to be dissimilar and reflect the underlying chirality of the homochiral pair and racemic nature of the heterochiral pair. The intermolecular energy surface of the l-l pair is more favorable than the corresponding energy surface of the d-l pair. The study, for the first time, reveals clear homochiral preference without use of parameters, which was unobserved in previous detailed simulations but predicted by theory. The electrostatic interaction further augments the chiral discrimination. The basis set superposition error (BSSE) corrected results show enhanced discrimination. Use of higher-level M?ller-Plesset perturbation theory (MP2) and further BSSE correction do not change the conclusions made at the Hartree-Fock (HF) level. The major conclusions based on HF and MP2 level calculations remain unaltered when the calculations of the potential energy surfaces for the neutral and zwitterionic pairs are repeated using the density functional theory (DFT) (B3LYP/6-311++G). The observed orientation dependence has significance in the biological chiral recognition as well as peptide synthesis at the peptidyl transferase center where the amino terminal and peptidyl terminal undergo mutual rotatory motion.     

Improved correlation energy extrapolation schemes based on local pair natural orbital methods

It is well-known that the basis set limit is difficult to reach in correlated post Hartree-Fock ab initio calculations. One possible route forward is to employ basis set extrapolation schemes. In order to avoid prohibitively expensive calculations, the highest level calculation (typically based on the "gold standard" coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T)) is only performed with the smallest basis set, and the remaining basis set incompleteness is estimated at a lower level of theory, typically second-order M?ller-Plesset perturbation theory (MP2). In this work, we provide a comprehensive investigation of alternative schemes where the MP2 extrapolation is replaced by the coupled-electron pair approximation, version 1 (CEPA/1) or the local pair natural orbital version of this method (LPNO-CEPA/1). It is shown that the MP2 method achieves apparent accuracy only due to error cancellation. Systematically more accurate results at small additional computational cost are obtained if the MP2 step is replaced by LPNO-CEPA/1. The errors of LPNO-CEPA/1 relative to canonical CEPA/1 are negligible. Owing to the highly systematic nature of the deviations between canonical and LPNO methods, basis set extrapolation reduces the LPNO errors in the total energies by 1 order of magnitude (~0.2 kcal/mol) and errors in energy differences to essentially zero. Using the CCSD(T)/LPNO-CEPA/1-based extrapolation scheme, new reference values are proposed for the recently published S66 set of interaction energies. The deviations between the new values and the original interactions energies are mostly very small but reach values up to 0.3 kcal/mol.     

A method of incorporating quadruple correction in the scheme of multi-reference singly and doubly excited configuration interaction — a CSF based coupled pair approximation

Summary We develop an approximate size consistent method within a framework of the multi-reference configuration interaction scheme. The Rayleigh-Schrödinger perturbation theory is employed with a specific selection of the unperturbed part of the electronic Hamiltonian. The second order energy is obtained by a set of equations similar to the quasidegenerate variational perturbation theory of Cave and Davidson. The approximate fourth order energy is obtained by solving a set of equations similar to the coupled electron pair approximation (CEPA). The method has been tested for two simple systems, BeH₂ and N₂, and the results are quite encouraging.     

Theoretical study of the pyrolysis of methyltrichlorosilane in the gas phase. 2. Reaction paths and transition states

The kinetics for the previously proposed 114-reaction mechanism for the chemical vapor deposition (CVD) process that leads from methyltrichlorosilane (MTS) to silicon carbide (SiC) are examined. Among the 114 reactions, 41 are predicted to proceed with no intervening barrier. For the remaining 73 reactions, transition states and their corresponding barrier heights have been explored using second-order perturbation theory (MP2) with the aug-cc-pVDZ basis set. Final energies for the reaction barriers were obtained using both MP2 with the aug-cc-pVTZ basis set and coupled cluster theory (CCSD(T)) with the aug-cc-pVDZ basis set. CCSD(T)/aug-cc-pVTZ energies were estimated by assuming additivity of basis set and correlation effects. Partition functions for the computation of thermodynamic properties of the transition states were calculated with MP2/aug-cc-pVDZ. Forward and reverse Gibbs free energy barriers were obtained at 11 temperatures ranging from 0 to 2000 K. Important reaction pathways are illustrated at 0 and 1400 K.     

Free energy simulations of uncatalyzed DNA replication fidelity: structure and stability of T.G and dTTP.G terminal DNA mismatches flanked by a single dangling nucleotide

A reference system for DNA replication fidelity was studied by free energy perturbation (FEP) and linear interaction energy (LIE) methods. The studied system included a hydrated duplex DNA with the 5'-CG dangling end of the templating strand, and dCTP4-.Mg2+ or dTTP4-.Mg2+ inserted opposite the dangling G to form a correct (i.e., Watson-Crick) or incorrect (i.e., wobble) base pair, respectively. The average distance between the 3'-terminal oxygen of the primer strand and the alpha-phosphorus of dNTP was found to be 0.2 A shorter for the correct base pair than for the incorrect base pair. Binding of the incorrect dNTP was found to be disfavored by 0.4 kcal/mol relative to the correct dNTP. We estimated that improved binding and more near-attack configurations sampled by the correct base pair should translate in aqueous solution and in the absence of DNA polymerase into a six times faster rate for the incorporation of the correct dNTP into DNA. The accuracy of the calculated binding free energy difference was verified by examining the relative free energy for melting duplex DNA containing GC and GT terminal base pairs flanked by a 5' dangling C. The calculated LIE and FEP free energies of 1.7 and 1.1 kcal/mol, respectively, compared favorably with the experimental estimate of 1.4 kcal/mol obtained using the nearest neighbor parameters. To decompose the calculated free energies into additive electrostatic and van der Waals contributions and to provide a set of rigorous theoretical data for the parametrization of the LIE method, we suggested a variant of the FEP approach, for which we coined a binding-relevant free energy (BRFE) acronym. BRFE approach is characterized by its unique perturbation pathway and by its exclusion of the intramolecular energy of a rigid part of the ligand from the total potential energy.     

Computational study of the release of H2 from ammonia borane dimer (BH3NH3)2 and its ion pair isomers

High-level electronic structure calculations have been used to map out the relevant portions of the potential energy surfaces for the release of H2 from dimers of ammonia borane, BH3NH3 (AB). Using the correlation-consistent aug-cc-pVTZ basis set at the second-order perturbation MP2 level, geometries of stationary points were optimized. Relative energies were computed at these points using coupled-cluster CCSD(T) theory with the correlation-consistent basis sets at least up to the aug-cc-pVTZ level and in some cases extrapolated to the complete basis set limit. The results show that there are a number of possible dimers involving different types of hydrogen-bonded interactions. The most stable gaseous phase (AB)2 dimer results from a head-to-tail cyclic conformation and is stabilized by 14.0 kcal/mol with respect to two AB monomers. (AB)2 can generate one or two H2 molecules via several direct pathways with energy barriers ranging from 44 to 50 kcal/mol. The diammoniate of diborane ion pair isomer, [BH4-][NH3BH2NH3+] (DADB), is 10.6 kcal/mol less stable than (AB)2 and can be formed from two AB monomers by overcoming an energy barrier of approximately 26 kcal/mol. DADB can also be generated from successive additions of two NH3 molecules to B2H6 and from condensation of AB with separated BH3 and NH3 molecules. The pathway for H2 elimination from DADB is characterized by a smaller energy barrier of 20.1 kcal/mol. The alternative ion pair [NH4+][BH3NH2BH3-] is calculated to be 16.4 kcal/mol above (AB)2 and undergoes H2 release with an energy barrier of 17.7 kcal/mol. H2 elimination from both ion pair isomers yields the chain BH3NH2BH2NH3 as product. Our results suggest that the neutral dimer will play a minor role in the release of H2 from ammonia borane, with a dominant role from the ion pairs as observed experimentally in ionic liquids and the solid state.     

A theoretical investigation of atmospheric sulfur chemistry. 1. The HSO/HOS energy separation and the heat of formation of HSO, HOS, and HS2

The energy separation between the ground-state structures of HSO and HOS has been determined by using two independent ab initio methods. In the first method, the optimized geometry of all species was obtained at the HF/6-31G(d) level, as were harmonic vibrational frequencies for zero-point energy corrections. The energies were calculated by using fourth-order Moller-Plesset perturbation theory and a 6-31G(d,p) basis set. After corrections for extrapolation of the Moller-Plesset series to infinite order and extension of the basis set to include diffuse sp-, extra d-, and f-type Gaussian functions, the predicted energy separation, including zero-point vibrational effects, is 2.5 kcal/mol. HOS is the more stable isomer. The second method uses a double-zeta basis augmented with an extra set of p functions and two sets of d functions on the sulfur and oxygen atoms and a double-zeta + p basis on hydrogen. With this basis, equilibrium structures of HSO and HOS were obtained from MCSCF calculations; the energy separation between these structures was corrected by using large scale configuration interaction. In good agreement with the first method, HOS is the more stable isomer by 3.1 kcal/mol. Through calculation of the energy change in the reaction HO2 + XY --> O2 + HXY, the first method predicts the heats of formation of HXY = HSO, HOS, and HS2 to be -0.4, -2.9, and 26.7 kcal/mol, respectively.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Perturbation expansion theory corrected from basis set superposition error. I. Locally projected excited orbitals and single excitations

The locally projected self-consistent field molecular orbital method for molecular interaction (LP SCF MI) is reformulated for multifragment systems. For the perturbation expansion, two types of the local excited orbitals are defined; one is fully local in the basis set on a fragment, and the other has to be partially delocalized to the basis sets on the other fragments. The perturbation expansion calculations only within single excitations (LP SE MP2) are tested for water dimer, hydrogen fluoride dimer, and colinear symmetric ArM+ Ar (M = Na and K). The calculated binding energies of LP SE MP2 are all close to the corresponding counterpoise corrected SCF binding energy. By adding the single excitations, the deficiency in LP SCF MI is thus removed. The results suggest that the exclusion of the charge-transfer effects in LP SCF MI might indeed be the cause of the underestimation for the binding energy.     

Scaling in second-order electron correlation calculations using systematic sequences of even-tempered basis sets

Improved results can often be obtained from second-order Rayleigh-Schrödinger perturbation calculations of electron correlation energies using large basis sets by introducing a scaling factor in the zero-order Hamiltonian. The scaling parameter may be determined from full third-order calculations using a smaller basis set. This scaling procedure can be applied in a systematic fashion by employing a sequence of even-tempered basis sets. Calculations illustrating this approach for the beryllium atom and the neon atom are presented. The scaling procedure is also employed in conjunction with a universal systematic sequence of basis functions. Calculations illustrating this Correlation energy — Mang-body perturbation theory.Work supported in part by S.R.C. Research Grant GR/B/4738.6.S.R.C. Advanced Fellow.     

AB initio calculations on intermolecular forces. The systems He…HF and He…H2O

The interaction energy between a He atom and a polar molecule (HF, H₂O) is calculated with a gaussian basis set both in the SCF approximation and with the inclusion of the intersystem correlation energy. The long range behaviour of the interaction energy is compared with results from perturbation theory.     

He-N2O的从头算势能面及振转能级

采用超分子MP4方法和较大的基组计算得到了He-N₂O体系的分子间势能面,发现该势能面有3个极小值点,分别对应T形构型及两个线性He-ONN和He-NNO构型.同时采用离散变量表象方法预测了体系的振转能级,计算结果表明,MP4势能面支持5个振动束缚态.     

Importance of structural motifs in liquid hydrogen fluoride

The investigation of liquid phases by means of accurate electronic structure methods is a demanding task due to the high computational effort. We applied second-order M?ller-Plesset perturbation theory and high-level quantum chemical calculations using the coupled-cluster method with single, double and perturbative triple excitations in combination with Dunnings correlation-consistent basis sets up to quintuple ζ quality. Based on these calculations, we extrapolated the correlation energy to the basis set limit in order to improve the results even further. For comparison to the correlated electronic structure methods, density functional calculations employing different functionals are presented as well. The investigated species are a cyclic pentamer as well as a set of branched structures. The quantum cluster equilibrium method is employed for the investigation of the liquid-phase structure of hydrogen fluoride. The pentamer is found to be present to a high extent and in the case of the MP2/QZVP data, its presence improves the results significantly. Accounting for branched structures slightly improves results, so that they are found to be present but not to dominate in liquid hydrogen fluoride. Concerning both the interaction energy and the result of the quantum cluster equilibrium calculation the basis set has a major influence, whereas the difference between M?ller-Plesset perturbation theory and coupled-cluster calculations is less pronounced.     

On the calculations of the variational correlation energy using Møller—Plesset first-order wavefunctions

A method is developed, based on first-order symmetry-adapted pair functions obtained within the framework of the Rayleigh—Schrödinger Hartree—Fock perturbation theory, for obtaining a variational upper bound to the correlation energy in the form of pair increments. The correlation-energy functional obtained is written in terms of second- and third-order energy increments of Møller—Plesset perturbation theory. Application of the procedure to the ground states of the Ne-like systems yields energies of greater accuracy than those obtained from CI calculations using very extensive sets of singly and doubly excited configurations. Our pair energies and the total correlation energy obtained for Zn²⁺ represent the most accurate variational results reported so far for atomic systems containing 3d-electrons.