On multireference superdirect configuration interaction in third order

The superdirect configuration interaction (Sup-CI ) method has the usual versatility and stability of the CI methods with computational efficiency typical to that of the many-body methods, such as the many-body perturbation theory (MBPT ). The Hamilton operator is projected into a space of a few trial vectors, such as Krylov, Nesbet, or Møller–Plesset correction vectors. In this space, Hamiltonian matrix elements may be directly computed in the many-body fashion, as weighted sums of integral products over orbital indices. The variation-perturbation method based on the first-order wave function is equivalent to the Sup-CI method with a single correction vector of the Møller–Plesset type. Different points of view on the superdirect CI method are discussed and a version in which third-order contributions are computed for a relatively small (10–100) space of reference and correction vectors is tested. Selection of the best “effective first-order spaces” and size-extensivity corrections in Sup-CI are briefly discussed. Møoller–Plesset, Epstein–Nesbet, and other correction vectors are included in the model calculations on the symmetric stretch of bonds in water, acetylene, and the NH₂ molecule. Errors are almost independent of molecular geometry and the method appears to be superior than the multireference second-order perturbation methods. © 1994 John Wiley & Sons, Inc.     

Many-body multireference Møller—Plesset and Epstein—Nesbet perturbation theory: Fast evaluation of second-order energy contributions

Multireference perturbation theory is examined in connection with the two partitions in the Møller—Plesset and Epstein—Nesbet schemes. The implementation of an efficient diagrammatic technique is described and two examples of application (diazene and the Cr₂ molecule), involving large variational spaces, are provided. © 1996 John Wiley & Sons, Inc.     

Different forms of perturbation theory for the calculation of the correlation energy

Different forms of perturbation theory for the calculation of correlation energy in both closed-and open-shell systems are discussed. For closed-shell systems, Epstein–Nesbet perturbation theory is compared with Møller–Plesset (MP ) perturbation theory based on canonical Hartree–Fock orbitals and with MP theory based on internally consistent SCF orbitals. The traditional MP theory gives superior results despite its use of an inferior zeroth-order Hamiltonian. This behavior is rationalized in terms of the larger denominators present in the traditional MP theory. These conclusions are used to support the restricted open-shell perturbation methods proposed recently by Murray and Davidson, and these new methods are compared with spin-restricted Epstein–Nesbet theory and the unrestricted MP (UMP ) approach. © 1992 John Wiley & Sons, Inc.     

An ab initio molecular orbital study of the potential energy surface of the N2H → N2 + H system

The N₂H potential energy surface has been examined by ab initio molecular orbital theory using the 6-31G^** basis set with correlation energy evaluated by Møller—Plesset perturbation theory to fourth order. The ΔE for N₂H → N₂ + H is ?14.4 kcal mol^?1 and the barrier to dissociation is 10.5 kcal mol^?1. Inclusion of zero-point vibrational energies reduces the barrier to 5.8 kcal mol^?1.     

Quadratic Padé approximants and the intruder state problem of multireference perturbation methods

Simple and quadratic Padé resummation methods are applied to high‐order series from multireference many‐body perturbation theory (MR‐MBPT) calculations using various partitioning schemes (Møller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low‐lying excited states of (i) CH₂, (ii) BeH₂ at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Padé approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Padé method generally outperforms the simple Padé resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Influence of the Delocalization Error and Applicability of Optimal Functional Tuning in Density Functional Calculations of Nonlinear Optical Properties of Organic Donor–Acceptor Chromophores

Nonempirically tuned hybrid density functionals with range‐separated exchange are applied to calculations of the first hyperpolarizability (β_∥) and charge‐transfer (CT) excitations of linear “push–pull” donor–acceptor‐substituted organic molecules with extended π‐conjugated bridges. An unphysical delocalization with increasing chain length in density functional calculations can be reduced significantly by enforcing an asymptotically correct exchange‐correlation potential adjusted to give frontier orbital energies representing ionization potentials. The delocalization error for a number of donor–acceptor systems is quantified by calculations with fractional electron numbers and from orbital localizations. Optimally tuned hybrid variants of the PBE functional incorporating range‐separated exchange can produce similar magnitudes for β_∥ as Møller–Plesset second‐order perturbation (MP2) correlated calculations. Improvements are also found for CT excitation energies, with results similar to an approximate coupled‐cluster model (CC2).     

Small elemental clusters. I. The structures of Be2, Be3, Be4, and Be5

The geometries and energies of beryllium clusters up to Be₅ are examined using ab initio molecular orbital theory. Allowances are made for electron correlation with Møller—Plesset perturbation theory to fourth order. Correlation is found to have a dramatic effect on the relative energies of the several structures examined for Be₄ and Be₅. Furthermore, the effect of d-type basis functions on the correlation energy results in an increased binding energy for the clusters. Be₂ is only weakly bound. For Be₃, the best estimate of the binding energy is 6 kcal/mole for the singlet equilateral triangle. Be₄ is tetrahedral in its ground state and the estimated binding is 56 kcal/mole. The best structure for Be₅ is a singlet trigonal bipyramid, and the binding energy is 88 kcal/mole at the highest level of theory used.     

The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods

Dipole moments and static dipole polarizabilities have been calculated for a number of small molecules using the linear combination of Gaussian-type orbitals–local spin density method. The effect of augmenting standard orbital basis sets with polarization functions has been investigated. A set of optimum ζ_d, for use in calculating polarizabilities, has been derived for the first-row atoms C, N, O, and F. The results of this optimized doubly polarized double-zeta basis set compare well with results obtained using a double-zeta basis set augmented by four even-tempered ζ_d polarization functions. The results of the optimized basis set, and a basis set augmented with only a single ζ_d polarization function derived from it, compare very favorably with those obtained from Møller–Plesset perturbation theory and with experimental data. They show a marked improvement on results obtained using standard Hartree–Fock self-consistent-field molecular orbital methods where no treatment of electron-correlation is included.     

New basis sets for the evaluation of interaction‐induced electric properties in hydrogen‐bonded complexes

Interaction‐induced static electric properties, that is, dipole moment, polarizability, and first hyperpolarizability, of the CO? (HF)_n and N₂? (HF)_n, n = 1–9 hydrogen‐bonded complexes are evaluated within the finite field approach using the Hartree–Fock, density functional theory, Møller–Plesset second‐order perturbation theory, and coupled cluster methods, and the LPol‐n (n = ds, dl, fs, fl) basis sets. To compare the performance of the different methods with respect to the increase of the complex size, we consider as model systems linear chains of the complexes. We analyze the results in terms of the many‐body and cooperative effects. © 2012 Wiley Periodicals, Inc.     

Charge density by the use of the hiller–sucher–feinberg identity. Perturbative corrections and configuration interaction effects

Configuration interaction (CI ) calculations are carried out for He atom and H₂, LiH, and BH molecules in order to obtain the value of the charge density at the nucleus by the use of the Hiller–Sucher–Feinberg (HSF ) identity. The HSF density also can be calculated with the double perturbation theory based on the Møller–Plesset-type theory and also on the Epstein–Nesbet type. It is found that each value of the HSF density for these perturbative corrections is very similar to the corresponding value by the CI with single- and double-electron excitations. Especially for the He atom, the HSF density value by the full-CI wave function coincides with the exact value of the charge density in three significant figures. The electron correlation effects are found to be small but cannot be ignored in the HSF density. It can be shown that the superiority of the HSF density over the usual delta-function-type density is excellently confirmed.     

Theoretical study of the relative stabilities of H+(X)2 and H+(X)3 conformers and their clustering energies: X  CO and N2

Third-order Møller–Plesset perturbation theory (MP 3) with a 6-31G** basis set was applied to study the relative stabilities of H⁺(X)₂ conformations (X ? CO and N₂) and their clustering energies. The effect of both basis set extensions and electron correlation is not negligible on the relative stabilities of the H⁺(CO)₂ clusters. The most stable conformation of H⁺(CO)₂ is found to be a C_∞v structure in which a carbon atom of CO bonds to the proton of H⁺(CO), whereas that of H⁺(N₂)₂ is a symmetry D_∞h structure. The second lowest energy conformations of H⁺(CO)₂ and H⁺(N₂)₂ lie within 2 kcal/mol above the energies of the most stable structures. Clustering energies computed using MP 3 method with the 6-31G** basis set are in good agreement with the experimental findings of Hiraoka, Saluja, and Kebarle. The low-lying singlet conformations of H⁺(X)₃ (X ? CO and N₂) have been studied by the use of the Hartree–Fock MO method with the 6-31G** basis set and second-order Møller–Plesset perturbation theory with a 4-31G basis set. The most stable structure is a T-shaped structure in which a carbon atom of CO (or a nitrogen atom of N₂) attacks the proton of the most stable conformation of H⁺(X)₂ clusters.     

Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn

The introduction of the resolution-of-the-identity (RI) approximation for electron repulsion integrals in quantum chemical calculations requires in addition to the orbital basis so-called auxiliary or fitting basis sets. We report here such auxiliary basis sets optimized for second-order Møller–Plesset perturbation theory for the recently published (Weigend and Ahlrichs Phys Chem Chem Phys, 2005, 7, 3297–3305) segmented contracted Gaussian basis sets of split, triple-ζ and quadruple-ζ valence quality for the atoms Rb–Rn (except lanthanides). These basis sets are designed for use in connection with small-core effective core potentials including scalar relativistic corrections. Hereby accurate resolution-of-the-identity calculations with second-order Møller–Plesset perturbation theory (MP2) and related methods can now be performed for molecules containing elements from H to Rn. The error of the RI approximation has been evaluated for a test set of 385 small and medium sized molecules, which represent the common oxidation states of each element, and is compared with the one-electron basis set error, estimated based on highly accurate explicitly correlated MP2–R12 calculations. With the reported auxiliary basis sets the RI error for MP2 correlation energies is typically two orders of magnitude smaller than the one-electron basis set error, independent on the position of the atoms in the periodic table.     

Multireference perturbation theory with optimized partitioning. II. Applications to molecular systems

The second‐order multireference perturbation theory using an optimized partitioning, denoted as MROPT(2), is applied to calculations of various molecular properties—excitation energies, spectroscopic parameters, and potential energy curves—for five molecules: ethylene, butadiene, benzene, N₂, and O₂. The calculated results are compared with those obtained with second‐ and third‐order multireference perturbation theory using the traditional partitioning techniques. We also give results from computations using the multireference configuration interaction (MRCI) method. The presented results show very close resemblance between the new method and MRCI with renormalized Davidson correction. The accuracy of the new method is good and is comparable to that of second‐order multireference perturbation theory using Møller‐Plesset partitioning. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1390–1400, 2003     

Ab initio study of reactions of 1‐halogen‐3‐methoxy‐1‐propynes with Grignard reagent

The structures of coordination complexes of methylmagnesium chloride with 1‐halogen‐3‐methoxy‐1‐propynes have been studied by means of ab initio methods (RHF/3‐21G*, RHF/6‐31G* and RHF/6‐31G**), taking into account the electron correlation by Møller‐Plesset perturbation theory (MP2). Two pathways of the nucleophilic halogen substitution reaction between the reagents have been considered. The calculations predict the addition–elimination mechanism as advantageous for the reaction. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Study of correlation effects on stretching force constants of the H3N⋯LiF lithium-bonded and H3N⋯HF hydrogen-bonded complexes

All quadratic, cubic and quartic force constants associated with high and low vibrational modes of the H₃N⋯HF hydrogen-bonded and H₃N⋯LiF lithium-bonded complexes have been calculated employing the Møller—Plesset perturbation theory to the second order (MP2) with the 4-31G** basis set.     

MRD-CI studies of vertical excitation energies of unsaturated hydrocarbon molecules

Systematic MRD-CI calculations using the AM1 Hamiltonian have been carried out for two polyenes and eight aromatic hydrocarbons ranging from benzene to ovalene (C₃₂H₁₄). Twenty singlet–singlet excitation energies in these compounds were calculated and compared with experimental data and ab initio STO-3G results. On an absolute scale, the AM1/MRD-CI approach underestimates the excitation energies to states with dominant covalent character by an average of 1.1 eV, whereas the errors for ionic states are between ?1.0 and 1.0 eV. The STO-3G calculated data are much too high by ≈ 1 eV and ≈ 5 eV, respectively. The inclusion of σπ-correlation effects through second-order Epstein–Nesbet perturbation theory combined with the use of localized orbitals leads to a significant improvement of the ab initio calculated state energies. In an analogous AM1 treatment, negligible corrections for the σπ correlations are found, which is attributed to the implicit account in the parameters and approximation of the semiempirical Hamiltonian. The possible error sources of the calculational methods are discussed. © 1994 by John Wiley & Sons, Inc.     

HNNH3, a new possible isomer of N2H4: An ab initio study

Ab initio studies applying the 3-21G, 6-31G, and 6-31G** basis sets and also including the MP2 correction were carried out on H₂NNH₂, HNNH₃, and the transition state of the reaction H₂NNH₂(DOUBLE BOND)HNNH₃. First, the geometries of molecules were optimized using the theoretical methods mentioned in the restricted Hartree–Fock (RHF) scheme. The energies of the molecules corresponding to RHF/6-31G** geometries were subsequently calculated including electron-correlation effects at the level of the second-order Møller–Plesset (MP2) perturbation theory. The vibrational frequencies, net charges, and dipole moments were obtained from the theoretical calculations. The results of our calculations indicate unambiguously that H₂NNH₂ is thermodynamically more stable than is HNNH₃. On the other hand, an isolated HNNH₃ molecule once created would be stable since barriers for its unimolecular isomerization and decomposition are relatively high. But HNNH₃ is unlikely to be isolated in measurable amounts because of bimolecular tautomerization. Nevertheless, HNNH₃ can be considered as an intermediate in chemical processes involving N₂H₄. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 447–452, 1997     

An approximate potential energy surface for HeI2 collisions

We have calculated the interaction potential for HeI₂ in T-shaped geometries using Hartree—Fock and Møller—Plesset third-order perturbation t     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000