Comment on symmetry-adapted perturbation theories

In a recent paper, Suzuki and I'Haya have criticized many of the proposed symmetry-adapted perturbation theories on the grounds that they are not physically adequate. We show that these criticisms are without merit.     

Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.     

Extended Koopmans' theorem at the second-order perturbation theory

The extended Koopmans' theorem (EKT), when combined with the second-order Møller−Plesset (MP2) perturbation theory through the relaxed density matrix approach [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys. 1997, 107, 6,804], provides a straightforward way to calculate the ionization potentials (IPs) as an one electron quantity. However, such an EKT-MP2 method often suffers from the negative occupation problem, failing to provide the complete IP spectra for a system of interest. Here a small positive number scheme is proposed to cure this problem so as to remove the associated unphysical results. In order to obtain an in-depth physical interpretation of the EKT-MP2 method, we introduce a Koopmans-type quantity, named KT-MP2, based on which the respective contribution from the relaxation and the correlation parts in the EKT-MP2 results are recognized. Furthermore, the close relationship between the EKT-MP2 method and the derivative approach of the MP2 energy with respect to the orbital occupation numbers [N. Q. Su and X. Xu, J. Chem. Theory Comput. 2015, 11, 4,677] is revealed. When these MP2-based methods are applied to a set of atoms and molecules, new insights are gained on the role played by the relaxation and the correlation effects in the electron ionization processes.     

Hard-sphere perturbation theories applied to concentrated colloidal dispersions

The application of hard-sphere perturbation theory to monodisperse colloidal dispersions is examined in detail. Osmotic pressures and radial distribution functions are calculated by these theories and compared with exact Monte Carlo results to allow a critical assessment of the accuracy of the theories. For most conditions encountered in practical colloidal dispersions the predictions of zero- and firstorder perturbation theories are very accurate.     

Efficient configuration selection scheme for vibrational second-order perturbation theory

A fast algorithm of vibrational second-order Moller-Plesset perturbation theory is proposed, enabling a substantial reduction in the number of vibrational self-consistent-field (VSCF) configurations that need to be summed in the calculations. Important configurations are identified a priori by assuming that a reference VSCF wave function is approximated well by harmonic oscillator wave functions and that fifth- and higher-order anharmonicities are negligible. The proposed scheme has reduced the number of VSCF configurations by more than 100 times for formaldehyde, ethylene, and furazan with an error in computed frequencies being not more than a few cm(-1).     

Analytic geometrical derivatives of second-order molecular properties from perturbation theory

Assuming the Born-Oppenheimer approximation for molecular wavefunctions satisfies the Hellmann-Feynman theorem, Rayleigh-Schrödinger perturbation theory is employed to develop an analytic formula for derivatives of expectation values and second-order properties with respect to nuclear coordinates.     

One-electron properties of molecules calculated using second-order multireference perturbation theory

A new form of second-order multireference perturbation theory coupled with finite-field perturbation theory is applied to evaluate some one-electron molecular properties. Several possible definitions of the zeroth-order Hamiltonian are considered and results tested against bench-mark full CI calculations. © 1995 John Wiley & Sons, Inc.     

Parallel direct four-index transformations

Summary Two parallel direct integral transformation algorithms are presented. Specific attention is directed to producing transformed integrals containing at least two active orbital indices. The number of active orbitals is typically much less than the total number of molecular orbitals reflecting the requirements of a wide range of correlated electronic structure methods. Sample direct second-order Møller-Plesset theory calculations are reported. For situations where multipassing of the integrals is required, superlinear speedup is obtained by exploiting the increase in global memory. As a consequence, for morphine in a 6-31G basis, a speedup of over 25 is observed in scaling from 32 to 512 processors.Pacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under contract DE-AC06-76RL0 1830     

Near-degeneracy corrections for second-order perturbation theory: comparison of two approaches

 We compare two approximate perturbation schemes which were developed recently to deal with the (quasi)degeneracy problem in many-body perturbation theory. We conclude that although the two methods were introduced on quite different theoretical grounds, their performances are quite similar, and present an improvement over traditional perturbation theory. Both methods are cheap in computation time, but cannot compete in accuracy with more sophisticated schemes such as complete-active-space perturbation theory or dressed particle theories. Received: 1 August 2000 / Accepted: 2 August 2000 / Published online: 19 January 2001     

Explicitly correlated second-order perturbation theory using density fitting and local approximations

Three major obstacles in electronic structure theory are the steep scalings of computer time with respect to system size and basis size and the slow convergence of correlation energies in orbital basis sets. Three solutions to these are, respectively, local methods, density fitting, and explicit correlation; in this work, we combine all three to produce a low-order scaling method that can achieve accurate MP2 energies for large systems. The errors introduced by the local approximations into the R12 treatment are analyzed for 16 chemical reactions involving 21 molecules. Weak pair approximations, as well as local resolution of the identity approximations, are tested for molecules with up to 49 atoms, over 100 correlated electrons, and over 1000 basis functions.     

Phase behavior of aqueous solutions containing dipolar proteins from second-order perturbation theory

Due to the interplay of Coulombic repulsion and attractive dipolar and van der Waals interactions, solutions of globular proteins display a rich variety of phase behavior featuring fluid-fluid and fluid-solid transitions that strongly depend on solution pH and salt concentration. Using a simple model for charge, dispersion and dipole-related contributions to the interprotein potential, we calculate phase diagrams for protein solutions within the framework of second-order perturbation theory. For each phase, we determine the Helmholtz energy as the sum of a hard-sphere reference term and a perturbation term that reflects both the electrostatic and dispersion interactions. Dipolar effects can induce fluid-fluid phase separation or crystallization even in the absence of any significant dispersion attraction. Because dissolved electrolytes screen the charge-charge repulsion more strongly than the dipolar attraction, the ionic strength dependence of the potential of mean force can feature a minimum at intermediate ionic strengths offering an explanation for the observed nonmonotonic dependence of the phase behavior on salt concentration. Inclusion of correlations between charge-dipole and dipole-dipole interactions is essential for a reliable calculation of phase diagrams for systems containing charged dipolar proteins and colloids.     

Comparison of two hard-sphere reference systems for perturbation theories for mixtures

The Carnahan—Starling equation of state for hard spheres can be extended to mixtures using either a one-fluid theory, or the generalization of scaled-particle (or Percus—Yevick theory) proposed by Boublik and by Mansoori and coworkers. The two reference systems are combined with a perturbation term of the van der Waals form; they are then used to correlate the phase behavior of binary mixtures of nonpolar molecules differing significantly in molecular size. In each case, one adjustable binary parameter (a₁₂) is used to correlate vapor—liquid equilibria over the entire composition range. Predicted Henry's constants and liquid densities for the saturated mixture are compared with experiment. The Boublik—Mansoori hard-sphere-mixture equation is superior to the Carnahan—Starling One-Fluid theory, expecially in the dilute region.     

Multiconfigurational second-order perturbation study of the decomposition of the radical anion of nitromethane

The doublet potential energy surfaces involved in the decomposition of the nitromethane radical anion (CH(3)NO(2) (-)) have been studied by using the multistate extension of the multiconfigurational second-order perturbation method (MS-CASPT2) in conjunction with large atomic natural orbital-type basis sets. A very low energy barrier is found for the decomposition reaction: CH(3)NO(2) (-)-->[CH(3)NO(2)](-)-->CH(3)+NO(2) (-). No evidence has been obtained on the existence of an isomerization channel leading to the initial formation of the methylnitrite anion (CH(3)ONO(-)) which, in a subsequent reaction, would yield nitric oxide (NO). In contrast, it is suggested that NO is formed through the bimolecular reaction: CH(3)+NO(2) (-)-->[CH(3)O-N-O](-)-->CH(3)O(-)+NO. In particular, the CASSCF/MS-CASPT2 results indicate that the methylnitrite radical anion CH(3)ONO(-) does not represent a minimum energy structure, as concluded by using density functional theory (DFT) methodologies. The inverse symmetry breaking effect present in DFT is demonstrated to be responsible for such erroneous prediction.