Configuration-based multi-reference second order perturbation theory

Various configuration-based multi-reference second order perturbation approaches were investigated and a new scheme averting intruder states was suggested. The codes based on these schemes were tested by example calculations.     

多参考态二级微扰方法的改进

本文提出一个新的扩大模型空间的方案用于改进多参考态二级微扰理论(MRPT2)计算. 新方案保持了原方案中扩大模型空间之前的简单程序结构, 理论上完全可以避免势能面计算中入侵态的出现, 并在一系列比较计算中得到证实. 新MRPT2程序是研究分子激发态和电子光谱的有用工具.     

A modified multi-reference second order perturbation theory

A new scheme with extended model space is proposed to improve the calculation of multi-reference second order perturbation theory (MRPT2). The new scheme preserves the concise code structure of the original program, and avoids intruder states in constructions of the potential energy surface, which is confirmed by a series of comparable calculations. The new MRPT2 program is an available tool for the research of molecular excited states and electronic spectrum.     

Kohn-Sham perturbation theory: simple solution to variational instability of second order correlation energy functional

The orbital-dependent correlation energy functional resulting from second order Kohn-Sham perturbation theory leads to atomic correlation potentials with correct shell structure and asymptotic behavior. The absolute magnitude of the exact correlation potential, however, is greatly overestimated. In addition, this functional is variationally instable, which shows up for systems with nearly degenerate highest occupied and lowest unoccupied levels like Be. In this contribution we examine the simplest resummation of the Kohn-Sham perturbation series which has the potential to resolve both the inaccuracy and the instability problem of the second order expression. This resummation includes only the hole-hole terms of the Epstein-Nesbet series of diagrams, which has the advantage that the resulting functional is computationally as efficient as the pure second order expression. The hole-hole Epstein-Nesbet functional is tested for a number of atoms and ions. It is found to reproduce correlation and ground state energies with an accuracy comparable to that of state-of-the-art generalized gradient approximations. The correlation potential, on the other hand, is dramatically improved compared to that obtained from generalized gradient approximations. The same applies to all quantities directly related to the potential, as, for instance, Kohn-Sham eigenvalues and excitation energies. Most importantly, however, the hole-hole Epstein-Nesbet functional turned out to be variationally stable for all neutral as well as all singly and doubly ionized atoms considered so far, including the case of Be.     

Multiconfiguration perturbation theory: size consistency at second order

A modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al. J. Chem. Phys. 119, 1922 (2003)] is presented. In the modified formulation size consistency is ensured at second order in energy, by omitting projectors from the zero order Hamiltonian operator. This MCPT formulation is abbreviated as SC2-MCPT (size consistent at second order). To ensure proper separability, we also require that energy denominators are constructed as differences of some one-particle energies. A similar choice for energy denominators also renders the well-known multireference Moller-Plesset (MRMP) energy size consistent at second order. The same thing applies to the related multireference perturbation theory by Witek, Nakano, and Hirao.     

Solvent effects on electronic spectra studied by multiconfigurational perturbation theory

The complete active space (CAS) self-consistent field (SCF) method combined with multiconfigurational second-order perturbation theory (CASPT2) and a self-consistent reaction field (SCRF) model is used to study the effect of solvation on excited states of different molecules such as acetone, pyrimidine, some aminobenzene derivatives, indole, and imidazole. The present SCRF model, in which the solute molecule is placed into a spherical cavity surrounded by a dielectric continuum, also includes a repulsive potential representing the solute–solvent exchange repulsion and considers the time dependence of the absorption process. In general, we find that our calculations do reproduce the trends observed in experiment but underestimate the solvatochromic shifts. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 167–181, 1997     

Application of second order BWEN perturbation theory to some simple reactions

The second order Brillouin-Wigner perturbation expansion with the Epstein-Nesbet partitioning is applied to some isomerization and insertion reactions, using the 6-31G^* basis set. BWEN2 is found to be comparable in accuracy with RSMP2 for predictions of energy barriers and isomerization energies.     

Solvent and concentration effects on fluorescence emission in MEH-PPV solution

We systematically studied the excitation and the fluorescence steady-state spectroscopy of poly[2-methoxy-5-(2′-ethylhexoxy)-p-phenylene vinylene] (MEH-PPV) in two solvents and several concentrations. Fluorescence spectra were recorded for solutions in several concentrations (10⁻⁵ mg/ml to 10⁻³ mg/ml), showing that tetrahydrofuran (THF) and toluene solvate the polymer chain differently. Dilute solution (10⁻⁵ mg/ml) in THF exhibit broader fluorescence spectra due to greater conformation disorder. The degree of the aggregation depends on both the solvent and the polymer concentration. Aggregation is promoted in toluene solution and hindered in THF solvent.     

Accuracy of second order perturbation theory in the polaron and variational polaron frames

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.     

Recent advances in multireference second order perturbation CI: The CIPSI method revisited

The evolution of the CIPSI method, with the latest modifications recently implemented in our laboratory, is described. A new version, based on a diagrammatic technique, is presented. Test calculations which have been run on water, ethylene, and transacrolein, show that the new method is a powerful tool for the study of medium-size molecular systems.     

Quasidegenerate scaled opposite spin second order perturbation corrections to single excitation configuration interaction

Scaled opposite spin (SOS) second order perturbative corrections to single excitation configuration interaction (CIS) are extended to correctly treat quasidegeneracies between excited states. Two viable methods, termed as SOS-CIS(D(0)) and SOS-CIS(D(1)), are defined, implemented, and tested. Each involves one empirical parameter (plus a second for the SOS-MP2 ground state), has computational cost that scales with the fourth power of molecule size, and has storage requirements that are cubic, with only quantities of the rank of single excitations produced and stored during iterations. Tests on a set of low-lying adiabatic valence excitation energies and vertical Rydberg excitations of organic and inorganic molecules show that the empirical parameter can be acceptably transferred from the corresponding nondegenerate perturbation theories without any further fitting. Further tests on higher excited states show that the new methods correctly perform for surface crossings for which nondegenerate approaches fail. Numerical results show that SOS-CIS(D(0)) appears to treat Rydberg excitations in a more balanced way than SOS-CIS(D(1)) and is, therefore, likely to be the preferred approach. It should be useful for exploring excited state geometries, transition structures, and conical intersections for states of medium to large organic molecules that are dominated by single excitations.     

Variation of surface partition in GEPOL: effects on solvation free energy and free-energy profiles

The problem of defining efficient strategies for partitioning the cavity surface in QM solvation procedures based on boundary elements methods is considered here. The GEPOL procedure to get the cavity surface, and its partition into tesserae is adopted as a starting point: a version with variable tesselation is presented. The procedure to build the new sphere tesselations is described and several different options to select the surface partition have been implemented. The effects of the variation of the surface partition on the free energy of solvation of several solutes are also presented. Two free energy of solvation profiles evaluated with several different cavity partitions are analysed. We find that a radius-driven tesselation for every sphere reduces the number and extension of the cavity artefacts. Received: 6 August 1997 / Accepted: 23 October 1997     

Localized bond model for molecular energy to fourth order in perturbation theory

The localized bond model of Malrieu, Diner, and Claverie is extended to fourth order in perturbation theory. Single, double, triple, and quadruple replacements from the doubly occupied bonding reference function are included utilizing a symmetric form of diagrammatic perturbation theory. The fourth order theory derived executes on a computer as quickly as does the third order theory. Results are examined utilizing the Pariser–Parr–Pople and CNDO/2 model Hamiltonians, and are compared with third order results and with either exact results where they are known, or with a configuration interaction of all singles and doubles. The influence of the initial hybridization, localization, and bond polarization is discussed. In general, the fourth order corrections are of comparable size to third order. Improvement in results appears to be marginal in the Nesbet–Epstein scheme in passing to fourth order because of the oscillating nature of the series; for Moller–Plesset theory errors are approximately halved. The relative energies as a function of modest geometry change about minima is about the same at third order as it is at fourth for most cases examined.     

The energy of the homogeneous electron gas to second order

The energy of an infinite, homogeneous electron gas is examined by second order perturbation theory using a Hartee-Fock rather than a noninteracting particle unperturbed state. The second order energy still diverges for small promotions k , albert than as ln|ln k| rather than as In k.     

First and second order effects in NMR spectral averaging

Many ways in which motional averaging can effect NMR spectra are illustrated with examples chosen from the literature on ferroelectrics and super-ionics. Both types of materials display very extensive local, short- and long-range motion. The familiar first order averaging, as well as second order effects which have been recently demonstrated to provide essentially the same information as spin-lattice relaxation experiments, are considered. While theoretical results will be outlined as necessary, emphasis is placed upon the experimental results and physical concepts.     

Explicitly correlated second order perturbation theory: introduction of a rational generator and numerical quadratures

A rational generator, which fulfills the cusp conditions for singlet and triplet electron pairs, is proposed and applied to explicitly correlated second order M?ller-Plesset perturbation theory calculations. It is shown that the generator in conjunction with frozen geminals improves the convergence of correlation energy without introducing any variational parameters in explicitly correlated functions. A new scheme for three-electron integrals based on numerical quadratures is also illustrated. The method is tested for the convergence of reaction enthalpies with various basis sets.     

Some remarks on the SCRF theory of solvent effects and the calculation of proton potentials

Some aspects concerning the self-consistent reaction field theory of solvent effects are discussed. In particular, the variational solution to the non-linear Schrödinger equation is considered; a necessary and sufficient constraint to be added to the standard variational procedure is discussed. The exact solution of the non-linear equation is presented within the molecular orbital approach; correlation defaults to the Hartree-Fock like solutions are stated. Some thermodynamical correspondences are established with the magnitudes calculated with the self-consistent reaction field theory. Finally, we have commented upon the proton potentials calculated within this theory. An INDO calculation of a water trimer has been used as an example to discuss different types of proton translocation potentials.