Quasi-degenerate second-order perturbation theory for occupation restricted multiple active space self-consistent field reference functions

A multi-configuration quasi-degenerate second-order perturbation method based on the occupation restricted multiple active space (ORMAS-PT/ORMAS) reference wavefunction is presented. ORMAS gives one the ability to approximate a complete active space self-consistent field (CASSCF) wavefunction using only a subset of the configurations from the CASSCF space. The essential idea behind ORMAS-PT is to use the multi-reference M?ller-Plesset formalism to correct the ORMAS reference energy. A computational scheme employing direct CI methodology is presented. Several tests are presented to demonstrate the performance of the ORMAS-PT method.     

Calculation of electric dipole transition moments using quasi-degenerate variational perturbation theory and averaged coupled-pair functional theory

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH₂, and A1H using multireference singles and doubles configuration interaction, quasi-degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi-degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH₂, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled-pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.     

Communication: extended multi-state complete active space second-order perturbation theory: energy and nuclear gradients

The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.     

Applicability of quasi-degenerate many-body perturbation theory to the ground state of the F2 molecule

The ground-state potential energy curve of the F₂ molecule as well as spectroscopic constants were calculated by means of the second-order quasi-degenerate many-body perturbation theory within a full (eight) valence orbital space using a DZP basis set. The problem encountered with a large number of valence electrons is avoided by a proper redefinition of the Fermi vacuum. A comparison with other related multireference techniques is also provided. © 1995 John Wiley & Sons, Inc.     

Quantum chemical modeling of components of dye-sensitized solar cells

Ab initio approaches of quantum chemistry, including the fragment molecular orbital (FMO) method, as well as the multiconfigurational quasidegenerate perturbation theory (XMCQDPT2) and time-dependent density functional theory (TD DFT) were applied to compute optical spectra of a polyene dye molecule on the surface of titanium dioxide.     

Initial excited‐state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited‐state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight‐membered ring (locked‐11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS‐CASPT2, MS‐CASPT2) as well as single‐reference coupled‐cluster CC2 method. The analysis of XMCQDPT2‐based geometries reveals rather weak coupling between in‐plane and out‐of‐plane structural evolution and minor energetical relaxation of three locked‐11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out‐of‐plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground‐state structures, the excited‐state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4–0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked‐11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.     

Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H(2)O, potential energy curves of LiF, and valence excitation energies of H(2)CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H(2)O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H(2)CO, the maximum deviation from available experimental values is 0.28 eV.     

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.     

Third-order multireference perturbation theory: the n-electron valence state perturbation-theory approach

A formulation of the n-electron valence state perturbation theory (NEVPT) at the third order of perturbation is presented. The present implementation concerns the so-called strongly contracted variant of NEVPT, where only a subspace of the first-order interacting space is taken into account. The resulting strongly contracted NEVPT3 approach is discussed in three test cases: (a) the energy difference between the 3B1 and 1A1 states of the methylene molecule, (b) the potential-energy curve of the N2 molecule ground state, and (c) the chromium dimer (Cr2) ground-state potential-energy profile. Particular attention is devoted to the last case where large basis sets comprising also h orbitals are adopted and where remarkable differences between the second- and third-order results show up.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

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.     

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     

A Simple Approximate Perturbation Approach to Quasi-degenerate Systems

In this paper a simple approximate approach for the study of quasi-degenerate systems is presented in the frame of multireference perturbation theory. The formulation can be considered as an approximation of the quasi-degenerate perturbation theory (QDPT) with the simplification that only the state specific (diagonal) perturbation corrections to the energy have to be computed. The new approach is discussed and compared with previous QDPT formulations using the weakly avoided crossing model (for which new properties are here presented) and applied to the case of the neutral/ionic energy crossing in the LiF molecule.     

Applicability of quasi-degenerate many-body perturbation theory to quasi-degenerate electronic states: The H4 model revisited

The performance of the quasi-degenerate many-body perturbation theory up to the third order is investigated for the ground state, five excited states, and the first quintet of a simple four-electron H₄ model system consisting of two stretched hydrogen molecules, in which the degree of quasi-degeneracy can be continuously varied from a nondegenerate to a full degenerate situation. We employ a DZP basis set. The effect of intruder states is considered and a comparison with other multireference correlation techniques is also provided. Finally, a criterion for the model space to be quasi-degenerate will be reformulated and generalized. © 1995 John Wiley & Sons, Inc.     

An ab initio multireference perturbation theory study on the manganese dimer

The potential energy curves of the ground state and of some excited states of the manganese dimer have been calculated over a wide range of internuclear distances using the second order n-electron valence state perturbation theory applied to a complete active space self-consistent field reference wave function. The ground state of Mn(2), for which also the third order NEVPT has been used, is calculated to be a singlet belonging to the Sigma(g) (+) symmetry, characterized by a large equilibrium internuclear distance R(e) of 3.7-3.8 A, by a low dissociation energy D(e) of 0.07-0.08 eV, and by a small harmonic frequency omega(e) of 43 cm(-1). The experimental evidence that Mn(2) is a van der Waals molecule is thus confirmed. Among the excited states, (11)Pi(u), which is usually indicated as the ground state by density functional theory studies, appears as a low-lying state with R(e)=2.50 A, D(e)=1.35 eV, and omega(e)=246 cm(-1).     

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.     

Quasi-degenerate rayleigh-schrödinger perturbation theory with hermitean model hamiltonian

A method for the construction of the hermitean model hamiltonian in the framework of the quasi-degenerate Rayleigh-Schrödinger perturbation theory is suggested. The approach of a model hamiltonian is based on the assumption that if it is diagonalized in a chosen finite-dimensional model space it will yield eigenvalues of the original hamiltonian in the entire Hilbert space. For a unitary operator transforming the unperturbed state vectors onto the perturbed state vectors, and a model-interaction operator, the perturbation-expansion formulae are developed.     

A new size extensive multireference perturbation theory

A new multireference perturbation series is derived based on the Rayleigh–Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller–Plesset perturbation theory. It is demonstrated numerically that the present multireference second‐ and third‐order energies are size extensive by two types of supermolecules composed of H₂ and BH monomers. Spectroscopic constants of as well as the ground state energies of H₂O, NH₂, and CH₂ at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH₄ and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances. © 2013 Wiley Periodicals, Inc.     

Multiconfigurational Green's function approach with quasidegenerate perturbation theory

The new approach to approximation of polarization propagator (PP) for electronic states of atoms and molecules with reference state wave function (RSWF) constructed on the base of a multidimensional model space is presented. This approach exploiting the apparatus of the quasidegenerate perturbation theory (QDPT) is realized in the zeroth QDPT order and through the first one. The original complete system of excitation operators introduced in the approach is consistent with the RSWF by the perturbation order. This factor in conjunction with the flexibility of the RSWF creates the capabilities of balanced accounting of correlation and quasidegeneracy effects at different locations of nuclei in a molecule and for all the states concerned. In this way, the transition characteristics in electronic shells of molecules in a wide area of nuclear geometry parameters may be appropriately evaluated. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002