Third-order many-body perturbation theory for the ground state of the carbon monoxide molecule

Many-body perturbation calculations have been performed for the ground state of the carbon monoxide molecule at its equilibrium internuclear separation. The calculations are complete through third order within the algebraic approximation; i.e., the state functions are parameterized by expansion in a finite basis set. All two-, three-, and four-body terms are rigorously determined, and many-body effects are found to be very important. A detailed comparison is made with a previously reported configuration interaction study. Padé approximants to the energy expansion are constructed. The many-body perturbative wave function is used in the Rayleigh quotient to produce upper bounds to the electronic energy.     

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.     

Intruder states in multireference perturbation theory: the ground state of manganese dimer

A detailed analysis of a severe intruder state problem in the multistate multireference perturbation theory (MS-MRPT) calculations on the ground state of manganese dimer is presented. An enormous number of detected intruder states (> 5000) do not permit finding even an approximate shape of the X(1)Sigma(g) (+) potential energy curve. The intruder states are explicitly demonstrated to originate from quasidegeneracies in the zeroth-order Hamiltonian spectrum. The electronic configurations responsible for appearance of the quasidegeneracies are identified as single and double excitations from the active orbitals to the external orbitals. It is shown that the quasidegeneracy problem can be completely eliminated using shift techniques despite of its severity. The resultant curves are smooth and continuous. Unfortunately, strong dependence of the spectroscopic parameters of the X(1)Sigma(g) (+) state on the shift parameter is observed. This finding rises serious controversies regarding validity of employing shift techniques for solving the intruder state problem in MS-MRPT. Various alternative approaches of removing intruder states (e.g., modification of the basis set or changing the active space) are tested. None of these conventional techniques is able to fully avoid the quasidegeneracies. We believe that the MS-MRPT calculations on the three lowest A(g) states of manganese dimer constitute a perfect benchmark case for studying the behavior of MRPT in extreme situations.     

A study of the ground state wave function of carbon monoxide

A large configuration-interaction calculation has been performed to determine the wave function, energy, and molecular properties of CO. The most important configurations were used to obtain the natural geminals and their occupation numbers. A pair-energy approach to the correlation energy was attempted with results which differ significantly from the configuration-interaction results.     

Diagrammatic analysis of adiabatic and time-independent perturbation theory for degenerate energy levels

Time-ordered folded diagrams are used to represent the effective hamiltonian in the adiabatic formalism. Resummation of the diagrams is shown to give a term-by-term correspondence with time-independent perturbation theory.     

A study of the ground state of manganese dimer using quasidegenerate perturbation theory

We study the electronic structure of the ground state of the manganese dimer using the state-averaged complete active space self-consistent field method, followed by second-order quasidegenerate perturbation theory. Overall potential energy curves are calculated for the 1Sigmag+, 11Sigmau+, and 11Piu states, which are candidates for the ground state. Of these states, the 1Sigmag+ state has the lowest energy and we therefore identify it as the ground state. We find values of 3.29 A, 0.14 eV, and 53.46 cm(-1) for the bond length, dissociation energy, and vibrational frequency, in good agreement with the observed values of 3.4 A, 0.1 eV, and 68.1 cm(-1) in rare-gas matrices. These values show that the manganese dimer is a van der Waals molecule with antiferromagnetic coupling.     

Potential energy curves and calculations of spectroscopic constants for the ground state of AlC and AlN

The density functional theory method with B3LYP/6-311++G(df,pd), B3LYP/6-311++G(2df, 2pd), and B3LYP/6-311++G(3df,3pd) basis sets is used to compute the geometrics and single point energy of aluminum carbide (AlC) and aluminium nitride (AlN) in their ground state. The Level 8.0 program is used to calculate spectroscopic constants and fit the energy potential curves. The effect of a basis set on the spectroscopic constants is discussed. The results show that the calculated potential curve matches well with the Level 8.0 fitting curve, and the calculated values of spectroscopic constants become more reliable with the improvement of the quality of basis sets. The spectroscopic constants are in good agreement with the existing experimental and theoretical values. For the first time, the reliable anharmonicity constant data of AlC are reported, which agrees so well with the experimental value.     

A comparison of different many-body perturbation theory calculations of the ground state of SiS

A comparison of different many-body perturbation theory (MBPT ) calculations of the ground state rotational and vibrational constants of SiS is made. The calculations are performed up to the complete fourth-order MBPT level, and in all cases two basis sets are utilized. The results of the third-order and some incomplete fourth-order calculations are in good agreement, but the complete fourth-order is among the worst as compared with the experimental data. Analysis of the different contributions to the calculated correlation eneriges points towards the necessity of including even higher-order terms of the(MBPT ) expansion.     

Accurate potential for the ground state of the hydrogen molecule

Starting from the spectroscopic constants, an electronic potential for the ground state hydrogen molecule is presented. Self-consistence is checked by numerical integration of the radial wave equation. The mean eigenvalue deviation is about 1 cm⁻¹. Comparison with the latest theoretical work is considered. New revised spectroscopic constants and vibrational quanta are calculated.     

Diagrammatic formulation of the second‐order many‐body multipartitioning perturbation theory

The second‐order multireference perturbation theory employing multiple partitioning of the many‐electron Hamiltonian into a zero‐order part and a perturbation is formulated in terms of many‐body diagrams. The essential difference from the standard diagrammatic technique of Hose and Kaldor concerns the rules of evaluation of energy denominators which take into account the dependence of the Hamiltonian partitioning on the bra and ket determinantal vectors of a given matrix element, as well as the presence of several two‐particle terms in zero‐order operators. The novel formulation naturally gives rise to a “sum‐over‐orbital” procedure of correlation calculations on molecular electronic states, particularly efficient in treating the problems with large number of correlated electrons and extensive one‐electron bases. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 395–401, 1999     

A modified LEPS surface for the ground state of the water molecule

A modified LEPS potential surface using a Sato parameter which is a function of the internuclear coordinates has been developed for the ground state of the water molecule. By adjusting the Sato parameter many of the known properties of the water potential are fitted with this surface.     

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.     

Equation of state based on the weeks-chandler-andersen perturbation theory

An equation of state based on the Weeks-Chandler-Andersen (WCA) perturbation theory utilizing the simplified random-phase approximation (RPA) term is p of state is applied successfully to calculate the P-V-T relationship for a spherical molecule, argon.For nonspherical molecules, the effects of anisotropic interactions are treated empirically. The calculated P-V-T relationships and saturated properties for nonspherical and nonpolar molecules agree well with experimental data. The potential parameters for nonpolar substances are well correlated with the acentric factors.     

Calibration of the n-electron valence state perturbation theory approach

Extensive tests have been performed to benchmark and to compare with second-order perturbation theory based on a complete active space self-consistent field reference function (CASPT2), the recently developed n-electron valence state perturbation theory at second order (NEVPT2). Test calculations included the group fifteen diatomic molecules X(2) (X=N, P, As, and Sb) and the (4)S/(2)D and (4)S/(2)P splittings for the corresponding atoms, the (1)A(1)-(3)B(1) splittings for CH(2) and SiH(2), and the absorption spectra of pyrrole and of Cu(Imidazole)(2)(SH)(SH(2))(+), which is a model for plastocyanin. Comparisons with full configuration-interaction calculations and experimental data show that the accuracy of NEVPT2 is in most cases even better than CASPT2. Where intruder states hamper the CASPT2 calculations, NEVPT2 performs significantly better. Care is needed in the choice of active orbitals, for example in the calculation of the (4)S/(2)D and (4)S/(2)P splittings for the group fifteen atoms. This is due to the different treatment of orbitals belonging to the inactive or active spaces, making the NEVPT2 not invariant for the choice of active space, even in cases where the multiconfiguration self-consistent field energy is invariant.     

Electric dipole polarizability of the hydrogen molecule by many-body perturbation theory

Many-body perturbation theory is used to calculate the static electric dipole polarizability of the hydrogen molecule with a basis set of gaussian orbitals. Corrections complete through second order in electron correlation are calculated, and partial summation of certain classes of diagrams are extensively explored. The results are discussed in connection with the geometric approximation incorporating higher-order corrections.     

New perspectives in multireference perturbation theory: the n-electron valence state approach

The n-electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory which is based on a zero order reference wavefunction of CAS-CI type (complete active space configuration interaction) and which is characterized by the utilization of correction functions (zero order wavefunctions external to the CAS) of multireference nature, obtained through the diagonalization of a suitable two-electron model Hamiltonian (Dyall’s Hamiltonian) in some well defined determinant spaces. A review of the NEVPT approach is presented, starting from the original second order state-specific formulation, going through the quasidegenerate multi-state extension and arriving at the recent implementations of the third order in the energy and of the internally contracted configuration interaction. The chief properties of NEVPT—size consistence and absence of intruder states—are analyzed. Finally, an application concerning the calculation of the vertical spectrum of the biologically important free base porphin molecule, is presented.     

Applicability of multireference many-body perturbation theory to the Ne2+ molecule

The ground state as well as some low-lying excited states of the Ne₂⁺ molecule are calculated by means of the third-order multireference many-body perturbation theory with the “full” eight-orbital valence space using DZP and polarized valence TZ basis sets. The problem encountered with a large number of valence electrons is avoided by a proper definition of the Fermi vacuum. The calculated equilibrium distance of 1.721 Å and chemical dissociation energy D₀ = 1.283 eV are in good agreement with experimental results. A comparison with other ab initio techniques is also provided. © 1997 John Wiley & Sons, Inc.