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 multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

Theoretical study on the size consistency of the second and third order energies of the multireference perturbation theory

The size consistency of the second and third order energies of the multireference perturbation theory(Chen F, Davidson E, Iwata S. Int J Quant Chem, 2002, 86: 256) is investigated theoretically with a su-per-molecular model composed of N-hydrogen molecules separated by a large distance. It is found that the two perturbation series corresponding to two Hamiltonian partitions are not size consistent at the second and third order. However, two size consistent forms are suggested for two Hamiltonian parti-tions at the second order, if some approximations to the denominators of the original second order energies are assumed.     

Scale‐adaptive tensor algebra for local many‐body methods of electronic structure theory

While the formalism of multiresolution analysis, based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent‐particle level and, recently, second‐order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many‐particle) theory based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this article, we present a formalism called scale‐adaptive tensor algebra, which introduces an adaptive representation of tensors of many‐body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability of certain local correlated many‐body methods of electronic structure theory, for example, those directly based on atomic orbitals (or any other localized basis functions in general). © 2014 Wiley Periodicals, Inc.     

Estimation of reliability of quantum-chemical calculations of electronic transitions in aqua complexes of transition metals

The correlation comparison of energy levels of aqua complexes of row IV transition metals was calculated using different methods on the basis of the WinGAMESS program with standard potentials of these systems and experimental values of the rate constants. The calculation showed that the use of DFT (density functional theory) considerably increases the reliability of calculations.     

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.     

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.     

State‐specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2, and N2

Adaptation of improved virtual orbitals (IVOs) in state‐specific multireference perturbation theory using Møller–Plesset multipartitioning of the Hamiltonian (IVO‐SSMRPT) is examined in which the IVO‐complete active space configuration interaction (CASCI) is used as an inexpensive alternative to the more involved CAS‐self‐consistent field (CASSCF) orbitals. Unlike the CASSCF approach, IVO‐CASCI does not bear tedious and costly iterations beyond those in the initial SCF calculation. The IVO‐SSMRPT is intruder‐free, and explicitly size‐extensive. In the present preliminary study, the IVO‐SSMRPT method which relies on a small reference space is applied to study potential energy surfaces (PES) of the ground state of challenging, multiconfigurational F₂, Be₂, and N₂ molecules. These systems provide a serious challenge to any ab initio methodology due to the presence of an intricate interplay of nondynamical and dynamical correlations to the entire PES. The quality of the computed PES has been judged by extracting spectroscopic parameters and vibrational levels. The reported results illustrate that the IVO‐SSMRPT method has a potential to yield accuracies as good as the CASSCF‐SSMRPT one with reduced computational labor. Even with small reference spaces, our estimates demonstrate a good agreement with the available experimental values, and some benchmark computations. The blend of accuracy and low computational cost of IVO‐SSMRPT should deserve future attention for the accurate treatment of electronic states of small to large molecular systems for which the wavefunction is characterized by various configurations. © 2015 Wiley Periodicals, Inc.     

Ab initio Study of Electronic Structure and Properties in Crystalline 1,1,3,3,5,5‐Hexaazidocyclotriphosphazene

The banding and electronic structures of crystalline 1,1,3,3,5,5‐hexaazidocyclotriphosphazene (P₃N₂₁) have been investigated at DFT‐B3LYP/6‐31G(d) level. Relaxed crystal structure compares well with experimental data. The energy gap is 5.57 eV, indicating that P₃N₂₁ is an insulator. The frontier orbital is mainly formed by atomic orbitals of azido group, so it is the most reactive part of the molecule. The intermolecular interaction is strong along the direction that is nearly perpendicular to the phosphazene ring. The distribution of electrostatic potential is quite uneven, so P₃N₂₁ has a very high impact sensitivity. The point charge electrostatic potential is very high between the azido groups of the neighboring molecules, which indicates that the crystal lattice in this position may easily be broken and becomes the explosion center when P₃N₂₁ is impacted. The overlap populations of P–N_α bonds are much less than those of other bonds, therefore the P–N_α bonds first rupture by external stimuli, which agrees well with the experimental study of mass spectrum.     

Real‐time feedback from iterative electronic structure calculations

Real‐time feedback from iterative electronic structure calculations requires to mediate between the inherently unpredictable execution times of the iterative algorithm used and the necessity to provide data in fixed and short time intervals for real‐time rendering. We introduce the concept of a mediator as a component able to deal with infrequent and unpredictable reference data to generate reliable feedback. In the context of real‐time quantum chemistry, the mediator takes the form of a surrogate potential that has the same local shape as the first‐principles potential and can be evaluated efficiently to deliver atomic forces as real‐time feedback. The surrogate potential is updated continuously by electronic structure calculations and guarantees to provide a reliable response to the operator for any molecular structure. To demonstrate the application of iterative electronic structure methods in real‐time reactivity exploration, we implement self‐consistent semiempirical methods as the data source and apply the surrogate‐potential mediator to deliver reliable real‐time feedback. © 2015 Wiley Periodicals, Inc.     

Ab initio calculations and Franck-Condon simulation of the absorption spectra of GeCl2 including anharmonicity.

Geometrical parameters, vibrational frequencies and relative electronic energies of the X1A1, ?3B1 and A1B1 states of GeCl2 have been calculated at the CCSD(T) and/or CASSCF/MRCI level with basis sets of up to aug-cc-pV5Z quality. Core electron correlation and relativistic contributions were also investigated. RCCSD(T)/ aug-cc-pVQZ potential energy functions (PEFs) of the X1A1 and ?3B, states, and a CASSCF/MRCl/aug-cc-pVQZ PEF of the A1B1 state of GeCl2 are reported. Anharmonic vibrational wavefunctions of these electronic states of GeCl2, obtained variationally using the computed PEFs, are employed to calculate the Franck-Condon factors (FCFs) of the ?-X and A-X transitions of GeCl2. Simulated absorption spectra of these transitions based on the computed FCFs are compared with the corresponding experimental laser-induced fluorescence (LIF) spectra of Karolczak et al. [J. Chem. Phys. 1993, 98, 60-70]. Excellent agreement is obtained between the simulated absorption spectrum and observed LIF spectrum of the ?-X transition of GeCl2, which confirms the molecular carrier, the electronic states involved and the vibrational assignments of the LIF spectrum. However, comparison between the simulated absorption spectrum and experimental LIF spectrum of the A-X transition of GeCl2 leads to a revision of vibrational assignments of the LIF spectrum and suggests that the X1A1 state of GeCl2 was prepared in the experimental work, with a non-Boltzmann vibrational population distribution. The X(0,0,1) level is populated over 4000 times more than expected from a Boltzmann distribution at 60 K, which is appropriate for the relative population of the other low-lying vibrational levels, such as the X(1,0,0) and X(0,1,0) levels.     

Ab initio assessment of the electronic structure of 5α-reduced progestins

Progesterone (P) yields to 5α-reduced progestins, namely 5α-pregnanedione (DHP), tetrahydroprogesterone (THP), and allopregnanolone (ALLO-P). The geometries and electronic structure of these steroids were assessed by ab initio calculations using the 6-31G* basis set. The parameters measured were bond distances, valence angles, and dihedral angles. Likewise, the following were calculated: total energy; frontier orbitals, i.e., highest occupied molecular orbital (HOMO); lowest unoccupied molecular orbital (LUMO); dipole moment; atomic charges; and electrostatic potentials. The frontier orbitals of P were located at the π-double bond. However, the HOMO of the 5α-progestins was extended into the molecule, while the LUMO was confined at the C20 carbonyl group. The atomic charges, electronic density surfaces and electrostatic potentials showed patterns according to the stereochemical arrangement of the C3 and C20 carbonyl and hydroxyl functional groups. Interestingly, P and THP showed the larger dipole moment and high electronic density at the A-ring because the double bond and the 3α-hydroxy group, respectively. The present results might explain to some extent the metabolism of the studied progestins. Similarly, some physicochemical properties, such as dipole moments and electrostatic potentials, seem related with important biological actions such as uterine contractility and control of gonadotropin secretion. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 329–338, 1998     

Comparative study of the electronic structure of pregnanolones by ab initio theory

Pregnanedione (5β‐pregnane, 3,20‐dione), pregnanolone (3β‐hydroxy‐5β‐pregnan‐20‐one), and epipregnanolone (3α‐hydroxy‐5β‐pregnan‐20‐one) result from the 5β‐reduction of progesterone [4‐pregnene, 3‐20‐dione (P)]. These P metabolites induce anesthesia and smooth muscle relaxation (nongenomic actions). In the present study, geometries and electronic structure of these steroids were assessed by ab initio calculations using the 6‐31G* basis set. Consequently, bond distances, valence angles, and dihedral angles were measured. In addition total energy, frontier orbitals, i.e., highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), dipole moment, and electrostatic potentials were calculated. Total energy was higher for P, followed by pregnanedione. Pregnanolones, the hydroxylated progestins, showed the lower energies. Concerning frontier orbitals, P showed the highest HOMO energy and the lowest LUMO energy. Pregnanedione showed lower HOMO and LUMO energy values than pregnanolone and epipregnanolone. P showed both HOMO and LUMO located at the A ring, including the π bond at C4, C5, and the carbonyl at C3. The HOMO in pregnanedione was included mostly in the A ring and the C3 carbonyl group, while the LUMO was shared by the carbonyl groups at C3 and C20. The frontier orbitals of pregnanolone and epipregnanolone were quite similar. The HOMO in both steroids included the B, C, and D rings and the carbonyl at C20. The LUMO was also similar in both pregnanolones including mostly the carbonyl at C20. The dipole moment was shorter for P and pregnanedione and directed toward the acetyl side chain at C17. Pregnanolone and epipregnanolone showed the dipole moment vector larger and directed toward the A ring. The electrostatic potentials were related mostly with the lone pairs of electrons from the oxygens. By the total energy and frontier orbitals energies of the hormones studied, it is concluded that the metabolism of progesterone toward its 5β‐reduced metabolites might be rationalized from the theoretical chemistry point of view. Besides, the importance of the A/B ring cis configuration, dipole moment, and electrostatic potential are highlighted as possible improving elements of molecular interactions to explain the nongenomic biological action of 5β‐reduced progestins. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 433–440, 1999     

Real‐space grid representation of momentum and kinetic energy operators for electronic structure calculations

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed‐form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.     

First‐principles calculations on the energetics,electronic structures and magnetism of SrFeO2

The electronic and magnetic properties of SrFeO₂ with different magnetic configurations have been calculated via the plane‐wave pseudopotential density functional theory method, using the experimental lattice parameters. The results give an antiferromagnetic ground state for SrFeO₂ with an absolute magnetic moment agreeing very well with the experimental report. In comparison with the counterparts whose magnetic moments are parallel to the c axis, the structures with spin moments parallel to the a (or b) axis exhibit no observable preference in total energy, but show different density distributions of the Fe 3d and Fe 3d states. The square‐planar crystal field splits the Fe 3d orbitals into a high‐level d, a low d, and intermediate d_xy and d_xz or d_yz components. The exchange splitting is larger than the crystal‐field splitting, resulting in the high‐spin Fe 3d states. Referred to the triplet O₂, the O‐vacancy formation energy from SrFeO₃ to SrFeO₂ has been deduced as well, along with its dependence on the temperature and O₂ partial pressure. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009