State-averaged Multiconfiguration Self-consistent Field Research Articles

Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density.

Lagrangians of the state-averaged multiconfigurational self-consistent field (SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density are defined. In addition, variational equations were derived to calculate the excitation energies of the target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions, and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines, including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role in predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.

Analytical Energy Gradient for State-Averaged Orbital-Optimized Variational Quantum Eigensolvers and Its Application to a Photochemical Reaction.

Elucidating photochemical reactions is vital to understanding various biochemical phenomena and developing functional materials such as artificial photosynthesis and organic solar cells, albeit with notorious difficulty in both experiments and theories. The best theoretical way so far to analyze photochemical reactions at the level of ab initio electronic structure is the state-averaged multiconfigurational self-consistent field (SA-MCSCF) method. However, the exponential computational cost of classical computers with the increasing number of molecular orbitals hinders applications of SA-MCSCF for large systems we are interested in. Utilizing quantum computers was recently proposed as a promising approach to overcome such computational cost, dubbed as state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE). Here, we extend a theory of SA-OO-VQE so that analytical gradients of energy can be evaluated by standard techniques that are feasible with near-term quantum computers. The analytical gradients, known only for the state-specific OO-VQE in previous studies, allow us to determine various characteristics of photochemical reactions such as the conical intersection (CI) points. We perform a proof-of-principle calculation of our methods by applying it to the photochemical cis-trans isomerization of 1,3,3,3-tetrafluoropropene. Numerical simulations of quantum circuits and measurements can correctly capture the photochemical reaction pathway of this model system, including the CI points. Our results illustrate the possibility of leveraging quantum computers for studying photochemical reactions.

Theoretical Investigations on the Oxidation of Heptafluoro-iso-butyronitrile by Atomic Oxygen in Dielectric Breakdown.

Heptafluoro-iso-butyronitrile [(CF3)2CFCN, in abbr., C4] with CO2 gas mixture is a promising dielectric candidate to replace sulfur hexafluoride (SF6) for the sake of environmental concern. Detailed mechanisms for the reactions of C4 with atomic oxygen in both triplet and singlet due to dissociation of CO2 were proposed using high-level ab initio methods including density functional theory, quadratic complete basis set, multireference Rayleigh-Schrodinger perturbation theory, and state-averaged multiconfiguration self-consistent field. The reaction of C4 with O(3P) proceeds via the stepwise C-O and N-O addition/elimination and direct displacement mechanisms. The reaction paths are bifurated into cis and trans conformations. The predominant product channel is the C-O association with the barriers 6.1-6.8 kcal/mol to form the C3F7C(O)N intermediates and followed by the C-C bond cleavage to produce C3F7 and NCO radicals. On the singlet surface, the three-center intramolecular conversion to form the C3F7OCN isomer becomes competitive. The singlet-triplet intersystem crossing is favorable due to the significant spin-orbital coupling. Master equation calculations were carried out to obtain the temperature- and pressure-dependent rate coefficients and yields of the O(3P) + C4 reaction and were compared with the analogous reactions of nitriles. It was found that only the NCO + C3F7 product channel is significant. The overall rate coefficients are pressure-independent in the range 1-10 atm and can be expressed by k∞(T/K)=(6.41 ± 0.22) × 10-13(T/298)1.30±0.01e-(3241.5±24.5)/T cm3 molecule-1 s-1. The present theoretical work provides useful insights into the breakdown diagnostic of the C4/CO2 insulation gas.

Revisiting 12C16O[formula omitted]first negative system: An experimental and theoretical study

In this article, a new study of the 12C16O+First Negative system (B2Σ+→X2Σ+), is performed both theoretically and experimentally. From an experimental point of view, high-resolution Fourier transform spectroscopy in the ultraviolet region was used. On the theoretical side, ab initioelectronic energies were calculated employing the state-averaged multiconfiguration self-consistent field (MCSCF) method, followed by the icMRCI/AV6Z level of theory with Davidson modification. Through these two analyses, theoretical and experimental, values for the spectroscopic constants, potential energy curves, and parameters concerning the transition are presented. The results, both theoretical and experimental, obtained in this work are compared with values obtained in previous works, pointing out certain discrepancies with more recent works and providing new and improved values for the band origins of this transition.

Implementation of state-averaged MCSCF method to RISM- and 3D-RISM-SCF schemes

The state-averaged multiconfiguration self-consistent field (MCSCF) method was implemented to the reference interaction site model and three-dimensional reference interaction site model (RISM and 3D-RISM) SCF schemes, where the electronic structures of multiple states and solvation structure are determined simultaneously by the state-averaged MCSCF method and state-specific RISM-SCF/3D-RISM-SCF scheme, respectively, in a single calculation. The method was applied to the potential energy curves of the low-lying states of NaCl in aqueous solution and solvation shifts of the excitation energy of formaldehyde and p-nitroaniline. The results showed good agreement with those of the state-specific MCSCF and/or experiments.

Mechanistic and Kinetic Investigations on the Thermal Unimolecular Reaction of Heptafluoroisobutyronitrile.

Heptafluoroisobutyronitrile (C4) has been utilized as a dielectric compound to replace sulfur hexafluoride for the sake of environmental concern. Energetic profiles of the potential energy surface for the unimolecular reaction of C4 were calculated using density functional theory (M06-2X), quadratic complete basis set (CBS-QB3), Gaussian-4, multireference Rayleigh-Schrodinger perturbation theory (RS2, RS2C), and state-averaged multiconfiguration self-consistent-field (SA-MCSCF) ab initio methods. Among 38 production channels, the most energetically accessible reaction path is the three-centered rearrangement of cyanide to isocyanide. The C-CF3 bond appears to be the weakest bond in C4(X1A') and the symmetry-breaking C-CF3 bond cleavage undergoes to form the ground-state CF3(X2A1) and CF3CFCN (X2A″) radicals. All the possible isomerization pathways involving F- and CF3-migration together with the concerted elimination and stepwise decomposition routes were revealed for C4 and i-C4. Various isomers and potential toxic byproducts including FCN, CF3CN, C2F5CN, CF2═CFCF3, CF2═CFCN, CF4, C2F6, and alkyne compounds have been identified for the first time. Master equation analysis has been carried out to obtain the temperature- and pressure-dependent thermal rate constants. Theoretical kinetics for the loss of C4 due to pyrolysis is in good agreement with the temperature-ramped flow-tube experiment. The present theoretical work provides new insights on the thermal stability and chemical reactivity of C4. Moreover, i-C4 and C2F6 are proposed to be the potential characteristic gas molecules to monitor the insulation breakdown of C4 in the electric equipment.

Production of the Q2 doubly excited states of the hydrogen molecule by electron impact in a single step

We calculate the single step cross sections for excitation of Q 2 states of H2 and its subsequent dissociation. The cross section calculations were performed within the first Born approximation and the electronic wave functions were obtained via State-Averaged Multiconfigurational Self-Consistent Field followed by Configuration Interaction. We have assumed autoionization is the only important process competing with dissociation into neutral atoms. We have estimated its probability through a semi classical approach and compared with results of literature. Special attention was given to the Q 2 1Σg +(1) state which, as has been shown in a previous work, may dissociate into H(2sσ) + H(2sσ) fragments (some figures in this article are in colour only in the electronic version).

Numerical Estimation of the Pseudo-Jahn-Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules.

The pseudo-Jahn-Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.

Electronic spectrum of the UO and UO(+) molecules.

Electronic theory calculations are applied to the study of the UO molecule and the UO(+) ion. Relativistic effective core potentials are used along with the accompanying valence spin-orbit operators. Polarized double-ς and triple-ς basis sets are used. Molecular orbitals are obtained from state-averaged multiconfiguration self-consistent field calculations and then used in multireference spin-orbit configuration interaction calculations with a number of millions of terms. The ground state of UO has open shells of 5f(3)7s(1), angular momentum Ω = 4, and a spin-orbit-induced avoided crossing near the equilibrium internuclear distance. Many UO excited states are studied with rotational constants, intensities, and experimental comparisons. The ground state of UO(+) is of 5f(3) nature with Ω = 9/2. Many UO(+) excited states are also studied. The open-shell nature of both UO and UO(+) leads to many low-lying excited states.

Optical-optical double resonance spectroscopy of the quasi-linear S2 state of CHF and CDF. I. Spectroscopic analysis

In this work, we report on our full results of the spectroscopic analysis of the quasi-linear S(2) state of the prototypical halocarbene, CHF, and its deuterated isotopomer CDF using optical-optical double resonance spectroscopy through the S(1) state. A total of 51 S(2) state vibrational levels with angular momenta in the range [script-l] = 0-3 were observed for CHF, and 76 levels for CDF. Progressions involving all three fundamental vibrations were observed, and rotational constants were determined for each of these levels by measuring spectra through different intermediate J levels of the S(1) state. Our experimental results are in excellent agreement with the predictions of vibrational calculations using the discrete variable representation method. The variational vibrational calculations were performed with an analytic potential energy surface fit to ab initio data by the method of interpolating moving least squares. The ab initio data are Davidson-corrected multi-reference configuration interaction calculations based on a state-averaged multiconfigurational self-consistent field reference incorporating a generalized dynamic weighting scheme.

Lagrangian approach for geometrical derivatives and nonadiabatic coupling terms in MRCISD

A new formulation for multireference configuration interaction method, with single and double excitations (MRCISD), energy gradients and nonadiabatic coupling terms based on a Lagrangian approach is suggested and the gradients demonstrated to be accurate with calculations on several molecules. Of particular interest, the suggested formalism can straightforwardly use state-averaged-multiconfiguration self-consistent field (SA-MCSCF) descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited 1Σ+ states of LiH, including calculations near an avoided crossing. The formalism can use either complete or incomplete model (i.e. reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. The formalism for nonadiabatic coupling shares many structural features with the energy gradient formalism, with the use of a function that corresponds to the energy for the coupling.

Theoretical and Experimental Spectroscopy of the S2 State of CHF and CDF: Dynamically Weighted Multireference Configuration Interaction Calculations for High-Lying Electronic States

Dynamically adjusting the weights in state-averaged multiconfigurational self-consistent field (SA-MCSCF) calculations using an energy-dependent functional allows the electronic wave function to smoothly evolve across the potential energy surface (PES) and correctly preserves differing asymptotic electronic-state degeneracy patterns. We have developed a generalized dynamic weighting (GDW) method to treat high-lying electronic states. To test the method, a global PES was constructed for the S2 (B̃) state of CHF (CDF), which lies nearly 31000 cm−1 above the minimum of the ground state. The GDW method was used to produce SA-MCSCF reference states for subsequent multireference configuration interaction (MRCI) calculations, whose Davidson-corrected energies were extrapolated to the complete basis set limit. Quantum mechanical vibrational energy calculations for CDF were performed using the fitted PES, and the predicted energy levels are in excellent agreement with an extensive set of experimentally determined (optical−optical double resonance) levels, with a mean unsigned error of only 12 cm−1.

Potential energy curve for isomerization of N2H2 and C2H4 using the improved virtual orbital multireference Møller–Plesset perturbation theory

Multireference Møller-Plesset (MRMP) perturbation theory [K. Hirao, Chem. Phys. Lett. 190, 374 (1992)] is modified to use improved virtual orbitals (IVOs) and is applied to study ground state potential energy curves for isomerization and dissociation of the N2H2 and C2H4 molecules. In contrast to traditional MRMP or multistate multiconfiguration quasidegenerate perturbation theory where the reference functions are obtained from (often difficult to converge) state averaged multiconfiguration self-consistent field methods, our reference functions are represented in terms of computationally efficient IVOs. For convenience in comparisons with other methods, a first order complete active space configuration interaction (CASCI) calculation with the IVOs is followed by the use of the IVOs in MRMP to incorporate residual electron correlation effects. The potential energy curves calculated from the IVO-MRMP method are compared with computations using state-of-the-art coupled cluster singles and doubles (CCSD) methods and variants thereof to assess the efficacy of the IVO-MRMP scheme. The present study clearly demonstrates that unlike the CCSD and its variants, the IVO-MRMP approach provides smooth and reliable ground state potential energy curves for isomerization of these systems. Although the rigorously size-extensive completely renormalized CC theory with noniterative triples corrections (CR-CC(2,3)) likewise provides relatively smooth curves, the CR-CC(2,3) calculations overestimate the cis-trans barrier height for N2H2. The ground state spectroscopic constants predicted by the IVO-CASCI method agree well with experiment and with other highly correlated ab initio methods.

An ab initio molecular dynamics study on the dissociative recombination reaction of HD2O+ + e−

An ab initio molecular dynamics simulations have been carried out for the dissociative recombination reaction of the deuterium-substituted hydronium cation, HD2O+ + e −, at the state-averaged multiconfigurational self-consistent field level. In the present simulations, five electronic states of HD2O were included explicitly, and nonadiabatic transitions among adiabatic electronic states were taken into account by the Tully’s fewest switches algorithm. It is shown that the dominant products, OD + D + H, were generated in 63% of trajectories, while the products, OH + 2D, were generated in only 11% of trajectories, indicating that the release of a light fragment H is favored over the release of a heavy fragment D. This result is in conformity with the observation that there is a larger amount of deuterium substituted species than the non-substituted species in the interstellar space.

Ab Initio Direct Trajectory Simulation with Nonadiabatic Transitions of the Dissociative Recombination Reaction HCNH++e−→ HNC/HCN + H

The dissociative recombination reaction of HCNH+ + e- via indirect radiative mechanism on relevant excited state potential energy surfaces has been studied to investigate the branching ratio of the products, HNC/HCN, by using an ab initio direct trajectory method at the state-averaged multiconfigurational self-consistent field level. In trajectory simulations using adiabatic potential energy surfaces, nonadiabatic transitions among the three electronic states of HCNH, i.e., 1 2Π, 1 2Σ+, and 2 2Σ+, were explicitly treated by Tully's surface-hopping algorithm. We show that HNC and HCN are produced with almost the same ratio from this reaction, supporting the picture that HCNH+ plays a significant role as the precursor for both HNC and HCN production in interstellar clouds.

Analytical energy gradients for internally contracted second-order multireference perturbation theory

The theory for computing analytical energy gradients for second-order multireference perturbation theory (MRPT2) with arbitrary multiconfiguration self-consistent field (MCSCF) reference functions is derived and implemented. MRPT2 with complete active space reference functions (CASPT2) is a special case. In our method the configurations with two electrons in the external orbital space are internally contracted. This ansatz strongly reduces the length of the configuration expansion as compared to uncontracted wave functions, but avoids bottlenecks occurring when fully contracted first-order wave functions are used. The method, which also allows the use of state-averaged MCSCF reference functions, is applied to optimize the structures of low-lying valence and Rydberg states of Pyrrole. Nonplanar equilibrium structures and large geometry relaxation effects on the excitation energies are found for the valence states. From the results it can be concluded that CASPT2 underestimates the excitation energies of the valence states, but leads to accurate results for the Rydberg states.

Electronic structure aspects of the spin-forbidden reaction CH3(X 2A2″)+N(4S)→HCN(X 1Σ+)+H2(X 1Σg+)

Second order configuration interaction wave functions based on molecular orbitals determined from a state-averaged multiconfigurational self-consistent field procedure are used to investigate the intermediate complex driven model for the spin-forbidden reaction CH3(X 2A2″)+N(4S)→HCN(X 1Σ+)+H2(X 1Σ+). The minimum energy crossing point (MECP), the minimum energy point on the surface of intersection connecting the reactant channel, A′′3 potential energy surface, and product channel A′1 potential energy surface, is determined directly, i.e., without a priori characterization of the individual potential energy surfaces. The MECP is found to be 8.2 kcal/mol below of the reactants. The structure at the MECP clearly evinces the incipient formation of a H2 bond. Barrierless paths from the reactants to the intermediate complex-methylnitrene, from the intermediate complex to the MECP, and from the MECP to the products are established. The absence of a barrier on these paths supports the intermediate complex mechanism. Spin–orbit interactions are determined to be ∼30 cm−1 for points on the surface of intersection in the vicinity of the MECP. Spin–orbit interactions and the local potential surface topology at the MECP are used to probe the efficiency of the intersystem crossing using the Landau–Zener model. A reduced dimensionality model is proposed.

Low-lying electronic states of lanthanocenes and actinocenes M(C8H8)2 (M=Nd, Tb, Yb, U)

Large-scale state-averaged multiconfiguration self-consistent field, multireference configuration interaction, and averaged coupled-pair functional calculations, including relativistic effects by means of energy-consistent quasirelativistic pseudopotentials, have been carried out for the ground and low-lying excited states of the di-π-cyclooctatetraene (or bis[8]annulene) metal sandwich complexes M(C8H8)2 (M=Nd, Tb, Yb, U). It is found that the ground state configurations for the lanthanocenes are 4fnπ3, while for the actinocenes they are 5fn−1π4. The ground states for the lighter and heavier lanthanocenes are, respectively, the lower and higher multiplicity states resulting from the coupling between the highest possible spin–multiplicity of the central metal 4fn subshell and the unpaired ligand π electron, whereas they always have the highest possible multiplicity of 5fn−1π4 for the actinocenes. The metal–ring distances and symmetric metal–ring stretching frequencies are reported. The special characteristics of the uranium 5f orbitals in uranocene are described. Extensive spin–orbit configuration interaction calculations were performed for uranocene and confirm the assignment of the ground state and first excited state of uranocene made previously by other authors. However, a different ordering is obtained for the higher states. The calculated term energy for the first excited state of uranocene is in excellent agreement with the experimental value.

Formally tetravalent cerium and thorium compounds: a configuration interaction study of cerocene Ce(C8H8)2 and thorocene Th(C8H8)2 using energy-adjusted quasirelativistic ab initio pseudopotentials

Abstract Large-scale state-averaged multi-configuration self-consistent field, configuration interaction, averaged coupled-pair functional and spin-orbit configuration interaction calculations have been carried out for the ground states and low-lying excited states of the bis(cyclooctatetraene)f-element sandwich complexes cerocene Ce(C 8 H 8 ) 2 and thorocene Th(C 8 H 8 ) 2 . Whereas for a single-determinant wavefunction thorocene may be pictured as a Th IV compound, i.e. a Th 4+ closed-shell ion complexed by two aromatic C 8 H 8 2− ligands, cerocene is to a first approximation a Ce III compound, i.e. a Ce 3+ ion with a 4f 1 configuration and two C 8 H 8 1.5− ligands. When cerocene is described by a multi-determinant wavefunction admixture of the Ce 4+ (C 8 H 8 2− ) 2 configuration leads to a 1 A 1g ground state of the same symmetry as in thorocene. For both compounds results for the metal-ring distance, the symmetric metal-ring stretching frequency, the photoelectron spectrum and the optical spectrum are compared to experimental data.

Quasidegenerate perturbation theory with multiconfigurational self-consistent-field reference functions

A quasidegenerate perturbation theory based on multiconfigurational self-consistent-field (MCSCF) reference functions is derived. The perturbation theory derived here is for multistate, where several MCSCF functions obtained by the state-averaged MCSCF method are used as the reference and an effective Hamiltonian is constructed by perturbation calculation. The energies of states interested in are obtained simultaneously by diagonalization of the effective Hamiltonian. An explicit formula of the effective Hamiltonian through second order is derived as well as general formalism, and is applied to calculate potential curves of the system H2, Be–H2, CO, NO, BN, and LiF. The results agree well with those of full configuration interaction or multireference single and double excitation configuration interaction methods for both the ground and the excited states.