Dongxia Ma

MOLCAS 8: New Capabilities for Multiconfigurational Quantum Chemical Calculations across the Periodic Table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas–Kroll–Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC‐PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large‐scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

The generalized active space concept in multiconfigurational self-consistent field methods.

A multiconfigurational self-consistent field method based on the concept of generalized active space (GAS) is presented. GAS wave functions are obtained by defining an arbitrary number of active spaces with arbitrary occupation constraints. By a suitable choice of the GAS spaces, numerous ineffective configurations present in a large complete active space (CAS) can be removed, while keeping the important ones in the CI space. As a consequence, the GAS self-consistent field approach retains the accuracy of the CAS self-consistent field (CASSCF) ansatz and, at the same time, can deal with larger active spaces, which would be unaffordable at the CASSCF level. Test calculations on the Gd atom, Gd(2) molecule, and oxoMn(salen) complex are presented. They show that GAS wave functions achieve the same accuracy as CAS wave functions on systems that would be prohibitive at the CAS level.

Multiconfiguration Pair-Density Functional Theory.

We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.

SplitGAS Method for Strong Correlation and the Challenging Case of Cr2

A new multiconfigurational quantum chemical method, SplitGAS, is presented. The configuration interaction expansion, generated from a generalized active space, GAS, wave function is split in two parts, a principal part containing the most relevant configurations and an extended part containing less relevant, but not negligible, configurations. The partition is based on an orbital criterion. The SplitGAS method has been employed to study the HF, N2, and Cr2 molecules. The results on these systems, especially on the challenging, multiconfigurational Cr2 molecule, are satisfactory. While SplitGAS is comparable with the GASSCF method in terms of memory requirements, it performs better than the complete active space method followed by second-order perturbation theory, CASPT2, in terms of equilibrium bond length, dissociation energy, and vibrational properties.

Diabatization based on the dipole and quadrupole: The DQ method

In this work, we present a method, called the DQ scheme (where D and Q stand for dipole and quadrupole, respectively), for transforming a set of adiabatic electronic states to diabatic states by using the dipole and quadrupole moments to determine the transformation coefficients. It is more broadly applicable than methods based only on the dipole moment; for example, it is not restricted to electron transfer reactions, and it works with any electronic structure method and for molecules with and without symmetry, and it is convenient in not requiring orbital transformations. We illustrate this method by prototype applications to two cases, LiH and phenol, for which we compare the results to those obtained by the fourfold-way diabatization scheme.

Infrared spectra and quantum chemical calculations of the uranium-carbon molecules UC, CUC, UCH, and U(CC)2.

Laser evaporation of carbon rich uranium/carbon alloy targets into condensing argon or neon matrix samples gives weak infrared absorptions that increase on annealing, which can be assigned to new uranium carbon bearing species. New bands at 827.6 cm(-1) in solid argon or 871.7 cm(-1) in neon become doublets with mixed carbon 12 and 13 isotopes and exhibit the 1.0381 carbon isotopic frequency ratio for the UC diatomic molecule. Another new band at 891.4 cm(-1) in argon gives a three-band mixed isotopic spectrum with the 1.0366 carbon isotopic frequency ratio, which is characteristic of the anti-symmetric stretching vibration of a linear CUC molecule. No evidence was found for the lower energy cyclic U(CC) isomer. Other bands at 798.6 and 544.0 cm(-1) are identified as UCH, which has a uranium-carbon triple bond similar to that in UC. Evidence is found for bicyclic U(CC)(2) and tricyclic U(CC)(3). This work shows that U and C atoms react spontaneously to form the uranium carbide U≡C and C≡U≡C molecules with uranium-carbon triple bonds.

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

Calculation of heats of formation for Zn complexes: Comparison of density functional theory, second order perturbation theory, coupled-cluster and complete active space methods

Heats of formation were predicted for nine ZnX complexes (X= Zn, H, O, F2, S, Cl, Cl2, CH3, (CH3)2) using fourteen density functionals, MP2 calculations and the CCSD and CCSD(T) coupled-cluster methods. Calculations utilized the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Heats of formation were most accurately predicted by the TPSSTPSS and TPSSKCIS density functionals, and the BLYP, B3LYP, MP2, CCSD and CCSD(T) levels were among the poorest performing methods based on accuracy. A wide range of Zn2 equilibrium bond distances were predicted, indicating that many of the studied levels of theory may be unable to adequately describe this transition metal dimer. To further benchmark the accuracy of the density functional methods, high-level CASSCF and CASPT2 calculations were performed to estimate bond dissociation energies, equilibrium bond lengths and heats of formation for the diatomic Zn complexes and the latter two quantities were compared with the results of DFT, MP2 and coupled-cluster calculations as well as experimental values.

Systematic Expansion of Active Spaces beyond the CASSCF Limit: A GASSCF/SplitGAS Benchmark Study

The applicability and accuracy of the generalized active space self-consistent field, (GASSCF), and (SplitGAS) methods are presented. The GASSCF method enables the exploration of larger active spaces than with the conventional complete active space SCF, (CASSCF), by fragmentation of a large space into subspaces and by controlling the interspace excitations. In the SplitGAS method, the GAS configuration interaction, CI, expansion is further partitioned in two parts: the principal, which includes the most important configuration state functions, and an extended, containing less relevant but not negligible ones. An effective Hamiltonian is then generated, with the extended part acting as a perturbation to the principal space. Excitation energies of ozone, furan, pyrrole, nickel dioxide, and copper tetrachloride dianion are reported. Various partitioning schemes of the GASSCF and SplitGAS CI expansions are considered and compared with the complete active space followed by second-order perturbation theory, (CASPT2), and multireference CI method, (MRCI), or available experimental data. General guidelines for the optimum applicability of these methods are discussed together with their current limitations.

Stretch Effects Induced by Molecular Strain on Weakening σ‑Bonds: Molecular Design of Long-Lived Diradicals (Biradicals)

Stretch effects induced by two types of molecular strain were examined by quantum chemical calculations at the B3LYP/6-31G(d), B3LYP/cc-PVDZ, CCSD/6-31G(d), and CASPT2/ANO-RCC-VTZP level of theory, to design persistent multiradicals such as localized diradicals and oxyallyls. The cooperative molecular strain (Type-1) induced by the spiro[5.5]undecane and bicyclo[2.1.0]cyclopentane structures was found to significantly destabilize in energy the ring-closed compounds of the diradicals, leading to small energy differences between the diradicals and the σ-bonded compounds. Another stretch effect (Type-2) induced by macrocyclic systems was also found to energetically destabilize the corresponding ring-closed structures of the 1,3-diradicals. The computational studies predict that the two types of stretch effects are quite effective in lowering the energy barriers of the bond-breaking reaction of the ring-closed compounds and in generating long-lived localized diradicals and oxyallyl derivatives.