New implementation of the configuration-based multi-reference second order perturbation theory

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Unraveling the Spin-State Energetics of FeN4 Complexes with Ab Initio Methods

A systematic analysis was conducted to explore the spin-state energetics of a series of 19 FeN4 complexes. The performance of a large number of multireference methods was assessed, highlighting the significant challenges associated with accurately describing the spin-state energetics of FeN4 complexes. Most multireference methods were found to be susceptible to errors originating from the reference CASSCF wavefunction, leading to an overstabilization of high-spin states. Nonetheless, a few multireference methods, namely, CASPT2/CC, DSRG-MRPT3, and LDSRG(2), demonstrated promising performance compared to the benchmark CCSD(T) method. Furthermore, our study revealed that FeN4 complexes having a quintet ground state are exceedingly rare. Accordingly, only one specific model (Fe(L2)) and one synthesized complex (Fe(OTBP)) have the quintet ground state among the studied complexes. This scarcity of quintet FeN4 complexes highlights the unique nature of these systems and raises intriguing questions regarding the factors influencing spin states, such as the size of the macrocycle cavity, the introduction of substituents, or the induction of out-of-plane deformation.

Block Effective Hamiltonian Theory and Its Application

Block effective Hamiltonian theory (BEHT) is presented in this work. Configuration interaction functions are divided into P, Q, and R spaces. Effective Hamiltonian is constructed with the partitioning technique within the P space. The eigenvalue problem of the effective Hamiltonian is then solved iteratively. It is demonstrated that the ground-state energies of N₂, HF, and F₂ calculated with BEHT converge to the multireference configuration interaction energies from below and the iteration number becomes smaller as BEHT energy becomes closer to the exact energy. The accuracy of BEHT is better than that of the second-order multireference perturbation theory, although the matrix elements in both methods are the same. The ionization potentials of the singlet state of HF, the doublet state of F, and the triplet state of NH and the potential energy curves of CH₄, C₂, and N₂ are calculated with BEHT and compared with experiments and results of CASSCF, CCSD, and CCSD(T) and the results of the full configuration interaction if available. The iteration numbers are all less than 10 in this study. These calculations show the good performances of BEHT in comparison with other theoretical approximation methods.

Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). II. The full rank NEVPT2 (FR-NEVPT2) formulation

In Paper I, the performances of pre-screening (PS), extended PS (EPS), and cumulant (CU) approximations to the fourth-order density matrix were examined in the context of second-order N-electron valence state perturbation theory (NEVPT2). It has been found that the CU, PS, and even EPS approximations with loose thresholds may introduce intruder states. In the present work, the origin of these "false intruder" states introduced by approximated density matrices is discussed. Canonical NEVPT2 implementations employ a rank reduction trick. By analyzing its residual error, we find that the omission of the rank reduction leads to a more stable multireference perturbation theory for incomplete active space reference wave functions. Such a full rank (FR)-NEVPT2 formulation is equivalent to the conventional NEVPT2 method for the complete active space self-consistent field/complete active space configuration interaction reference wave function. A major drawback of the FR-NEVPT2 formulation is the necessity of the fifth-order density matrix. To avoid the construction of the high-order density matrices, the combination of the FR-NEVPT2 with the CU approximation is studied. However, we find that the CU approximation remains problematic as it still introduces intruder states. The question of how to robustly and efficiently perform internally contracted multireference perturbation theories with approximate densities remains a challenging field of investigation.

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.

Topology of conical/surface intersections among five low-lying electronic states of CO2: multireference configuration interaction calculations

Multi-reference configuration interaction with single and double excitation method has been utilized to calculate the potential energy surfaces of the five low-lying electronic states (1)A1, (1)A2, (3)A2, (1)B2, and (3)B2 of carbon dioxide molecule. Topology of intersections among these five states has been fully analyzed and is associated with double-well potential energy structure for every electronic state. The analytical potential energy surfaces based on the reproducing kernel Hilbert space method have been utilized for illustrating topology of surface crossings. Double surface seam lines between (1)A1 and (3)B2 states have been found inside which the (3)B2 state is always lower in potential energy than the (1)A1 state, and thus it leads to an angle bias collision dynamics. Several conical∕surface intersections among these five low-lying states have been found to enrich dissociation pathways, and predissociation can even prefer bent-geometry channels. Especially, the dissociation of O((3)P) + CO can take place through the intersection between (3)B2 and (1)B2 states, and the intersection between (3)A2 and (1)B2 states.