Mickaël G. Delcey

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.

Calibration of Cholesky Auxiliary Basis Sets for Multiconfigurational Perturbation Theory Calculations of Excitation Energies

The accuracy of auxiliary basis sets derived from Cholesky decomposition of two-electron integrals is assessed for excitation energies calculated at the state-average complete active space self-consistent field (CASSCF) and multiconfigurational second order perturbation theory (CASPT2) levels of theory using segmented as well as generally contracted atomic orbital basis sets. Based on 196 valence excitations in 26 organic molecules and 72 Rydberg excitations in 3 organic molecules, the results show that Cholesky auxiliary basis sets can be used without compromising the accuracy of the multiconfigurational methods. Specifically, with a decomposition threshold of 10(-4) au, the mean error due to the Cholesky auxiliary basis set is 0.001 eV, or smaller, decreasing with increasing atomic orbital basis set quality.

Restricted active space calculations of L-edge X-ray absorption spectra: From molecular orbitals to multiplet states

The metal L-edge (2p → 3d) X-ray absorption spectra are affected by a number of different interactions: electron-electron repulsion, spin-orbit coupling, and charge transfer between metal and ligands, which makes the simulation of spectra challenging. The core restricted active space (RAS) method is an accurate and flexible approach that can be used to calculate X-ray spectra of a wide range of medium-sized systems without any symmetry constraints. Here, the applicability of the method is tested in detail by simulating three ferric (3d(5)) model systems with well-known electronic structure, viz., atomic Fe(3+), high-spin [FeCl6](3-) with ligand donor bonding, and low-spin [Fe(CN)6](3-) that also has metal backbonding. For these systems, the performance of the core RAS method, which does not require any system-dependent parameters, is comparable to that of the commonly used semi-empirical charge-transfer multiplet model. It handles orbitally degenerate ground states, accurately describes metal-ligand interactions, and includes both single and multiple excitations. The results are sensitive to the choice of orbitals in the active space and this sensitivity can be used to assign spectral features. A method has also been developed to analyze the calculated X-ray spectra using a chemically intuitive molecular orbital picture.

Chemiluminescence and Fluorescence States of a Small Model for Coelenteramide and Cypridina Oxyluciferin: A CASSCF/CASPT2 Study

Fluorescence and chemiluminescence phenomena are often confused in experimental and theoretical studies on the luminescent properties of chemical systems. To establish the patterns that distinguish both processes, the fluorescent and chemiluminescent states of 2-acetamido-3-methylpyrazine, which is a small model of the coelenterazine/coelenteramide and Cypridina luciferin/oxyluciferin bioluminescent systems, were characterized by using the complete active space second-order perturbation (CASPT2) method. Differences in geometries and electronic structures among the states responsible for light emission were found. On the basis of the findings, some recommendations for experimental studies on chemiluminescence are suggested, and more appropriate theoretical approaches are proposed.

Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors: Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections.

Analytical state-average complete-active-space self-consistent field derivative (nonadiabatic) coupling vectors are implemented. Existing formulations are modified such that the implementation is compatible with Cholesky-based density fitting of two-electron integrals, which results in efficient calculations especially with large basis sets. Using analytical nonadiabatic coupling vectors, the optimization of conical intersections is implemented within the projected constrained optimization method. The standard description and characterization of conical intersections is reviewed and clarified, and a practical and unambiguous system for their classification and interpretation is put forward. These new tools are subsequently tested and benchmarked for 19 different conical intersections. The accuracy of the derivative coupling vectors is validated, and the information that can be drawn from the proposed characterization is discussed, demonstrating its usefulness.

Benzophenone Ultrafast Triplet Population : Revisiting the Kinetic Model by Surface-Hopping Dynamics

The photochemistry of benzophenone, a paradigmatic organic molecule for photosensitization, was investigated by means of surface-hopping ab initio molecular dynamics. Different mechanisms were found to be relevant within the first 600 fs after excitation; the long-debated direct (S1 → T1) and indirect (S1 → T2 → T1) mechanisms for population of the low-lying triplet state are both possible, with the latter being prevalent. Moreover, we established the existence of a kinetic equilibrium between the two triplet states, never observed before. This fact implies that a significant fraction of the overall population resides in T2, eventually allowing one to revisit the usual spectroscopic assignment proposed by transient absorption spectroscopy. This finding is of particular interest for photocatalysis as well as for DNA damages studies because both T1 and T2 channels are, in principle, available for benzophenone-mediated photoinduced energy transfer toward DNA.

Accurate calculations of geometries and singlet-triplet energy differences for active-site models of (NiFe) hydrogenase†

We have studied the geometry and singlet-triplet energy difference of two mono-nuclear Ni(2+) models related to the active site in [NiFe] hydrogenase. Multiconfigurational second-order perturbation theory based on a complete active-space wavefunction with an active space of 12 electrons in 12 orbitals, CASPT2(12,12), reproduces experimental bond lengths to within 1 pm. Calculated singlet-triplet energy differences agree with those obtained from coupled-cluster calculations with single, double and (perturbatively treated) triple excitations (CCSD(T)) to within 12 kJ mol(-1). For a bimetallic model of the active site of [NiFe] hydrogenase, the CASPT2(12,12) results were compared with the results obtained with an extended active space of 22 electrons in 22 orbitals. This is so large that we need to use restricted active-space theory (RASPT2). The calculations predict that the singlet state is 48-57 kJ mol(-1) more stable than the triplet state for this model of the Ni-SIa state. However, in the [NiFe] hydrogenase protein, the structure around the Ni ion is far from the square-planar structure preferred by the singlet state. This destabilises the singlet state so that it is only ∼24 kJ mol(-1) more stable than the triplet state. Finally, we have studied how various density functional theory methods compare to the experimental, CCSD(T), CASPT2, and RASPT2 results. Semi-local functionals predict the best singlet-triplet energy differences, with BP86, TPSS, and PBE giving mean unsigned errors of 12-13 kJ mol(-1) (maximum errors of 25-31 kJ mol(-1)) compared to CCSD(T). For bond lengths, several methods give good results, e.g. TPSS, BP86, and M06, with mean unsigned errors of 2 pm for the bond lengths if relativistic effects are considered.

Viewing the Valence Electronic Structure of Ferric and Ferrous Hexacyanide in Solution from the Fe and Cyanide Perspectives

The valence-excited states of ferric and ferrous hexacyanide ions in aqueous solution were mapped by resonant inelastic X-ray scattering (RIXS) at the Fe L2,3 and N K edges. Probing of both the central Fe and the ligand N atoms enabled identification of the metal- and ligand-centered excited states, as well as ligand-to-metal and metal-to-ligand charge-transfer excited states. Ab initio calculations utilizing the RASPT2 method were used to simulate the Fe L2,3-edge RIXS spectra and enabled quantification of the covalencies of both occupied and empty orbitals of π and σ symmetry. We found that π back-donation in the ferric complex is smaller than that in the ferrous complex. This is evidenced by the relative amounts of Fe 3d character in the nominally 2π CN(-) molecular orbital of 7% and 9% in ferric and ferrous hexacyanide, respectively. Utilizing the direct sensitivity of Fe L3-edge RIXS to the Fe 3d character in the occupied molecular orbitals, we also found that the donation interactions are dominated by σ bonding. The latter was found to be stronger in the ferric complex, with an Fe 3d contribution to the nominally 5σ CN(-) molecular orbitals of 29% compared to 20% in the ferrous complex. These results are consistent with the notion that a higher charge at the central metal atom increases donation and decreases back-donation.

Parallelization of a multiconfigurational perturbation theory

In this work, we present a parallel approach to complete and restricted active space second‐order perturbation theory, (CASPT2/RASPT2). We also make an assessment of the performance characteristics of its particular implementation in the Molcas quantum chemistry programming package. Parallel scaling is limited by memory and I/O bandwidth instead of available cores. Significant time savings for calculations on large and complex systems can be achieved by increasing the number of processes on a single machine, as long as memory bandwidth allows, or by using multiple nodes with a fast, low‐latency interconnect. We found that parallel efficiency drops below 50% when using 8–16 cores on the shared‐memory architecture, or 16–32 nodes on the distributed‐memory architecture, depending on the calculation. This limits the scalability of the implementation to a moderate amount of processes. Nonetheless, calculations that took more than 3 days on a serial machine could be performed in less than 5 h on an InfiniBand cluster, where the individual nodes were not even capable of running the calculation because of memory and I/O requirements. This ensures the continuing study of larger molecular systems by means of CASPT2/RASPT2 through the use of the aggregated computational resources offered by distributed computing systems.

Analytical gradients of the state-average complete active space self-consistent field method with density fitting.

An efficient implementation of the state-averaged complete active space self-consistent field (SA-CASSCF) gradients employing density fitting (DF) is presented. The DF allows a reduction both in scaling and prefactors of the different steps involved. The performance of the algorithm is demonstrated on a set of molecules ranging up to an iron-Heme b complex which with its 79 atoms and 811 basis functions is to our knowledge the largest SA-CASSCF gradient computed. For smaller systems where the conventional code could still be used as a reference, both the linear response calculation and the gradient formation showed a clear timing reduction and the overall cost of a geometry optimization is typically reduced by more than one order of magnitude while the accuracy loss is negligible.