The DFT/MRCI method

Abstract

In the past two decades, the combined density functional theory and multireference configuration interaction (DFT/MRCI) method has developed from a powerful approach for computing spectral properties of singlet and triplet excited states of large molecules into a more general multireference method applicable to states of all spin multiplicities. In its original formulation, it shows great efficiency in the evaluation of singlet and triplet excited states which mainly originate from local one-electron transitions. Moreover, DFT/MRCI is one of the few methods applicable to large systems that yields the correct ordering of states in extended π-systems where double excitations play a significant role. A recently redesigned DFT/MRCI Hamiltonian extends the application range of the method to bichromophores such as hydrogen-bonded or π-stacked dimers and loosely coupled donor-acceptor systems. In conjunction with a restricted-open shell Kohn-Sham optimization of the molecular orbitals, even electronically excited doublet and quartet states can be addressed. After a short outline of the general ideas behind this semi-empirical method and a brief review of alternative approaches combining density functional and multireference wavefunction theory, formulae for the DFT/MRCI Hamiltonian matrix elements are presented and the adjustments of the two-electron contributions are discussed. The performance of the DFT/MRCI variants on excitation energies of organic molecules and transition metal compounds against experimental or ab initio reference data is analyzed and case studies are presented which show the strengths and limitations of the method. Finally, an overview over the properties available from DFT/MRCI wavefunctions and further developments is given.ABBREVIATIONS: ACRXTN, 3-(9,9-dimethylacridin-10[9H]-yl)-9H-xanthen-9-one; AO, atomic orbital; CASSCF, Complete active space self-consistent field; CASPT2, Complete active space second-order perturbation theory; CCSD(T), Coupled-cluster with singles and doubles and perturbative treatment of triples; CC2, Coupled-cluster with approximate treatment of doubles; CD, Circular dichroism; CI, Configuration interaction; CIPSI, configuration interaction by perturbation with multiconfigurational zeroth-order wave functions selected by iterative

Surface hopping dynamics including intersystem crossing using the algebraic diagrammatic construction method

“…23,24 On the other hand, it is often necessary to include the coupling between electronic and nuclear degrees of freedom. Whereas for slow ISC processes it is possible to use perturbative approaches, e.g., Fermi's Golden Rule, 25 explicit dynamics simulations are required to simulate ultrafast ISC. It is possible to simulate ISC dynamics by means of grid-based quantum dynamics or multi-configurational time-dependent Hartree.…”

Constructing spin‐adiabatic states for the modeling of spin‐crossing reactions. I. A shared‐orbital implementation

“…For a comparison, we calculated the SOC strength between S 0 and T 1 states using SOMF Hamiltonian, which should have a higher accuracy. [9,48] Smaller S 0 -T 1 SOC around 90 cm −1 were produced in SOMF calculations, with the value decreasing to nearly zero for the product geometry. The reason why SOMF gives much smaller S 0 -T 1 SOCs is in part because of the mean-field treatment and in part because the SOMF Hamiltonian is based on the TDDFT/TDA framework.…”

“…Such spin-crossing reactions are known to be enabled by the spin-orbit coupling (SOC) between different spin states. [9,10] While usually slower than their spin-conserved counterparts (especially in cases with a weak SOC), spin-crossing reactions can play an important role in biochemical processes, homogeneous/heterogeneous catalysis, energy storage/conversion, etc.…”

“…Such spin-crossing reactions are known to be enabled by the spin-orbit coupling (SOC) between different spin states. [9,10] While usually slower than their spin-conserved counterparts (especially in cases with a weak SOC), spin-crossing reactions can play an important role in biochemical processes, homogeneous/heterogeneous catalysis, energy storage/conversion, etc.In the study of spin-crossing reactions, one can explore either the spin-diabatic or spin-adiabatic potential energy surfaces. In the spindiabatic approach, the central task is to reach the crossing seam of two spin-diabatic potential energy surfaces, and then locate the minimum energy crossing point (MECP) on the crossing seam.…”

“…Inspired by the TS-SOC and TSSMM approaches, in this work, we explored the construction of spin-adiabatic surfaces using a different SOC Hamiltonian. Specifically, we employed the Breit-Pauli one-electron spin-orbit operator, [9,39] which is also widely available for nonrelativistic quantum chemistry calculations. [40][41][42][43][44][45] Recently, the Breit-Pauli one-electron spin-orbit operator was also employed to construct spin-adiabatic excited states within both configuration interaction singles (CIS) [46] and the Tamm-Dancoff approximation to time-dependent density functional theory (TDDFT/TDA) [47] frameworks.…”