Michael Filatov

A spin-restricted ensemble-referenced Kohn-Sham method and its application to diradicaloid situations

The energy and density of situations with strong non-dynamic correlation are formulated as weighted sums ensembles of energies and densities of symmetry-adapted reference KS determinants. A computational scheme termed the spin-re- . stricted ensemble-referenced Kohn-Sham REKS method is devised for these cases. An optimal set of orthonormal one-electron orbitals and their optimal occupation numbers are obtained from minimization of the ground state energy with respect to the density. The REKS method is applied to several model problems, rotation in C H , dissociation of H , and 24 2

Spin-restricted density functional approach to the open-shell problem

Abstract Open-shell one-electron equations are derived by application of Roothaans coupling operator technique to the variational procedure of finding the Kohn–Sham orbitals and minimizing the energy of an open-shell system, represented within the density functional vector coupling scheme. The final equations are presented in a form suitable for standard quantum-chemical codes using finite basis set Kohn–Sham calculations. Examples of multiplets for which the theory is applicable are discussed.

Application of spin-restricted open-shell Kohn–Sham method to atomic and molecular multiplet states

A recently proposed spin-restricted open-shell Kohn–Sham (ROKS) method is applied to investigate various atomic and molecular multiplet states. A wide range of multiplets is considered: multiplet terms for which the spin-restricted open-shell theory of Roothaan applies, as well as state situations which cannot be described by Roothaan’s theory (e.g., states of square cyclobutadiene, etc.). Problems associated with the use of approximate density functionals and possible perspectives of the ROKS method are discussed.

Surface Hopping Excited-State Dynamics Study of the Photoisomerization of a Light-Driven Fluorene Molecular Rotary Motor

We report a theoretical study of the photoisomerization step in the operating cycle of a prototypical fluorene-based molecular rotary motor (1). The potential energy surfaces of the ground electronic state (S0) and the first singlet excited state (S1) are explored by semiempirical quantum-chemical calculations using the orthogonalization-corrected OM2 Hamiltonian in combination with a multireference configuration interaction (MRCI) treatment. The OM2/MRCI results for the S0 and S1 minima of the relevant 1-P and 1-M isomers and for the corresponding S0 transition state are in good agreement with higher-level calculations, both with regard to geometries and energetics. The S1 surface is characterized at the OM2/MRCI level by locating two S0-S1 minimum-energy conical intersections and nearby points on the intersection seam and by computing energy profiles for pathways toward these MECIs. Semiclassical Tully-type trajectory surface hopping (TSH) simulations with on-the-fly OM2/MRCI calculations are carried out to study the excited-state dynamics after photoexcitation to the S1 state. Fast relaxation to the ground state is observed through the conical intersection regions, predominantly through the lowest-energy one with a strongly twisted central C═C double bond and pyramidalized central carbon atom. The excited-state lifetimes for the direct and inverse photoisomerization reactions (1.40 and 1.79 ps) and the photostationary state ratio (2.7:1) from the TSH-OM2 simulations are in good agreement with the available experimental data (ca. 1.7 ps and 3:1). Excited-state lifetimes, photostationary state ratio, and dynamical details of the TSH-OM2 simulations also agree with classical molecular dynamics simulations using a reparametrized optimized potentials for liquid simulations (OPLS) all-atom force field with ad-hoc surface hops at predefined conical intersection points. The latter approach allows for a more extensive statistical sampling.

Comment on "about the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error" [J. Chem. Phys. 123, 164110 (2005)]

The use of density functional theory to obtain energy differences related to magnetic coupling constants is debated with special emphasis to the claims by Ruiz et al. [J. Chem. Phys.123, 164110 (2005)] that good agreement with experiment using the B3LYP potential is obtained by ignoring spin symmetry in case self-interaction error cannot be removed.

Restricted Ensemble-Referenced Kohn-Sham versus Broken Symmetry Approaches in Density Functional Theory: Magnetic Coupling in Cu Binuclear Complexes †

The performance of density functional theory in estimating the magnetic coupling constant in a series of Cu(II) binuclear complexes is investigated by making use of two open shell formalisms:  the broken symmetry and the spin-restricted ensemble-referenced Kohn-Sham methods. The strong dependence of the calculated magnetic coupling constants with respect to the exchange-correlation functional is confirmed and found to be independent of whether spin symmetry is imposed or not. The use of a method which guarantees the spin state does not improve the correlation with the experiment and indeed shows some worsening due to an overestimation of the ferromagnetic interactions. However, with the present exchange-correlation functionals, a rather systematic deviation is found. Therefore, it would be possible to develop improved density functionals which will allow for a rigorous treatment of open shell systems in density functional theory.

A first principles study of fluorescence quenching in rhodamine B dimers: how can quenching occur in dimeric species?

Rhodamine B (RhB) is widely used in chemistry and biology due to its high fluorescence quantum yield. In high concentrations, the quantum yield of fluorescence decreases considerably which is attributed to the formation of RhB dimers. In the present work, a possible mechanism of fluorescence quenching in RhB dimers is investigated with the use of time-dependent density functional theory (TD-DFT). The excited states of monomeric and dimeric RhB species have been studied both in the gas phase and in solution with the use of the TD-BLYP/6-311G* method. Results of the calculations suggest that quenching can occur via an internal conversion to the charge-transfer singlet excited states, which can be followed by an intersystem crossing with the charge-transfer triplet states. A possibility to reduce the loss of the fluorescence quantum yield is discussed.

Shape of Multireference, Equation-of-Motion Coupled-Cluster, and Density Functional Theory Potential Energy Surfaces at a Conical Intersection.

We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.

Understanding the Dynamics Behind the Photoisomerization of a Light-Driven Fluorene Molecular Rotary Motor

Light-driven molecular rotary motors derived from chiral overcrowded alkenes represent a broad class of compounds for which photochemical rearrangements lead to large scale motion of one part of the molecule with respect to another. It is this motion/change in molecular shape that is employed in many of their applications. A key group in this class are the molecular rotary motors that undergo unidirectional light-driven rotation about a double bond through a series of photochemical and thermal steps. In the present contribution we report a combined quantum chemical and molecular dynamics study of the mechanism of the rotational cycle of the fluorene-based molecular rotary motor 9-(2,4,7-trimethyl-2,3-dihydro-1H-inden-1-ylidene)-9H-fluorene (1). The potential energy surfaces of the ground and excited singlet states of 1 were calculated, and it was found that conical intersections play a central role in the mechanism of photo conversion between the stable conformer of 1 and its metastable conformer. Molecular dynamics simulations indicate that the average lifetime of the fluorene motor in the excited state is 1.40 +/- 0.10 ps when starting from the stable conformer, which increases to 1.77 +/- 0.13 ps for the reverse photoisomerization. These simulations indicate that the quantum yield of photoisomerization of the stable conformer is 0.92, whereas it is only 0.40 for the reverse photoisomerization. For the first time, a theoretical understanding of the experimentally observed photostationary state of 1 is reported that provides a detailed picture of the photoisomerization dynamics in overcrowded alkene-based molecular motor 1. The analysis of the electronic structure of the fluorene molecular motor holds considerable implications for the design of molecular motors. Importantly, the role of pyramidalization and conical intersections offer new insight into the factors that dominate the photostationary state achieved in these systems.

Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn-Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties.