Analytical derivative coupling for multistate CASPT2 theory

The probability of non-radiative transitions in photochemical dynamics is determined by the derivative couplings, the couplings between different electronic states through the nuclear degrees of freedom. Efficient and accurate evaluation of the derivative couplings is, therefore, of central importance to realize reliable computer simulations of photochemical reactions. In this work, the derivative couplings for multistate multireference second-order perturbation theory (MS-CASPT2) and its 'extended' variant (XMS-CASPT2) are studied, in which we present an algorithm for their analytical evaluation. The computational costs for evaluating the derivative couplings are essentially the same as those for calculating the nuclear energy gradients. The geometries and energies calculated with XMS-CASPT2 for small molecules at minimum energy conical intersections (MECIs) are in good agreement with those computed by multireference configuration interaction. As numerical examples, MECIs are optimized using XMS-CASPT2 for stilbene and a GFP model chromophore (the 4-para-hydroxybenzylidene-1,2-dimethyl-imidazolin-5-one anion)

Assessing Excited State Energy Gaps with Time-Dependent Density Functional Theory on Ru(II) Complexes

A set of density functionals coming from different rungs on Jacob's ladder are employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical excitation energies, in this work we focus on the energy gaps between the electronic excited states, of the same and different multiplicity. Excited state energy gaps are important for example to determine radiationless transition probabilities. Besides energies, a functional should deliver the correct state character and state ordering. Therefore, wavefunction overlaps are introduced to systematically evaluate the effect of different functionals on the character of the excited states. As a reference, the energies and state characters from multi-state second-order perturbation theory complete active space (MS-CASPT2) are used. In comparison to MS-CASPT2, it is found that while hybrid functionals provide better vertical excitation energies, pure functionals typically give more accurate excited state energy gaps. Pure functionals are also found to reproduce the state character and ordering in closer agreement to MS-CASPT2 than the hybrid functionals

On-the-fly CASPT2 surface hopping dynamics

We report the development of programs for on-the-fly surface hopping dynamics simulations in the gas and condensed phases on the potential energy surfaces computed by multistate multireference perturbation theory (XMS-CASPT2) with full internal contraction. On-the-fly nonadiabatic dynamics simulations are made possible by improving the algorithm for XMS-CASPT2 nuclear energy gradient and derivative coupling evaluation. The program is interfaced to a surface hopping dynamics program, Newton-X, and a classical molecular dynamics package, tinker, to realize such simulations. On-the-fly XMS-CASPT2 surface-hopping dynamics simulations of 9H-adenine and an anionic GFP model chromophore (para-hydroxybenzilideneimidazolin-5-one) in water are presented to demonstrate the applicability of our program to sizable systems. Our program is implemented in the bagel package, which is publicly available under the GNU General Public License

On the accuracy of retinal protonated Schiff base models

We investigate the molecular geometries of the ground state and the minimal energy conical intersections (MECIs) between the ground and first excited states of the models for the retinal protonated Schiff base in the gas phase using the extended multistate complete active space second-order perturbation theory (XMS-CASPT2). The biggest model in this work is the rhodopsin chromophore truncated between the {\epsilon} and {\delta} carbon atoms, which consists of 54 atoms and 12-orbital {\pi} conjugation. The results are compared with those obtained by the state-averaged complete active space self-consistent field (SA-CASSCF). The XMS-CASPT2 results suggest that the minimum energy conical intersection associated with the so-called 13-14 isomerization is thermally inaccessible, which is in contrast to the SA-CASSCF results. The differences between the geometries of the conical intersections computed by SA-CASSCF and XMS-CASPT2 are ascribed to the fact that the charge transfer states are more stabilized by dynamical electron correlation than the diradicaloid states. The impact of the various choices of active spaces, basis sets, and state averaging schemes is also examined.Comment: Contribution to the special issue in honor of the 80th birthday of Professor Michael Bae

Excited State Specific Multi-Slater Jastrow Wave Functions

We combine recent advances in excited state variational principles, fast multi-Slater Jastrow methods, and selective configuration interaction to create multi-Slater Jastrow wave function approximations that are optimized for individual excited states. In addition to the Jastrow variables and linear expansion coefficients, this optimization includes state-specific orbital relaxations in order to avoid the compromises necessary in state-averaged approaches. We demonstrate that, when combined with variance matching to help balance the quality of the approximation across different states, this approach delivers accurate excitation energies even when using very modest multi-Slater expansions. Intriguingly, this accuracy is maintained even when studying a difficult chlorine-anion-to-$\pi^{*}$ charge transfer in which traditional state-averaged multi-reference methods must contend with different states that require drastically different orbital relaxations.Comment: 16 pages, 6 figures, 2 table

A comparative analysis of the UV/Vis absorption spectra of nitrobenzaldehydes.

In a joint experimental and theoretical study, the UV/Vis absorption spectra of the three isomers (ortho, meta, para) of nitrobenzaldehyde (NBA) were analyzed. Absorption spectra are reported for NBA vapors, cyclohexane and acetonitrile solutions. All spectra are poor in vibronic structure and hardly affected in shape by the surroundings (vapor or solution). Moderate solvatochromic shifts of [similar]−0.2 eV are measured. For all isomers vertical transition energies, oscillator strengths, and excited state dipole moments were computed using the MS-CASPT2/CASSCF and CC2 methods. Based on these calculations the experimental transitions were assigned. The spectra of all isomers are characterized by weak (εmax ≈ 100 M−1 cm−1) transitions around 350 nm (3.6 eV), arising from nπ* absorptions starting from the lone pairs of the nitro and aldehyde moieties. The next band of intermediate intensity peaking around 300 nm (4.2 eV, εmax ≈ 1000 M−1 cm−1) is dominated by ππ* excitations within the arene function. Finally, strong absorptions (εmax ≈ 10 000 M−1 cm−1) were observed around 250 nm (5.0 eV) which we ascribe to ππ* excitations involving the nitro and benzene groups

Exploration of H2 binding to the [NiFe]-hydrogenase active site with multiconfigurational density functional theory

The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions. These methods can potentially be employed to elucidate reaction mechanisms in bio-inorganic chemistry, where many other methods become either too computationally expensive or too inaccurate. In this paper, a complete active space (CAS) short-range DFT (CAS-srDFT) hybrid was employed to investigate a bio-inorganic system, namely H2 binding to the active site of [NiFe] hydrogenase. This system was previously investigated with coupled-cluster (CC) and multiconfigurational methods in form of cumulant-approximated second-order perturbation theory, based on the density matrix renormalization group (DMRG). We find that it is more favorable for H2 to bind to Ni than to Fe, in agreement with previous CC and DMRG calculations. The accuracy of CAS-srDFT is comparable to both CC and DMRG, despite that much smaller active spaces were employed. This enhanced efficiency at smaller active spaces shows that CAS-srDFT can become a useful method for bio-inorganic chemistry.Comment: 22 page