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The density functional theory (DFT) calculations are used for studying the potential-energy surface of the first excited state of the 11-cis-retinal protonated Schiff base (PSB11) chromophore. The studies have suggested few reaction pathways on the potential-energy surface of the excited state leading toward the conical interaction and resulting in a cis to trans isomerization of the retinal chromophore.

We investigate how the reduction of the virtual space affects coupled-cluster excitation energies at the approximate singles and doubles coupled-cluster level (CC2). In this reduced-virtual-space (RVS) approach, all virtual orbitals above a certain energy threshold are omitted in the correlation calculation. The effects of the RVS approach are assessed by calculations on the two lowest excitation energies of 11 biochromophores using different sizes of the virtual space. Our set of biochromophores consists of common model systems for the chromophores of the photoactive yellow protein, the green fluorescent protein, and rhodopsin. The RVS calculations show that most of the high-lying virtual orbitals can be neglected without significantly affecting the accuracy of the obtained excitation energies. Omitting all virtual orbitals above 50 eV in the correlation calculation introduces errors in the excitation energies that are smaller than 0.1 eV. By using a RVS energy threshold of 50 eV, the CC2 calculations using triple-ζ basis sets (TZVP) on protonated Schiff base retinal are accelerated by a factor of 6. We demonstrate the applicability of the RVS approach by performing CC2/TZVP calculations on the lowest singlet excitation energy of a rhodopsin model consisting of 165 atoms using RVS thresholds between 20 eV and 120 eV. The calculations on the rhodopsin model show that the RVS errors determined in the gas-phase are a very good approximation to the RVS errors in the protein environment. The RVS approach thus renders purely quantum mechanical treatments of chromophores in protein environments feasible and offers an ab initio alternative to quantum mechanics/molecular mechanics separation schemes. [ABSTRACT FROM AUTHOR]

First-order nonadiabatic coupling matrix elements (NACMEs) are key for phenomena such as nonradiative transitions and excited-state decay, yet a consistent and practical first principles treatment has been elusive for molecules with more than a few heavy atoms. Here we present theory, implementation using Gaussian basis sets, and benchmarks of first-order NACMEs between ground and excited states in the framework of time-dependent hybrid density functional theory (TDDFT). A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined. In contrast to previous approaches, the present treatment produces exact analytical derivative couplings between time-dependent Kohn–Sham (TDKS) determinants in a finite atom-centered basis set. As in analytical gradient theory, derivative molecular orbital coefficients can be eliminated, making the computational cost independent of the number of nuclear degrees of freedom. Our expression reduces to the exact Chernyak–Mukamel formula for first-order NACMEs in the complete basis-set limit, but greatly improves basis-set convergence in finite atom-centered basis sets due to additional Pulay type terms. The Chernyak–Mukamel formula is shown to be equivalent to the Hellmann–Feynman contribution in analytical gradient theory. Our formalism may be implemented in TDDFT analytical excited-state gradient codes with minor modifications. Tests for systems with up to 147 atoms show that evaluation of first-order NACMEs causes total computation times to increase by an insignificant 10% on average. The resolution-of-the-identity approximation for the Coulomb energy (RI-J) reduces the computational cost by an order of magnitude for nonhybrid functionals, while errors are insignificant with standard auxiliary basis sets. We compare the computed NACMEs to full configuration interaction (FCI) in benchmark results for diatomic molecules; hybrid TDDFT and FCI are found to be in agreement for regions of the potential energy curve where the Kohn–Sham ground-state reference is stable and the character of the excitation is properly captured by the present functionals. With these developments, nonadiabatic molecular dynamics simulations of molecular systems in the 100 atoms regime are within reach. [ABSTRACT FROM AUTHOR]

The electronic excitation spectra of trans-1,3-butadiene (CH2=CH–CH=CH2) and trans-2-propeniminium (CH2=CH–CH=NH2+) have been studied at several coupled-cluster and time-dependent density functional theory levels using the linear response approach. Systematic studies employing large correlation-consistent basis sets show that approximate singles and doubles coupled-cluster calculations yield excitation energies in good agreement with experiment for all states except for the two lowest excited Ag states of trans-1,3-butadiene which have significant multiconfigurational character. Time-dependent density functional theory calculations employing the generalized gradient approximation and hybrid functionals yield too low excitation energies in the basis set limit. In trans-1,3-butadiene, increasing the basis set size by augmenting multiple diffuse functions is observed to reduce the high-lying excitation energies with most density functionals. The decrease in the energies is connected to the incorrect asymptotic behavior of the exchange-correlation potential. The results also demonstrate that standard density functionals are not capable of providing excitation energies of sufficient accuracy for experimental assignments. [ABSTRACT FROM AUTHOR]

The density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations show that the Franck-Condon step of the photochemical event of the retinal protonated Schiff base (PSB) chromophore involves a 60 degree change in the bihedral angle between the beta-ionone ring and the retinyl chain. The Franck-Condon relaxation increases the bond length alternation making the conjugated double bonds in the retinyl chain shorter for the excited state than for the ground state.

Accurate predictions of photoexcitationproperties are a majorchallenge for modern methods of theoretical chemistry. We show herehow approximate coupled-cluster singles and doubles (CC2) calculationsin combination with the reduced virtual space (RVS) approach can beemployed in studies of excited states of large biomolecular systems.The RVS-CC2 approach is used for accurately predicting optical propertiesof the p-hydroxybenzylidene-dihydroimidazolinone(p-HBDI) chromophore embedded in green fluorescentprotein (GFP) models using quantum mechanical calculations in combinationwith large basis sets. We study the lowest excited states for theisolated and protein-embedded chromophore in two different protonationstates, and show how omitting high-lying virtual orbitals in the RVScalculation of excitation energies renders large-scale CC2 studiescomputationally feasible. We also discuss how the error introducedby the RVS approach can be systematically estimated and controlled.The obtained CC2 excitation energies of 3.13–3.27 and 2.69–2.77eV for the two protonation states of different protein models arein excellent agreement with the maxima of the experimental absorptionspectra of 3.12–3.14 and 2.61–2.64 eV, respectively.Thus, the calculated energy splitting between the excited states ofthe two protonation states is 0.44–0.52 eV, which agrees verywell with the experimental value of 0.48–0.51 eV. The calculationsat the RVS-CC2 level on the protein models show the importance ofusing large QM regions in studies of biochromophores embedded in proteins. [ABSTRACT FROM AUTHOR]