On the calculation of Mössbauer isomer shift

A quantum chemical computational scheme for the calculation of isomer shift in Mössbauer spectroscopy is suggested. Within the described scheme, the isomer shift is treated as a derivative of the total electronic energy with respect to the radius of a finite nucleus. The explicit use of a finite nucleus model in the calculations enables one to incorporate straightforwardly the effects of relativity and electron correlation. The results of benchmark calculations carried out for several iron complexes as well as for a number of atoms and atomic ions are presented and compared with the available experimental and theoretical data.

Designing Conical Intersections For Light-driven Single Molecule Rotary Motors: From Precessional To Axial Motion

In the past, the design of light-driven single molecule rotary motors has been mainly guided by the modification of their ground-state conformational properties. Further progress in this field is thus likely to be achieved through a detailed understanding of light-induced dynamics of the system and the ways of modulating it by introducing chemical modifications. In the present theoretical work, the analysis of model organic chromophores and synthesized rotary motors is used for rationalizing the effect of electron-withdrawing heteroatoms (such as a cationic nitrogen) on the topography and branching plane of mechanistically relevant conical intersections. Such an analysis reveals how the character of rotary motion could be changed from a precessional motion to an axial rotational motion. These concepts are then used to design and build quantum chemical models of three distinct types of Schiff base rotary motors. One of these models, featuring the synthetically viable indanylidenepyrroline framework, has conical intersection structures consistent with an axial rotation not hindered by ground-state conformational barriers. It is expected that this type of motor should be capable of funneling the photon energy into specific rotary modes, thus achieving photoisomerization quantum efficiencies comparable to those seen in visual pigments

Excitation Energies from Spin-Restricted Ensemble-Referenced Kohn-Sham Method:A State-Average Approach

A time-independent density functional approach to the calculation of excitation energies from the ground states of molecules typified by the strong nondynamic electron correlation is suggested. The new method is based on the use of the spin-restricted ensemble-referenced Kohn-Sham formalism [Filatov, M.; Shaik, S. Chem. Phys. Lett. 1999, 304, 429] for the calculation of the ground state. In the new method, the average energy of the ground state and a state created by a single excitation thereof is minimized with respect to the Kohn-Sham orbitals and their fractional occupation numbers. The lowest singlet excitation energies obtained with the help of the new formalism for a number of model systems, such as the hydrogen molecule with stretched bond, twisted ethylene, and twisted hexa-1,3,5-triene, are compared with the results of the time-dependent density functional theory, with the results of ab initio CASSCF/CASPT2 calculations, and with the experimental data. Applicability of the new method to the description of photochemical reactions is discussed

Obtaining stable solutions of the optimized-effective-potential method in the basis set representation

Equations of the optimized-effective-potential method in a basis set representation are solved with the use of the incomplete Cholesky decomposition technique. The resulting local potential is expanded in terms of the products of occupied and virtual Kohn-Sham orbitals thus avoiding the use of auxiliary basis sets. It is demonstrated that, for a sufficiently large orbital basis set satisfying the condition of linear dependence of these products, stable and numerically accurate solutions of the OEP method can be obtained with the use of the suggested computational approach

Computation of Molecular Electron Affinities Using an Ensemble Density Functional Theory Method

The computation of electron attachment energies (electron affinities) was implemented in connection with an ensemble density functional theory method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn–Sham (SI-SA-REKS or SSR) method. With the use of the extended Koopmans’ theorem, the electron affinities and the respective Dyson orbitals are obtained directly for the neutral molecule, thus avoiding the necessity to compute the ionized system. Together with the EKT-SSR (extended Koopmans’ theorem-SSR) method for ionization potentials, which was developed earlier, EKT-SSR for electron affinities completes the implementation of the EKT-SSR formalism, which can now be used for obtaining electron detachment as well as the electron attachment energies of molecules in the ground and excited electronic states. The extended EKT-SSR method was tested in the calculation of several closed-shell molecules. For the molecules in the ground states, the EKT-SSR energies of Dyson’s orbitals are virtually identical to the energies of the unoccupied orbitals in the usual single-reference spin-restricted Kohn–Sham calculations. For the molecules in the excited states, EKT-SSR predicts an increase of the most positive electron affinity by approximately the amount of the vertical excitation energy. The electron affinities of a number of diradicals were calculated with EKT-SSR and compared with the available experimental data. With the use of a standard density functional (BH&HLYP), the EKT-SSR electron affinities deviate on average by ca. 0.2 eV from the experimental data. It is expected that the agreement with the experiment can be improved by designing density functionals parametrized for ionization energies

Structural or population dynamics: what is revealed by the time-resolved photoelectron spectroscopy of 1,3-cyclohexadiene? A study with an ensemble density functional theory method

Time-resolved photoelectron spectra during the photochemical ring-opening reaction of 1,3-cyclohexadiene (CHD) are modeled by an ensemble density functional theory (eDFT) method. The computational methodology employed in this work is capable of correctly describing the multi-reference effects arising in the ground and excited electronic states of molecules, which is important for the correct description of the ring-opening reaction of CHD. The geometries of molecular species along the non-adiabatic molecular dynamics (NAMD) trajectories reported in a previous study of the CHD photochemical ring-opening were used in this work to calculate the ionization energies and the respective Dyson orbitals for all possible ionization channels. The obtained theoretical time-resolved spectra display decay characteristics in a reasonable agreement with the experimental observations; i.e., the decay (and rise) of the most mechanistically significant signals occurs on the timescale of 100–150 fs. This is very different from the excited state population decay characteristics (τ _(S1) = 234 ± 8 fs) obtained in the previous NAMD study. The difference between the population decay and the decay of the photoelectron signal intensity is traced back to the geometric transformation that the molecule undergoes during the photoreaction. This demonstrates the importance of including the geometric information in interpretation of the experimental observations

Computation of Molecular Electron Affinities Using an Ensemble Density Functional Theory Method

The computation of electron attachment energies (electron affinities) was implemented in connection with an ensemble density functional theory method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn–Sham (SI-SA-REKS or SSR) method. With the use of the extended Koopmans’ theorem, the electron affinities and the respective Dyson orbitals are obtained directly for the neutral molecule, thus avoiding the necessity to compute the ionized system. Together with the EKT-SSR (extended Koopmans’ theorem-SSR) method for ionization potentials, which was developed earlier, EKT-SSR for electron affinities completes the implementation of the EKT-SSR formalism, which can now be used for obtaining electron detachment as well as the electron attachment energies of molecules in the ground and excited electronic states. The extended EKT-SSR method was tested in the calculation of several closed-shell molecules. For the molecules in the ground states, the EKT-SSR energies of Dyson’s orbitals are virtually identical to the energies of the unoccupied orbitals in the usual single-reference spin-restricted Kohn–Sham calculations. For the molecules in the excited states, EKT-SSR predicts an increase of the most positive electron affinity by approximately the amount of the vertical excitation energy. The electron affinities of a number of diradicals were calculated with EKT-SSR and compared with the available experimental data. With the use of a standard density functional (BH&HLYP), the EKT-SSR electron affinities deviate on average by ca. 0.2 eV from the experimental data. It is expected that the agreement with the experiment can be improved by designing density functionals parametrized for ionization energies

Structural or population dynamics: what is revealed by the time-resolved photoelectron spectroscopy of 1,3-cyclohexadiene? A study with an ensemble density functional theory method

Time-resolved photoelectron spectra during the photochemical ring-opening reaction of 1,3-cyclohexadiene (CHD) are modeled by an ensemble density functional theory (eDFT) method. The computational methodology employed in this work is capable of correctly describing the multi-reference effects arising in the ground and excited electronic states of molecules, which is important for the correct description of the ring-opening reaction of CHD. The geometries of molecular species along the non-adiabatic molecular dynamics (NAMD) trajectories reported in a previous study of the CHD photochemical ring-opening were used in this work to calculate the ionization energies and the respective Dyson orbitals for all possible ionization channels. The obtained theoretical time-resolved spectra display decay characteristics in a reasonable agreement with the experimental observations; i.e., the decay (and rise) of the most mechanistically significant signals occurs on the timescale of 100–150 fs. This is very different from the excited state population decay characteristics (τ _(S1) = 234 ± 8 fs) obtained in the previous NAMD study. The difference between the population decay and the decay of the photoelectron signal intensity is traced back to the geometric transformation that the molecule undergoes during the photoreaction. This demonstrates the importance of including the geometric information in interpretation of the experimental observations

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas–Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac–Hartree–Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10−9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change