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The analytic derivative algorithm for the effective contact densities obtained by the exact two-component (X2C) relativistic Hamiltonian is extended to the local approximations to X2C to achieve a higher computational efficiency without losing accuracy. The new algorithm has been implemented in a standalone program, which can utilize the molecular orbitals from state-of-the-art ab initio or density functional theory (DFT) calculations by other quantum chemistry programs in connection with various relativistic Hamiltonians. With the help of the utility program, the effective contact densities as well as the related Mössbauer isomer shifts can be studied by various advanced single-reference and multi-reference ab initio methods as long as the canonical or natural orbitals are available. Using the developed algorithm, the effective contact densities and the Mössbauer isomer shifts in a series of iron compounds and in HgFn (n = 1, 2, 4, and 6) molecules were studied. The obtained results show that (1) adequate account of the static electron correlation significantly improves the agreement of the theoretical 57Fe effective contact densities with the experimental isomer shifts, and (2) the non-monotonous changes of the effective contact density in a series of HgFn compounds are caused by the increasing screening effect due to shrinking of the Hg 5d orbitals.

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.

A new family of light driven molecular rotary motors, which can be synthesized from easily available precursor compounds and which are capable of completing a full 360° revolution by two photoisomerization steps only, is proposed. The non-adiabatic molecular dynamic simulations show that the photoisomerization steps of the motor's working cycle occur on an ultrafast time scale (ca. 200-300 fs), have a very high quantum yield of isomerization (0.91-0.97), and display high selectivity of torsion in the same direction. It is expected that the new motor should remain operational at lower temperatures than the currently existing motors.

Photodecomposition of cyclopropanone is investigated by static quantum chemical calculations and non-adiabatic molecular dynamics (NAMD) simulations. The quantum chemical calculations are carried out by an ensemble density functional theory (eDFT) method capable of delivering high quality results for the ground and excited electronic states of molecules with dissociating bonds. In the NAMD simulations, this method is combined with a novel trajectory surface hopping (TSH) methodology derived from the exact factorization of the electronic-nuclear wavefunction. An ultrafast biexponential decay of the S1 state of cyclopropanone is predicted, where the short (ca. 30 fs) decay time is due to the trajectories reaching the conical intersection (CI) seam on the first approach and the long (ca. 120 fs) decay time is due to recrossing of the CI seam. The experimentally observed dependence of the dissociation (C3H4O* → C2H4 + CO) quantum yield on the excitation wavelength is correctly reproduced by the NAMD simulations. The dependence is explained by the necessity to excite certain vibrational normal modes (e.g., a ring stretching mode with the frequency of 769 cm-1) to break a lateral C-C bond remaining intact at the geometries of the CI seam.

Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.

The 2A″ state of ClOO and BrOO is investigated using single- and multi-reference DFT (density functional theory). Unrestricted DFT (UDFT) carried out with the BLYP functional exaggerates the ionic character of the X–OO bond (X=Cl, Br) and by this its bond dissociation energy, while UDFT with the B3LYP functional underestimates ionic character and bond dissociation energies. In previous investigations, this was overlooked and has led to a misleading interpretation of single determinant UDFT results for XOO(2A″). The correct description of the two radicals can only be achieved by an appropriate configurational state mixing between the doublet ground state (leading to ionic character) and the first excited state, a quartet state leading to covalent character of the X–OO bond. REKS (spin-restricted ensemble-referenced Kohn–Sham) theory provides a multireference description and is capable of describing bonding in XOO correctly provided it is carried out with the hybrid functional B3LYP rather than BLYP, which is the result of the self-interaction error of pure exchange functionals and the inclusion of non-specific non-dynamic electron correlation effects suppressing the specific ones introduced by REKS. The relevance of results for the DFT description of related compounds (HOOO radical, MOO with M =Cu, Ag or Au) or multi-reference problems in general is discussed.

Density functional theory (DFT) is used to study model ferryl species of cytochrome P-450 and horseradish peroxidase (HRP), as well as of the product complex due to oxidation of H2 by the P-450 species (1–4 and 7). The ferryl species studied include neutral and cation radical states of the porphyrin, as well as high- and low-spin situations. A few issues are addressed concerning the mechanism of alkane hydroxylation, and theoretical support is provided for: (i) the contention that spin inversion occurs along the reaction path, (ii) that the cation radical state of the porphyrin is an essential feature required to accommodate an excess electron from the ferryl moiety and thereby stabilize the ground state of the hydroxylation product, and (iii) that the donor property of the proximal ligand has a significant influence on the energy of the ferryl-to-ring charge-transfer states which are essential to convert the reactant state to the hydroxylation product state. In this sense, our study sheds some light on the difference between the oxidized and reduced HRP forms, HRP(I) and HRP(II), and suggests that the combination of a cation radical porphyrin state and a good π-donor proximal ligand like thiolate, could be the underlying reason for the potent hydroxylation ability of the P-450 ferryl-complex.

Spin-restricted ensemble-referenced Kohn–Sham (REKS) calculations have been performed on isomeric benzyne systems. The density functional results compare favorably with those of multi-reference CASPT2 and CASRS3 methods. In general for enthalpies of isodesmic reactions, the REKS energies are in better agreement with experiment compared with the ab initio calculations. Experimental singlet–triplet energy gaps are reproduced to within 1 kcal mol−1 of experimental values.

The relative stability of palladium superoxido complexes, formed viaσ- or π-type co-ordination of a superoxide ion in monomeric and trimeric palladium species, has been investigated by CNDO-S2, a semi-empirical quantum chemical SCF-m.o. method. The CNDO-S2 method has been adapted to calculate the energetic and geometric properties of transition-metal compounds. A π-type co-ordination for O2– is calculated to be most stable for monomeric palladium species, while σ-type co-ordination is favoured for trimeric species. Experimental data on the reactivity of palladium superoxido complexes towards the epoxidation of simple alkenes are in agreement with the results of CNDO-S2 calculations.

Using linear response approach to the Mossbauer isomer shift, the calibration constant alpha(Fe-57) was obtained from high level ab initio calculations carried out for a representative set of iron compounds. The importance of the effects of relativity and electron correlation for an accurate description of the Fe-57 isomer shift is demonstrated on the basis of the Hartree-Fock, coupled cluster with singles and doubles and of the double hybrid density functional calculations. A reliable value of the calibration constant (alpha(Fe-57) = -0.306 +/- 0.009 mm s(-1)) was obtained with the use of the B2-PLYP double hybrid density functional. This value is in good agreement with the experimentally estimated constant of -0.31 +/- 0.04 a(0)(3) mm s(-1) and can be recommended for theoretical modeling of Fe-57 isomer shifts.