Journal of Theoretical and Computational Chemistry

Full vibrational energies and corresponding analytical potential energy functions (APEFs) for $A^{\prime }2({}^3\mathrm{\Pi })$ of ClF, $X^1{\mathrm{\Sigma }}^{+}$ of ICl, $X^1{\mathrm{\Sigma }}^{+}$ of IBr, and $X^1{\mathrm{\Sigma }}^{+}$of IF are obtained by four-term variational algebraic energy-consistent method [VAECM(4)]. Three major methods are used to handle the regularization problems and make the results more reliable: (1) physical constraints like progressive dissociation behavior are used to overcome overfitting problems; (2) reasonable variational method is used to expand the experimental dataset and make the model optimization much faster; and (3) validation dataset is used to further enhance the reliability. After these treatments, our results agree well with experiment and have a good physical converged behavior in molecular dissociation and asymptotic region. This study provides important reference data for the related molecules.

We review the fundamental ideas of free complement (FC) method through its application on both ground and first excited states of helium atom. We have found that lower energies can be obtained with fewer number of terms in the FC expansion of the ground state wavefunction. In this case, the optimization of orbital exponents was not necessary for achieving spectroscopic accuracy, especially at higher orders where the structure of the FC wavefunction converges to that of the exact one. We have discovered that permanents naturally appear in the FC expansion of the first triplet excited state wavefunction. Including permanents in the FC expansion is shown to be energetically important for the first triplet excited state of helium atom whereas it is not computationally favorable at higher orders. Finally, considering the group theoretical properties of the symmetric group $S_2$ and using immanants, a compact and more elegant form for the FC expansion of the first triplet excited state of the helium atom is achieved.

The charge transport properties and the stability of imidazoles with axial-coordinated protoheme molecules have been investigated by the density functional theory (DFT) at B3LYP/6-31$+$G(d) level. With energy of each compound, we find that all heme Fe${}^{3+}$ and Fe${}^{2+}$ complex compounds axially coordinate the imidazoles by strong field in low-spin state. Meanwhile, binding energies were calculated, the structure feature and the frontier orbital distribution of complex compounds were also analyzed. On the basis of Marcus theory, the reorganization energy, matrix element and charge transport rate constant were calculated. The results show that the charge transport rate of the complex compound coordinated imidazole is greater than that of the complex compound coordinated 2-methyl imidazole, which indicates that the charge transfer between the imidazole and the heme iron is more favorable to the heme iron than the 2-methyl imidazole. The results are in good agreement with the experimental ones obtained by Battistuzzi.

A technique for constructing the correlation dependencies of the thermodynamic properties of similar compounds was proposed. This technique is based on the Taylor expansion in the supposed analytic relationship between properties. The constructed correlation dependencies were used to estimate the thermodynamic properties of the condensed bromides and iodides of hafnium HfG_n (G $=$ Br, I and $n=1$, 2, 3, 4) and the compounds formed in the PbO–SiO₂ system. Standard formation enthalpy $\mathrm{\Delta }{H}_{298}^{\mathrm{\text{o}}}$, entropy $S_{298}^{\mathrm{\text{o}}}$, heat capacity $C_{p,298}^{\mathrm{\text{o}}}$ and temperature dependencies $C_p(T)$ at temperatures T$=298$k to 3000k were estimated. The standard estimation error of the thermodynamic properties of the compounds in the PbO–SiO₂ system does not exceed 2% for all the estimated properties. For condensed halides, the standard estimation error was (1) $S<8$% for enthalpy, (2) $S<5.6$% for entropy, (3) $S<4.6$% for heat capacity.

In this report, we present three generalized expressions of Shannon’s entropy using the electron densities of position and momentum spaces. Such expressions were obtained using the definition of deformed logarithm introduced by Tsallis. We show that only one expression fulfils the dimensionless criterion, it is strictly positive overall space and follows a growing behavior with respect to the electron number. We also found that by using some values of $q$, it is possible to reproduce the general trends of the radial distribution in position space and momentum space of the neon atom.

The performance of exchange-correlation (xc) functionals for the description of electron affinities of atomic and molecular systems is investigated. A benchmark set is constructed and experimental adiabatic electron affinities are compared to Density Functional Theory (DFT) predictions. The results show that although good overall accuracy may be achieved from DFT-based approaches, there still exist outliers for any of the approximations applied. Apart from employing the standard DFT models, the possibility of the optimization of range-separated xc functionals has also been tested, however, no large improvement in accuracy is observed.

The gas-phase reaction mechanism of NO₂ with NH₂ on the singlet potential energy surface is investigated at the B3LYP, MP2, CCSD(T) and G3B3 levels of calculation in connection with the 6-311$++$G(3df, 3pd) basis sets. Seven different kinds of products have been obtained. The results reveal that P7 [N₂$\text{O}+\text{H}$₂O] is the main product in thermodynamic viewpoint with the Gibbs free energy of $\mathrm{\Delta }{G}^{\circ }=-62.1$kcal/mol. The product P2 due to less number of transition states and low level barrier height of transition states is introduced as the kinetic product. The calculation of rate constants in different temperatures confirms our predication for P7 adduct in comparison with other products. In the first step, the reactions without catalytic effects are considered. All of these reactions begin with pre-reactive collision complex CR [NO₂–NH₂]. This complex has been produced from barrier-less process via collision of reactants. From variation of bond lengths and angles or dissociation of this complex, other species are produced. In the second step, the catalytic effect of water and water dimer molecules on the reaction rate of kinetic path, P2, have been attended. Calculation of the rate constant was done in the temperature range from 500K to 3000K. Our results showed that the rate constant of path P2 increases with temperature and the number of water molecules. So, we can conclude that the number of water molecules corresponding to relative humidity of atmosphere has catalytic effect on the mentioned reaction rate.

The geometrical and electronic structures of [M₆O${}_{19}$]${}^{n-}$ (M $=$ Mo, W, $n=2$; M $=$ V, Nb, Ta, $n=8$) and their derivatives were investigated by using density functional theory methods. The results indicate that the geometrical structure of [V₆O${}_{19}$]${}^{8-}$ is not different from other Lindqvist-type anions. The energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) (HOMO$-$LUMO energy gap) of [V₆O${}_{19}$]${}^{8-}$ is smaller than those of same charge anions, [Nb₆O${}_{19}$]${}^{8-}$ and [Ta₆O${}_{19}$]${}^{8-}$. In addition, the charge density ${\rho }_{\mathrm{\text{CD}}}$ of [V₆O${}_{19}$]${}^{8-}$ is larger when compared with those of other studied clusters. The investigation on the derivatives shows that the valence of V atom (V${}^{4+}$ or V${}^{5+}$) and the methoxy ligand influence the HOMO$-$LUMO energy gap and the charge density ${\rho }_{\mathrm{\text{CD}}}$ of the studied clusters.

For sigmatropic reactions, such as [1,3] and [1,5] hydrogen shifts, the Cope and Claisen rearrangements, and the Berson–Nelson rearrangement, no correlation diagrams consistent with the classical electronic formulas have been reported. Here, we report dynamic correlation diagrams for these sigmatropic reactions based on orbital phase conservation theory. The diagrams are consistent with both the selection rules of sigmatropic reactions proposed by Woodward and Hoffmann and classical electronic formulas.