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The normalized elimination of the small component method is a first principles two-component relativistic approach that leads to the Dirac-exact description of one-electron systems. Therefore, it is an ideal starting point for developing procedures, by which first- and second-order response properties can be routinely calculated. We present algorithms and methods for the calculation of molecular response properties such as geometries, dipole moments, hyperfine structure constants, vibrational frequencies and force constants, electric polarizabilities, infrared intensities and so forth. The described formalisms are applied to molecules containing mercury and other heavy elements, which require a relativistic treatment. Perspectives for the future development and application of Dirac-exact methods are outlined. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Multireference averaged quadratic coupled cluster (MRAQCC) (4,5)/cc-pVTZ calculations predict that bond pseudorotation (BPR) in the first excited singlet state of the cyclopentadienyl cation (CPC) proceeds with a barrier of just 0.35 kcal/mol, where five dienylic forms present the minima and five allylic forms the transition states of the pseudorotation process. Vibrational and entropic corrections revert the order of stabilities and lead to a Δ G(298) of just 0.05 kcal/mol indicating that BPR is unhindered at room temperature. The description of the CPC ring in terms of curvilinear deformation coordinates (seven for C5, seven for X5, and three coupling coordinates) make it possible to explore both the six-dimensional (6D) Jahn-Teller and the 8D pseudo-Jahn-Teller space and assess the importance of Jahn-Teller and pseudo-Jahn-Teller deformations of the CPC ring. The latter dominate the ring deformations along the BPR path. The only somewhat larger Jahn-Teller contribution results from a E [ABSTRACT FROM AUTHOR]

Next‐generation quantum theory of atoms in molecules was applied to analyze, along an entire bond path, intramolecular interactions known to influence the photoisomerization dynamics of a light‐driven rotary molecular motor. The 3D bond‐path framework set B0,1 constructed from the least and most preferred directions of electronic motion, provided new insights into the bonding leading to different S1 state lifetimes including the first quantification of covalent character of a closed‐shell intramolecular bond path. We undertook the first use of the stress tensor trajectory Tσ(s) analysis on selected nonadiabatic molecular dynamics trajectories with the electron densities obtained using the ensemble density functional theory method. The stress tensor Tσ(s) analysis was found to be well suited to follow the dynamics trajectories that included the S0 and S1 electronic states through the conical intersection and also provided to a new measure to assess the degree of purity of the axial bond rotation for the design of rotary molecular motors. [ABSTRACT FROM AUTHOR]

The conical intersections corresponding to the C─O and C─C ring opening were optimized and the reaction paths traversing these intersections were obtained. Investigation of the C─O ring opening revealed that when traversing the lowest energy conical intersection, the reaction path returns to the closed ring geometry. The C─O path traversing the intersection featuring torsion of terminal CH2 group however, led to a ring‐opened geometry, an H‐shift and the formation of acetaldehyde that can undergo further dissociation. The observation of different reaction paths was explained by the 3‐D paths from quantum theory of atoms in molecules (QTAIM) that defined the most preferred direction of electronic motion that precisely tracked the mechanisms of bond breaking and formation throughout the photo‐reactions. The size, orientation, and location of these most preferred 3‐D paths indicated the extent and direction of motion of atoms, bonds, and the degree of torsion or planarity of a bond indicating a predictive ability. [ABSTRACT FROM AUTHOR]

A balanced treatment of the covalent and ionic contributions to the ground and excited states originating from torsion about double bonds is known to be strongly dependent on the presence of dynamic electron correlation. We undertake an analysis of the minimum energy pathways corresponding to deactivation of the first excited singlet state of PSB3. In doing so we consider torsion about the three double bonds including other intramolecular degrees of freedom, such as the bond length alternation. The 3‐D bond‐path analysis provides a new 'bond‐localized orbital‐like' directional interpretation of bonding. Therefore, we present a more sophisticated method of determination of the degree of covalent and ionic contributions known to be responsible for altering the relative stability of the S1/S0 conical intersections. The results presented suggest that the commonly used simplified multi‐reference methodologies that often result in incorrect predictions for the excited state deactivation reaction mechanism. The bond‐path framework set B visualization of the spectrum of the chemical character (covalent–biradical‐ionic) displayed of each of the back‐bone bonds as well as the influence on neighboring bonds. The most preferred directions of accumulation of charge density, q‐ and q′‐paths along the backbone bond‐path (r) corresponding to the torsional C10‐N12 BCP for the S0 (top) and S1 (below) states at a value of the torsion q = 90.0°. [ABSTRACT FROM AUTHOR]

The factors underlying the experimentally observed branching ratio (70:30) of the (1,3‐cyclohexadiene) CHD → HT (1,3,5‐hexatriene) photochemical ring‐opening reaction are investigated. The ring‐opening reaction path is optimized by a high‐level multi‐reference DFT method and the density along the path is analyzed by the quantum theory of atoms in molecules (QTAIM) and stress tensor methods. The performed density analysis suggests that, in both S1 and S0 electronic states, there exists an attractive interaction between the ends of the fissile σ‐bond of CHD that steers the ring‐opening reaction predominantly in the direction of restoration of the ring. It is suggested that opening of the ring and formation of the reaction product (HT) can only be achieved when there is a sufficient persistent nuclear momentum in the direction of stretching of the fissile bond. As this orientation of the nuclear momentum vector can be expected relatively rare during the dynamics, this explains the observed low quantum yield of the ring‐opening reaction. Experimentally observed branching ratio (70:30) of the (1,3‐cyclohexadiene) CHD → HT (1,3,5‐hexatriene) photochemical ring‐opening reaction is investigated by first‐principles calculations and next‐generation quantum theory of atoms in molecules. It is suggested that opening of the ring and formation of the reaction product can only be achieved when there is a sufficient persistent nuclear momentum in the direction of stretching of the fissile bond. [ABSTRACT FROM AUTHOR]

A vector‐based representation of the chemical bond is introduced, which we refer to as the bond‐path framework set B = {p, q, r}, where p, q, and r represent 3 eigenvector‐following paths with corresponding lengths H*, H, and the familiar quantum theory of atoms in molecules (QTAIM) bond‐path length (BPL). The intended application of B is for molecules subjected to various types of reactions and distortions, including photoisomerization reactions, applied torsions θ, or normal modes of vibration. The lengths H* and H of the eigenvector‐following paths are constructed using the e1 and e2 Hessian eigenvectors, respectively, along the bond path, these corresponding to the least and most preferred directions of charge density accumulation. In particular, the paths p and q provide a vector representation of the scalar QTAIM ellipticity ε. The bond‐path framework set B is applied to the excited state deactivation of fulvene that involves distortions along various intramolecular degrees of freedom, such as the bond stretching/compression of bond‐length alternation and bond torsion distortions. We find that the H* and H lengths can differentiate between the ground and excited electronic states, in contrast to the QTAIM BPL. Five unique paths were presented for B= {(p0,p1), (q0,q1), r} for the ground and first excited states where the profile of the scaling factor, the ellipticity ε, reveals a large unexpected asymmetry for the excited state. A "next‐generation" quantum theory of atoms in molecules (QTAIM) is introduced to analyze all types of bonding in molecules subjected to various types of reactions and distortions, including photoisomerization reactions, applied torsions θ, or normal modes of vibration. The double‐bond isomerization of fulvene is used as test model for this "next‐generation" QTAIM approach. [ABSTRACT FROM AUTHOR]