Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces.

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

Communication: automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory.

Analytical nuclear gradients for fully internally contracted complete active space second-order perturbation theory (CASPT2) are reported. This implementation has been realized by an automated code generator that can handle spin-free formulas for the CASPT2 energy and its derivatives with respect to variations of molecular orbitals and reference coefficients. The underlying complete active space self-consistent field and the so-called Z-vector equations are solved using density fitting. The implementation has been applied to the vertical and adiabatic ionization potentials of the porphin molecule to illustrate its capability.

From ordinary to blue emission in peralkylated n-oligosilanes: the calculated structure of delocalized and localized singlet excitons.

Excited singlet state structures believed to be responsible for the Franck-Condon-allowed and the strongly Stokes-shifted (blue) emissions in linear permethylated oligosilanes (Si(n)Me(2n+2)) have been found and characterized with time-dependent density functional (TD-DFT) methods for chain lengths 4 ≤ n ≤ 16. For chain lengths with n > 7, the S1 relaxed structures closely resemble the S0 equilibrium structures where all valence angles are tetrahedral and all backbone dihedral angles are transoid. At chain lengths with n < 8 more strongly distorted structures with one long Si-Si bond built from silicon 3p orbitals are encountered. The large Stokes shift is due more to a large destabilization of the ground state than the relaxation in the S1 excited state. For n = 7, both types of minima were located, exactly reproducing the borderline between the large-radius and the small-radius self-trapped excitons known from experiments.

Fifth stereoactive orbital on silicon: relaxation of the lowest singlet excited state of octamethyltrisilane.

We address relaxation pathways in the excited singlet states S(1) of saturated molecules, specifically alkylated oligosilanes. Unlike their longer peralkylated homologues, disilanes and trisilanes do not fluoresce even at low temperatures. An examination of the S(1) potential energy surface of Si(3)Me(8) with density functional (TDDFT, LC-TDDFT), and ab initio (RICC2, RIADC(2)) methods with TZVP basis sets revealed only extremely shallow minima in the vicinity of funnels, accounting for the absence of fluorescence, rapid internal conversion, and photoproducts. Relaxed singlet excited state structures either contain one approximately trigonal bipyramidal Si atom or two that are halfway between tetrahedral and trigonal bipyramidal. Four of the ligands are those that the Si atom had in the ground state. Natural bond orbital analysis suggests that the fifth one is a nonbonding hybrid orbital of the lone-pair type and size intermediate between valence and Rydberg, with an only very small occupancy, yet stereochemically active. The fifth natural hybrid orbital is composed primarily of 4s, 4p, and usually to a lesser degree, also 3d atomic orbitals. The trigonal bipyramidal structure allows an optimal accommodation of the presence of both a negative and a positive charge in the Lewis structures. The excess negative charge on the distorted Si atom is shared between the nonbonding fifth hybrid orbital and σ* antibonding orbitals associated with its bonds. The positive charge resides in an adjacent σ SiSi bond orbital. A Rydberg minimum also occurs on the S(1) surface at the geometry of the radical cation.

Toward designed singlet fission: electronic states and photophysics of 1,3-diphenylisobenzofuran.

Single crystal molecular structure and solution photophysical properties are reported for 1,3-diphenylisobenzofuran (1), of interest as a model compound in studies of singlet fission. For the ground state of 1 and of its radical cation (1(+*)) and anion (1(-*)), we report the UV-visible absorption spectra, and for neutral 1, also the magnetic circular dichroism (MCD) and the decomposition of the absorption spectrum into purely polarized components, deduced from fluorescence polarization. These results were used to identify a series of singlet excited states. For the first excited singlet and triplet states of 1, the transient visible absorption spectra, S(1) --> S(x) and sensitized T(1) --> T(x), and single exponential lifetimes, tau(F) = approximately 5.3 ns and tau(T) = approximately 200 micros, are reported. The spectra and lifetimes of S(1) --> S(0) fluorescence and sensitized T(1) --> T(x) absorption of 1 were obtained in a series of solvents, as was the fluorescence quantum yield, Phi(F) = 0.95-0.99. No phosphorescence has been detected. The first triplet excitation energy of solid 1 (11,400 cm(-1)) was obtained by electron energy loss spectroscopy, in agreement with previously reported solution values. The fluorescence excitation spectrum suggests an onset of a nonradiative channel at approximately 37,000 cm(-1). Excitation energies and relative transition intensities are in agreement with those of ab initio (CC2) calculations after an empirical 3000 cm(-1) adjustment of the initial state energy to correct differentially for a better quality description of the initial relative to the terminal state of an absorption transition. The interpretation of the MCD spectrum used the semiempirical PPP method, whose results for the S(0) --> S(x) spectrum require no empirical adjustment and are otherwise nearly identical with the CC2 results in all respects including the detailed nature of the electronic excitation. The ground state geometry of 1 was also calculated by the MP2, B3LYP, and CAS methods. The calculations provided a prediction of changes of molecular geometry upon excitation or ionization and permitted an interpretation of the spectra in terms of molecular orbitals involved. Computations suggest that 1 can exist as two nearly isoenergetic conformers of C(2) or C(s) symmetry. Linear dichroism measurements in stretched polyethylene provide evidence for their existence and show that they orient to different degrees, permitting a separation of their spectra in the region of the purely polarized first absorption band. Their excitation energies are nearly identical, but the Franck-Condon envelopes of their first transition differ to a surprising degree.

Five Stereoactive Orbitals on Silicon: Charge and Spin Localization in the n-Si4Me10(-•) Radical Anion by Trigonal Bipyramidalization.

RIUMP2/def2-TZVPPD calculations show that in addition to its usual conformation with charge and spin delocalized over the Si backbone, the isolated Si4Me10(-•) radical anion also has isomeric conformations with localized charge and spin. A structure with localization on a terminal Si atom has been examined in detail. In vacuum, it is calculated to lie 11.5 kcal/mol higher in energy than the charge-and-spin delocalized conformation, and in water the difference is as little as 1.6 kcal/mol. According to natural orbital and localized orbital analyses, the charge-and-spin-carrying terminal Si atom uses five stereoactive hybrid orbitals in a trigonal bipyramidal geometry. Four are built mostly from 3s and 3p atomic orbitals (AOs) and are used to attach a Si3(CH3)7 and three CH3 groups, whereas the larger equatorial fifth orbital is constructed from 4s and 4p AOs and acts as a nonbonding (radical) hybrid orbital with an occupancy of about 0.65 e.