In this work we apply the line-integral technique to study possible geometric phase effects in the 2×2 diabatic double many-body expansion (DMBE) potential energy surface of three hydrogenic systems, namely, H3, DH2, and HD2. First, we show that the phase obtained by employing the line-integral method is identical (up to a constant) to the ordinary diabatic angle of the orthogonal transformation that diagonalizes the diabatic potential matrix. Next this angle is studied numerically along the line formed by fixing the two hyperspherical coordinates ρ and θ and letting φ change along the interval [0, 2π]. We find that in the H3 system, where this line always encircles the seam, the corresponding line integral always produces the value π for the geometric (Berry) phase. In the cases of the two isotopic systems we usually find the same results, but we also verify that for substantial regions in configuration space these lines do not encircle the seam and that, therefore, the line integrals produce the value of zero for the geometric phase. Analyzing the results, we establish that the Longuet-Higgins phase, which is usually assumed to be equal to φ/2, is in general significantly different from this value for all studied mass combinations.

A combined quantum mechanics/molecular mechanics method is described here for considering the solvatochromic shift of excited states in solution. The quantum mechanical solute is described using high level multireference configuration interaction methods (MRCI), while molecular dynamics is used for obtaining the structure of the solvent around the solute. The electrostatic effect of the solvent is included in the quantum description of the solute in an averaged way. This method is used to study solvent effects on the n(O) --> pi* electronic transition of formaldehyde in aqueous solution. The effects of solute polarization, basis sets, and dynamical correlation on the solvatochromic shift, and on dipole moments, have been investigated.

On the basis of a new, highly accurate potential energy hypersurface for the lowest triplet state of H+3, (3)Sigma(+)(u), the bound ro-vibronic states are calculated for J

Based on the equivalence of the gauge transformations for the nuclear and electronic wave functions, the physical meaning of the geometric phase effect has been disclosed for a two coupled-state system. It is found that the geometric phase A(R) is defined by the argument of the complex electronic vector state in the complex plane spanned by the two real-valued electronic components. Such an angle is identical (up to a constant) to the mixing angle γ(R). Novel generalized Born–Oppenheimer equations for the two coupled-state problem in the vicinity of the crossing seam have been derived, and numerical calculations of vibrational spectra done for H3. The results demonstrate significant differences in relation to those obtained from the assumption that A(R)=φ/2.

We present J s 0 calculations of all bound and pseudobound vibrational states of Li in its first-excited electronic doublet state by using a realistic double 3 many-body expansion potential-energy surface and a minimum-residual filter diagonalization technique. The action of the system Hamiltonian on the wave function was evaluated by the spectral transform method in hyperspherical coordinates. Calculations of the vibrational spectra were carried out both without consideration and with consideration of geometric-phase effects. Dynamic Jahn᎐Teller and geometric-phase effects are found to play a significant role, while the calculated fundamental symmetric stretching frequency is larger by 8.3% than its reported experimental value of 326 cm y1 . From the neighbor-spacing distributions of the levels, it is observed that the title vibrational spectrum is quasiregular in the short range and quasi-irregular in the long range. By the ⌬ standard defined in this article, it is found that the spectra are more 2 nonuniform than those of the ''trough'' states for the ground electronic state.