Search results for "ground states"
showing 10 items of 15 documents
A theoretical study of the 1B2u and 1B1u vibronic bands in benzene
2000
The two lowest bands, 1B2u and 1B1u, of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space (CAS) self-contained field (SCF) method (with six active π-orbitals) was used to compute harmonic force field for the ground state and the 1B2u and 1B1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory (CASPT2) was used to obtai…
A theory ofnonverticaltriplet energy transfer in terms of accurate potential energy surfaces: The transfer reaction from π,π* triplet donors to 1,3,5…
2004
Triplet energy transfer (TET) from aromatic donors to 1,3,5,7-cyclooctatetraene (COT) is an extreme case of "nonvertical" behavior, where the transfer rate for low-energy donors is considerably faster than that predicted for a thermally activated (Arrhenius) process. To explain the anomalous TET of COT and other molecules, a new theoretical model based on transition state theory for nonadiabatic processes is proposed here, which makes use of the adiabatic potential energy surfaces (PES) of reactants and products, as computed from high-level quantum mechanical methods, and a nonadiabatic transfer rate constant. It is shown that the rate of transfer depends on a geometrical distortion paramet…
Full configuration interaction calculation of singlet excited states of Be3
2004
The full configuration interaction (FCI) study of the singlets vertical spectrum of the neutral beryllium trimer has been performed using atomic natural orbitals [3s2p1d] basis set. The FCI triangular equilibrium structure of the ground state has been used to calculate the FCI vertical excitation energies up to 4.8 eV. The FCI vertical ionization potential for the same geometry and basis set amounts to 7.6292 eV. The FCI dipole and quadrupole transition moments from the ground state are reported as well. The FCI electric quadrupole moment of the X (3)A(1) (') ground state has been also calculated with the same basis set (Theta(zz)=-2.6461 a.u., Theta(xx)=Theta(yy)=-1/2Theta(zz)). Twelve of …
Full configuration interaction calculation of BeH adiabatic states.
2008
An all-electron full configuration interaction (FCI) calculation of the adiabatic potential energy curves of some of the lower states of BeH molecule is presented. A moderately large ANO basis set of atomic natural orbitals (ANO) augmented with Rydberg functions has been used in order to describe the valence and Rydberg states and their interactions. The Rydberg set of ANOs has been placed on the Be at all bond distances. So, the basis set can be described as 4s3p2d1f3s2p1d(BeH)+4s4p2d(Be). The dipole moments of several states and transition dipole strengths from the ground state are also reported as a function of the R(Be-H) distance. The position and the number of states involved in sever…
Magic numbers, excitation levels, and other properties of small neutral math clusters (N < 50)
2006
The ground-state energies and the radial and pair distribution functions of neutral math clusters are systematically calculated by the diffusion Monte Carlo method in steps of one math atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the “magic numbers” observed in experimental math cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the e…
Nonequilibrium Green's function approach to strongly correlated few-electron quantum dots
2009
The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's function theory. The ground and equilibrium states are self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second-order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for…
Multiplicity of ground states for the scalar curvature equation
2019
We study existence and multiplicity of radial ground states for the scalar curvature equation $$\begin{aligned} \Delta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n, \quad n>2, \end{aligned}$$when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ is bounded above and below by two positive constants, i.e. $$0 0$$, it is decreasing in (0, 1) and increasing in $$(1,+\infty )$$. Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we ar…
Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry
2022
AbstractWe study existence and multiplicity of positive ground states for the scalar curvature equation $$\begin{aligned} \varDelta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n\,, \quad n>2, \end{aligned}$$ Δ u + K ( | x | ) u n + 2 n - 2 = 0 , x ∈ R n , n > 2 , when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ K : R + → R + is bounded above and below by two positive constants, i.e. $$0<\underline{K} \le K(r) \le \overline{K}$$ 0 < K ̲ ≤ K ( r ) ≤ K ¯ for every $$r > 0$$ r > 0 , it is decreasing in $$(0,{{{\mathcal {R}}}})$$ ( 0 , R ) and increasing in $$({{{\mathcal {R}}}},+\infty )$$ ( R , + ∞ ) for a certain $${{{\mathcal {R}}}}&g…
A combined theoretical and experimental determination of the electronic spectrum of acetone
1996
A combined ab initio and experimental investigation has been performed of the main features of the electronic spectrum of acetone. Vertical transition energies have been calculated from the ground to the ny→π∗, π→π∗, σ→π∗, and the n=3 Rydberg states. In addition, the 1A1 energy surfaces have been studied as functions of the CO bond length. The 1A1 3p and 3d states were found to be heavily perturbed by the π→π∗ state. Resonant multiphoton ionization and polarization‐selected photoacoustic spectra of acetone have been measured and observed transitions were assigned on internal criteria. The calculated vertical transition energies to the ny→π∗ and all Rydberg states were found to be in agreeme…
Ab initio study on the low-lying excited states of retinal
1997
Ab initio results for the electronic spectrum of all-trans-retinal and its truncated model 3-methyl-all-trans (10-s-cis)-2,4,6,8,10-undecapentaen-1-al are presented. The study includes geometry determination of the ground state. Vertical excitation energies have been computed using multiconfigurational second-order perturbation theory through the CASPT2 formalism. The lowest singlet excited state in gas phase is predicted to be of nπ∗ character. The lowest triplet state corresponds, however, to a ππ∗ state. The most intense feature of the spectrum is due to the strongly dipole-allowed ππ∗ transition, in accordance with the observed maximum in the one-photon spectra. The vertical excitation …