Low-lying Excitation Energies Research Articles

Collision-induced dissociation of oriented CO + ions. Probing potential energy curves by ion collision spectrometry

Translational energy spectra of C + and O + fragments produced in the collision-induced dissociation of ground state CO + ions have yielded kinetic energy release distribution functions. These are compared with theoretical simulations that have been carried out by reflecting the probability distribution of the zeroth vibrational state of the 2Σ state onto various low-lying excited state potential energy curves of the CO + molecular ion which have been computed using contemporary ab initio molecular orbital techniques.

Ground and excited states of benzil: A theoretical study

The ground and low-lying excited state potential energy curves of benzil have been studied. The ground state geometry is fully optimized by the AM1 method. The excited states are calculated by using the CNDO/S-CI method. The calculations confirm that benzil in the ground state has a skewed conformation whereas the first excited singlet and triplet states of this molecule are trans-planar. The geometry relaxation in the excited states of benzil agrees well with the experimental findings. The absorption and emission bands of benzil have been compared with the observed bands. The dipole moments of the ground and excited states at some conformations are also reported. The effect of solvents on the electronic states of benzil has been studied using the continuum dielectric model.

Electron donor-acceptor complexes as potential high-efficiency second-order nonlinear optical materials. A computational investigation

The second-order nonlinear optical response of model molecular 1:1 and asymmetric 2:1 organic [pi] electron donor-acceptor (EDA) complexes is investigated using the INDO/S sum-over-excited particle-hole-states formalism. It is found that intermolecular charge-transfer transitions in EDA complexes represent a promising approach to achieving sizable second-order optical nonlinearities. Calculated hyperpolarizabilities may be generally related to the strength of the donor-acceptor interaction in the complex, affording for a given acceptor, the largest values in the case of aminoarene donors. The large change in dipole moment that accompanies intermolecular charge-transfer transitions and the relatively low-lying charge-transfer excitation energies are the major sources of the large calculated second-order nonlinearities. The relative orientation of donor and acceptor components is also an important feature, leading to stabilization of the ground state as well as to maximization of the oscillator strength of the lowest energy charge-transfer excitation and, in turn, the NLO response. In the case of asymmetric 2:1 EDA complexes, calculated hyperpolarizability enhancements over the 1:1 complexes can be related to the red-shift of the charge-transfer excitation as well as to an increase in dipole moment change between ground and excited states. The perturbation theoretical two-level' model is a useful first approximation for predicting the second-order nonlinearmore » response of such complexes. 29 refs., 2 figs., 3 tabs.« less

Electronic structures and photoelectron spectra of Si−3 and Si−4

Vibrationally resolved photoelectron spectra of Si−3 and Si−4, recently reported by Kitsopoulos, Chick, Weaver, and Neumark, are interpreted using ab initio quantum chemical calculations of the ground and excited electronic states of the corresponding neutral clusters. The calculated electron affinities as well as the low-lying excitation energies agree within 0.1–0.2 eV of the experimental values, thus confirming the theoretically predicted structures of neutral and anionic Si3 and Si4 reported previously.

A b i n i t i o study of the t r a n s-butadiene π-valence states using the effective valence shell Hamiltonian method

Low-lying π-electron vertical excitation energies of trans-butadiene are calculated using the effective valence shell Hamiltonian method. The results are compared with previous experimental and theoretical analyses of this molecule’s congested electronic spectra. The computations employ a large basis set (126 functions) which includes both diffuse functions on the carbon atoms and polarization functions on all atoms. Good agreement is obtained with the experimentally well known vertical excitation energies to the 1 3Bu, 1 3Ag, and 1 1Bu states where deviations from experiment are only 0.01, 0.01, and 0.22 eV, respectively. We confirm the experimental assignment of a valence like 1Ag state around 7.4 eV (calculated at 7.49 eV). Likewise, a member of a symmetry allowed 3p Rydberg series (of Au or Bu symmetry) in the electron impact spectrum with origin at 7.07 eV is assigned as the 2 1Bu state (with calculated vertical excitation energy of 7.00 eV). Most experiments place the 2 1Ag state above the 1 1Bu state; however, a resonance Raman assignment places it below. Our calculated excitation to the 2 1Ag state is 0.05 eV above the 2 1Bu state, about 0.5 eV lower than previous ab initio determinations. The computed vertical excitation energies are in good agreement with the interpretation of experimental electronic spectra, are in much better agreement with experiment than previously published ab initio calculations, provide the first definitive assignment of the 2 1Bu state at 7.08 eV, and conclusively assign the 3 1Ag state at 7.4 eV. The accuracy of the large basis effective valence shell Hamiltonian is, in part, due to retention of both valence and Rydberg orbitals in the valence space, a feature which has a bearing on intruder state problems and on current semiempirical π-electron theories.

Particle-hole symmetry, F-spin, and r-process parameters.

We exploit approximate symmetry under particle-hole conjugation and the systematics associated with a classification scheme (inspired by the neutron-proton interacting boson model) to obtain estimates of binding energies and low-lying excitation energies for even-even r-process nuclei drawn from the major proton and neutron shells, 50Z82 and 82N126. We anticipate that our simple formalism for binding energies, depending on only six parameters, has an accuracy of \ensuremath{\sim}0.8 MeV. We argue that the particular dual particle-hole conjugation symmetry required to relate excitation energies in neutron-rich nuclei to the known excitation energies of the corresponding conjugated nuclei holds to within 10% or so.

Langevin simulations of quantum systems.

We explore the potential of the Langevin simulation of quantum systems. A generalized quantum sine-Gordon chain, a generalized Toda chain, and impenetrable bosons on a ring are treated specifically to estimate low-lying excitation energies from the long-time behavior of the Langevin process. In the sine-Gordon case, we investigated the dependence of the bound-state frequency on the coupling constant, while in the Toda chain the phonon dispersion curves are obtained for different coupling constants. Finally, for impenetrable bosons the estimated dynamic form factor for density fluctuations is compared with exact results.

Excitation energies in Be: A comparison of multiconfigurational linear response and full configuration interaction calculations

Using a 〈9s9p5d〉 contracted GTO basis we have calculated low-lying excitation energies of singlet and triplet symmetry for the Be atom using Δfull CI, ΔCI(1s) with double occupancy in the 1s orbital, multiconfiguration linear response (MCLR), and ΔMCSCF approaches. The Δfull CI results agree very closely with the experimental excitation energies except for higher excitations where obvious basis set defects occur. The MCLR calculations shows that with an adequately chosen MCSCF reference state the MCLR calculation is capable of mimicking the Δfull CI results. The MCLR results are closer to the Δfull CI results than the ΔCI(1s). The ΔMCSCF excitation energies show that this approach can only be used with extreme care to determine excitation energies.

A minimal basis-set CNDO/2(S + DES CI) study on the excited states of hydrogenated polysilane model compounds

Minimal basis-set CNDO/2(S+DES CI) computations on trans-H-(SiH 2) 5-H and H-(SiH 2) 9-H yield low-lying excitation energies and oscillator strengths which parallel existing experimental spectra. The S 0 → S 1 transition moments are shown to be particularly sensitive to configuration mixing.

Unified large basis set diatomics-in-molecules models for ground and excited states of H3

A recently developed systematic diatomics-in-molecules (DIM) procedure has been applied to the system H+H2 in order to generate large basis set models capable of approximating both the ground and low-lying excited state potential energy surfaces in a unified manner. The procedure, based exclusively on an analysis of diatomic ab initio wave functions, suggests that a 20-structure model including structures with not more than one excited H atom (2s or 2p) should suffice for the H3 (2A′) states. An 80-structure model including up to two excited H atoms yielded potential energy surfaces in close agreement with the smaller model. The ground state surface shows a greatly improved behavior in D3h configurations when compared to the simplest, two-structure DIM model for H3 but is otherwise very similar to that surface. This result exemplifies the stability of our systematic DIM methodology to increases in the size of the basis set. A number of excited state surfaces, including the lower 2A″ and quartet states, are reported and the implications for reaction kinetics are discussed. In particular, we predict the reaction H*(2s or 2p)+H2→H+H+H to have a large cross section.

Droplet wave functions for the fractional quantum Hall effect.

Trial wave functions which, in the thermodynamic limit, describe states relevant to the fractional quantum Hall effect are explicitly constructed for up to eight electrons. Estimates are given for the ground-state energies and pair-correlation functions and for the low-lying excitation energies for states associated with the filling factors \ensuremath{\nu}=(1/3), (2/7), and (2/5). The results help explain why the filling factors \ensuremath{\nu}=${\ensuremath{\nu}}_{m}$=m/(2m+1), m=1,2,..., and \ensuremath{\nu}=1-${\ensuremath{\nu}}_{m}$ show strong quantum Hall effects.

An augmented coupled cluster method and its application to the first-row homonuclear diatomics

An augmented coupled cluster scheme to evaluate the higher order electron correlation effects is proposed. The method is carried out in two steps. First, a coupled cluster calculation with all double substitutions (CCD) is performed. The converged CCD wave function is then used in the evaluation of the contribution of single and triple substitutions. The method is correct to fourth order in a perturbation expansion and includes significant fifth and higher order terms. Illustrative calculations on the excitation and dissociation energies of first-row homonuclear diatomic molecules are reported. The low-lying excitation energies of B2 and C2 are accurately calculated. The dissociation energies of B2, C2, N2, O2, and F2 are all uniformly underestimated by 0.1–0.3 eV using large spdf basis sets.

Higher-order ion-size effects in pseudopotential theory

The ion size effects formulated by R.H. Bartram, A.M. Stoneham and P. Gash (1968) for colour centres, later extended by R.D. Zwicker (1975) are examined for the convergence of higher-order terms. When applied to the evaluation of the low-lying excited state energies of alkali and rare gas atoms, it is found that the convergence is very doubtful for heavier elements. This is shown to be due to the outermost electron shells with extended charge density. A hybrid scheme in which the outermost s and p shells of the ion core are represented by the exact evaluation of various terms is shown to give excellent results. Its potential application in solids is indicated.

Calculations of low-lying collective excitation energies in 168Yb at high angular momenta

The excitation energy of the lowest I-odd states in 168Yb is calculated in a wide range of spins ( I) by using the microscopic model suggested earlier by two of the authors (D.J. and I.M.). This family of states has close relation to the γ-vibrational states at low spins and to the one-phonon precessional excitations when I is large.

Self-consistent many-body theory for π electron systems. I. The ethylene molecule

We present a general many-body theory of molecular electron systems based on a Green’s function formalism. The theory introduces directly the dynamical screened electron–electron interaction and produces an exact expansion for the one-body and two-body (i.e., density–density) Green’s functions, suitable for self-consistent calculations. In first order we get the usual random-phase approximation (RPA). The successive terms can be interpreted as being due to local field corrections to the self-consistent field. Applications within the Pariser–Parr–Pople model are presented. Explicit calculations of the low-lying excitation energies of ethylene molecule show good agreement with ’’exact’’ calculations, and some of the difficulties of other methods, especially for triplet states, are overcome.

55Mn NMR of Impurity Spin in Metamagnetic CoCl2·2H2O

Nuclear magnetic resonance of 55 Mn of an impurity Mn 2+ spin has been investigated in three metamagnetic phases of CoCl 2 ·2H 2 O at liquid helium temperatures. The hyperfine field at 1.6 K was found to be -594.1±0.3 kOe. A strong temperature dependence of the spin-echo decay time observed at low temperatures indicates that low-lying excitation energies of the Mn 2+ spins are much lower than those of the host Co 2+ spin system. However, there was no temperature dependence of the hyperfine field in the range from 1.6 to 4.2 K, and this was attributed tentatively to the long relaxation time of Mn 2+ spins. When external field was applied parallel to the b -axis, jumps of the hyperfine field associated with metamagnetic transitions and an anomalous change of the electric field gradient were observed.

Magnetic properties of transition-metal surfaces: An energy comparison of different Hartree-Fock solutions

A Hartree-Fock treatment of the surface of ferromagnetic transition metals will often lead to three self-consistent surface solutions. They correspond to different magnetic properties of the surface. We present here an energy comparison of these surface solutions. Two models, each having a different bulk density of states, are considered in order to study how sensitive our findings are to the shape of the bulk density of states. In many cases the solutions corresponding to a ferromagnetic and to an antiferromagnetic coupling of the surface layer to the bulk are found to have almost equal energy. This implies the possibility of low-energy magnetic surface excitations corresponding to a change of the surface layer from ferromagnetic to antiferromagnetic coupling or vice versa. For temperatures higher than this low-lying excitation energy but lower than the Curie temperature, the ferromagnetically and antiferromagnetically coupled states are equally populated and the surface layer has no net moment.

Application of rayleigh-schrödinger perturbation theory to calculation of excitation energies

Low-lying excitation energies are calculated by the use of the many-body quasi-degenerate Rayleigh-Schrödinger perturbation theory. An eigenvalue problem is derived for the third-order estimation of the low-lying excitation energies. The elements of the hermitian matrix appearing in this eigenvalue problem are determined up to the third order by the diagrammatic method. Some simple illustrative calculation on π-electron systems are carried out.

Vertical-Arrow Correlation Length in the Eight-Vertex Model and the Low-Lying Excitations of theX−Y−ZHamiltonian

We consider the correlation function ${G}_{R}$ for two vertical arrows in the same column. We calculate the critical index $\ensuremath{\nu}$ of the correlation length, and we find the scaling relation $\ensuremath{\nu}=1\ensuremath{-}\frac{\ensuremath{\alpha}}{2}$ is satisfied. In the decoupling limit, we prove that the correlation length is not determined by the next-largest eigenvalue. In order to obtain the correct correlation length, it is necessary to integrate over the entire band of complex next-largest eigenvalues. We argue that this is also the situation in the general case of the eight-vertex model. Under certain well-defined assumptions, we compute the correlation length of ${G}_{R}$. We also calculate the low-lying excitation energies of the $X\ensuremath{-}Y\ensuremath{-}Z$ Hamiltonian. In addition to free states existing for $0<\ensuremath{\mu}<\ensuremath{\pi}$, there are bound states appearing in the spectrum for $\ensuremath{\mu}>\frac{\ensuremath{\pi}}{2}$. In the course of our work, we have rewritten the results of Cheng and Wu for the Ising-model correlation functions in an elegant form, using Baxter's elliptic-function parametrization.

Four approaches to the function of inertia in a solvable model

Four different methods of calculating the mass function for large-amplitude collective motion are applied to the Lipkin model: adiabatic time-dependent Hartree-Fock (ATDHF), infinitesimal generators (IG), constrained RPA and the generator coordinate method (GC). ATDHF and GC give identical results. IG and RPA lead to the same result only in the limit of vanishing constraint. The corresponding collective Hamiltonian gives good results for the low-lying excitation energies while the cranking approximation seems to be rather poor for this case.