Showing papers on "Ground state published in 1993"

Ab initio molecular dynamics for open-shell transition metals.

Abstract: We show that quantum-mechanical molecular-dynamics simulations in a finite-temperature local-density approximation based on the calculation of the electronic ground state and of the Hellmann-Feynman forces after each time step are feasible for liquid noble and transition metals. This is possible with the use of Vanderbilt-type ``ultrasoft'' pseudopotentials and efficient conjugate-gradient techniques for the determination of the electronic ground state. Results for liquid copper and vanadium are presented.

The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties

Abstract: A comprehensive overview of the equation of motion coupled‐cluster (EOM‐CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM‐CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single‐reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled‐cluster density matrices, providing a link between EOM‐CC and traditional ground state CC theory.Excitation energy,oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.

On concentration of positive bound states of nonlinear Schrödinger equations

Abstract: We study the concentration behavior of positive bound states of the nonlinear Schrodinger equation $$ih\frac{{\partial \psi }}{{\partial t}} = \frac{{ - h^2 }}{{2m}}\Delta \psi + V\left( x \right)\psi - \gamma \left| \psi \right|^{p - 1} \psi .$$ Under certain condition ofV, we show that positive ground state solutions must concentrate at global minimum points ofV ash→0+; moreover, a point at which a sequence of positive bound states concentrates must be a critical point ofV. In cases thatV is radial, we prove that the positive radial solutions with least energy among all nontrivial radial solutions must concentrate at the origin ash→0+.

Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of (H2O)2.

Abstract: A method for calculations of the ground-state energy and structure of finite systems and for molecular-dynamics simulations of the evolution of the nuclei on the Born-Oppenheimer ground-state electronic potential-energy surface is described. The method is based on local-spin-density functional theory, using nonlocal pseudopotentials and a plane-wave basis set. Evaluations of Hamiltonian matrix elements and the operations on the wave functions are performed using a dual-space representation. The method, which does not involve a supercell, affords accurate efficient simulations of neutral or charged finite systems which possess, or may develop, multipole moments. Since the ground-state electronic energy and the forces on the ions are calculated for each nuclear configuration during a dynammical simulation, a relatively large time step can be used to integrate the classical equations of motion of the nuclei (1--10 fs, depending on the characteristic frequencies of the ionic degrees of freedom). The method is demonstrated via a study of the energetics, structure, and dynamics of the water dimer, (${\mathrm{H}}_{2}$O${)}_{2}$, yielding results in agreement with experimental data and other theoretical calculations. In addition to the properties of the ground state of the dimer, higher-energy transition structures involved in transformations between equivalent structures of the (${\mathrm{H}}_{2}$O${)}_{2}$ molecule, were studied, and finite temperature simulations of the dynamics of such transformations are presented.

Threshold and resonance phenomena in ultracold ground-state collisions

Abstract: We study the magnetic-field dependence of the cross sections for elastic and inelastic collisions of pairs of ultracold cesium atoms in a magnetic trap, calculated with the coupled-channels method. We pay special attention to atoms in the f=3, mf=-3 weak-field seeking state of the lower hyperfine manifold. The cross sections show a pronounced resonance structure. We discuss its origin, starting from the pure bound singlet and triplet rovibrational Cs2 states and introducing perturbations due to the hyperfine and Zeeman interactions. We also discuss the role of the centrifugal barrier in the final collision channel in reducing the loss of atoms from the trap due to transitions induced by the magnetic dipole-dipole interaction

N -electron ground state energies of a quantum dot in magnetic field

Abstract: Using single-electron capacitance spectroscopy, we map the magnetic field dependence of the ground state energies of a single quantum dot containing from 0 to 50 electrons. The experimental spectra reproduce many features of a noninteracting electron model with an added fixed charging energy. However, in detailed observations deviations are apparent: Exchange induces a two-electron singlet-triplet transition, self-consistency of the confinement potential causes the dot to assume a quasi-two-dimensional character, and features develop which are suggestive of the fractional quantum Hall effect.

Specific CI calculation of energy differences: Transition energies and bond energies

Abstract: A general strategy for the calculation of energy differences is proposed. It proceeds through the definition of a minimal model space and the low-order perturbative development of the corresponding Hamiltonian is used to establish a set of determinants contributing to the searched energy difference. The so-selected CI is treated variationally. This general strategy is applied here to the calculation of observables basically involving two electrons in two orbitals. The first one concerns the transition energies from the ground state to the lowest singlet and triplet states of atoms (Ar 1 S → 3,1 P, Ca 1 S → 3,1 P) or molecules (CH 2 1 A 1 → 3 B 1 , 2 1 A 1 ). The second problem concerns the CH bond energy in ethylene. In all cases the agreement of the results of that simple procedure with either experiment or full-CI is quite satisfactory.

Bistable saturation in coupled quantum dots for quantum cellular automata

Abstract: A simple model quantum dot cell containing two electrons is analyzed as a candidate for quantum cellular automata implementations. The cell has eigenstates whose charge density is strongly aligned along one of two directions. In the presence of the electrostatic perturbation due to a neighboring cell, the ground state is nearly completely aligned (polarized) in one direction only. The polarization is a highly nonlinear function of the perturbing electrostatic fields and shows the strong bistable saturation important for cellular automation function.

Bare transition metal atoms in the gas phase: reactions of M, M+, and M2+ with hydrocarbons

Abstract: This Account focuses on gas-phase measurements and high quality ab initio calculations that are beginning to explain how metal atom electronic structure determines chemical reactivity The authors have an enormous body of basic chemical reactivity data for M[sup +] and a growing body of data for M[sup 2+] and neutral M Sophisticated experiments can control the kinetic energy and the electronic state of M[sup +] reactants One can study the reactivity of Fe[sup +] in the 3d[sup 6]4s, high-spin ground state, the 3d[sup 7], high-spin first excited state, or the 3d[sup 6]4s, low-spin second excited state The authors have learned to follow the elimination of H[sub 2] and C[sub 2]H[sub 6] from bimolecular Ni[sup +](n-butane) complexes in real time, on a 50-ns time scale In M[sup +] reactions, the authors can control the kinetic energy and the electronic state of the reactants A key advantage in interpreting these results is that one understands the electronic structure of the bare metal atom reactants very well Solution-phase chemists might well question the relevance of atomic species with genuine 1+ or 2+ charges and no ligands or solvent to the [open quotes]real world[close quotes] of organometallic chemistry Yet connections surely exist, as witnessedmore » by the fact that Rh and Ir atoms are unusually reactive in all phases Theoretical chemists are beginning to provide a conceptual framework that will unify seemingly diverse branches of experimental chemistry Of necessity, the ab initio quantum chemist works on model transition metal systems, draws experimental evidence from all available sources, and tries to abstract from the calculations what is robust and common to all phases Gas-phase metal atoms are idealized model systems well matched to the capabilities of modern theory Many new conceptual insights in the next 10 years will come from careful analysis of ab initio wave functions informed by incisive gas-phase experiments 30 refs, 5 figs, 1 tab« less

Electronic-structure and spin-state transition of lacoo3

Abstract: We present soft-x-ray-absorption spectra (XAS) of ${\mathrm{LaCoO}}_{3}$ taken at different temperatures (80--630 K). The shape of the multiplets in the Co 2p XAS spectra conveys information on the symmetry and spin of the ground state. The O 1s XAS spectra are related to unoccupied metal bands through covalent mixing. The changes in the spectra taken at different temperatures provide information on the spin-state transition in this compound. At low temperature, 80 and 300 K, the material is in a highly covalent low-spin state. The main contribution to the ground state in this case is given by ${\mathit{t}}_{2\mathit{g}}^{6}$${(}^{1}$${\mathit{A}}_{1}$) with an occupancy of 0.56. At higher temperature, 550 and 630 K, the results indicate a gradual transition to a mixed-spin state. The main contribution to the high-spin part of the mixture is given by ${\mathit{t}}_{2\mathit{g}}^{4}$${\mathit{e}}_{\mathit{g}}^{2}$${(}^{5}$${\mathit{T}}_{2}$) with an occupancy of 0.71. There is no evidence of charge disproportionation in the temperature range 80--630 K. The O 1s XAS spectra reflect important changes in the unoccupied Co 3d bands across the spin-state transition.

Relativistic energies of the ground state of the hydrogen molecule

Abstract: Relativistic corrections, Born–Oppenheimer energies and adiabatic corrections are computed for R ≤ 120 bohr for the electronic ground state of the hydrogen molecule The Born–Oppenheimer potential is slightly lower than ever reported The problem of linear dependencies in the basis set is removed and the same set is used for all internuclear distances which assures continuity of the results The radiative corrections are evaluated approximately and—for that purpose—the polarizability of the molecule is also computed Vibrational energies are computed and— corrected for nonadiabatic effects—compared with experiment for several isotopes It is argued on the basis of the remaining discrepancies that an improvement in the ab initio nonadiabatic corrections is necessary

Comparison of a Hartree, a Hartree-Fock, and an exact treatment of quantum-dot helium.

Abstract: We compare energies, pair correlation functions, and particle densities of the ground state of quantum-dot helium in a magnetic field obtained by a Hartree, a Hartree-Fock (HF), and an exact treatment. The exact and HF results for the triplet state agree well, which illustrates the importance of the exchange interaction for systems of few electrons. The results for the singlet state differ significantly and we show that this is caused by a lack of correlation between the angular momenta of the electrons in the HF approximation.

Matrix Product Ground States for One-Dimensional Spin-1 Quantum Antiferromagnets

Abstract: We have found the exact ground state for a large class of antiferromagnetic spin-1 models with nearest-neighbour interactions on a linear chain. All ground-state properties can be calculated. The ground state is determined as a matrix product of individual site states and has the properties of the Haldane scenario.

Resonance Raman studies of the ground and lowest electronic excited state in CdS nanocrystals

Abstract: The size dependence of the resonance Raman spectrum of CdS nanocrystals ranging in size from 10 to 70 A radius has been studied. We find that while the lowest electronic excited state is coupled strongly to the lattice, this coupling decreases as the nanocrystal size is decreased. We demonstrate that the lifetime of the initially prepared excited state can influence the apparent strength of electron‐vibration coupling. Absolute resonance Raman cross section measurements can be used to determine the value of the excited state lifetime, thus removing this parameter. The coupling to the lattice, while less in nanocrystals than in the bulk, is still greater than what is predicted assuming an infinite confining potential. The width of the observed LO mode broadens with decreasing size, indicating that the resonance Raman process is intrinsically multimode in its nature. The frequency of the observed longitudinal optic (LO) mode has a very weak dependence on size, in contrast to results obtained from multiple quantum well systems. The temperature dependence of the frequency and linewidth of the observed LO mode is similar to the bulk and indicates that the LO mode decays into acoustic vibrations in 2.5 ps.

Single-barrier problem and Anderson localization in a one-dimensional interacting electron system.

Abstract: Transport through a single barrier in a one-dimensional (1D) interacting electron system is studied theoretically. By using renormalization group and duality mapping, the phase diagram of the ground state is shown to be divided into four regions in terms of the zero-temperature limits of the charge and spin conductances. The conductances are calculated perturbatively for both limits of weak and strong potential. The results are applied to clarify the crossover and scaling of the Anderson localization in a 1D system with dilute impurities. It is shown that the temperature dependence of the resistivity of the system can change significantly around a characteristic temperature corresponding to discretization energy.

Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations

Abstract: Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two‐center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm−1, and ΔDe=57 cm−1.

Negative ion photoelectron spectroscopy of Cr2

Abstract: The 476-514-nm photoelectron spectra of Cr 2 - , recorded at 4-meV resolution, show vibrationally resolved transitions to the ground state and to one excited electronic state of neutral Cr 2 . The measured electron affinity of Cr 2 is 0.505±0.005 eV. Observed vibrational energies in the 1 Σ g + ground state of Cr 2 up to υ=9, 3040 cm -1 above the zero point level, fit a Morse potential with ω c =480.6±0.5 cm -1 and ω e x e =14.1±0,3 cm -1

Bose-Einstein condensation of paraexcitons in stressed Cu 2 O

Abstract: Reducing the multiplicity of the orthoexciton ground state in ${\mathrm{Cu}}_{2}$O by applying uniaxial stress greatly increases the quantum degeneracy of the excitonic gas produced by intense pulsed excitation. Simultaneously, the paraexciton luminescence spectrum develops an extra component at low energy which is interpreted as a Bose-Einstein condensate of paraexcitons.

A conical intersection mechanism for the photochemistry of butadiene. A MC-SCF study

Abstract: The excited state (2 1 Ag) reaction paths involved in the photochemical transformations of butadiene have been studied via ab initio MC-SCF methods. It is demonstrated that the reaction funnel assumes the form of a conical intersection region where the ground (1 1 Ag) and first excited (2 1 Ag) potential energy surfaces are degenerate. This mechanism is consistent with experimental results for the photochemical isomerization and is also consistent with the observed absence of fluorescence from the 2 1 Ag state. Thus the currently accepted mechanisms for butadiene photochemistry which involve radiationless decay at avoided crossing minima need to be replaced with a model that involves fully efficient return to the ground state via a conical intersection

Many‐body methods for excited state potential energy surfaces. I. General theory of energy gradients for the equation‐of‐motion coupled‐cluster method

Abstract: The formal theory is presented for calculating the analytic first derivative of the energy with respect to arbitrary perturbations within the equation‐of‐motion coupled‐cluster (EOM‐CC) approximation. Through use of the Dalgarno–Stewart interchange theorem (Z‐vector method), terms involving derivatives of the ground state cluster amplitudes are eliminated, leading to the definition of a new quasiparticle de‐excitation operator which simplifies the theory and significantly reduces the expected cost associated with studying potential energy surfaces for excited electronic states. For both illustrative and pragmatic reasons, the final equations are cast in a form similar to that developed for ground state CC energy derivatives, involving contraction of effective one‐ and two‐particle density matrices with matrix elements of the differentiated Hamiltonian. Some aspects regarding calculation of the gradient are discussed with particular attention devoted to similarities between the structure of the present formulas and those which have been previously implemented for the ground state problem.

Nitrogen donors in 4H‐silicon carbide

Abstract: Hall‐effect and infrared‐absorption measurements are performed on n‐type 4H‐SiC samples to investigate the energy positions of the ground state and the excited states of the nitrogen donor in the 4H polytype of silicon carbide. Two electrically active levels (Hall effect) and three series of absorption lines (infrared spectra) are assigned to two nitrogen donor species which substitute on the two inequivalent lattice sites (h,k) in 4H‐SiC. Valley‐orbit splitting of the ground‐state level of the nitrogen donors on hexagonal sites (h) is found to be equal to ΔEvo(h)=7.6 meV. It is shown that the energy position of excited states of both nitrogen donors can be calculated by the effective‐mass approximation by assuming anisotropic effective masses m⊥=0.18m0 and m∥=0.22m0. The influence of the two inequivalent lattice sites on the values of ionization energy and valley orbit splitting of the nitrogen donor ground‐state levels is discussed.

Photoassociation spectrum of ultracold Rb atoms.

Abstract: We study the photoassociative collisional loss of laser-cooled Rb atoms from a far-off resonance optical dipole force atom trap. We obtain a well-resolved photoassociation spectrum from 50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to 980 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ below the first excited dissociation limit of the ${\mathrm{Rb}}_{2}$ molecule. Two vibrational series associated with excited ${\mathrm{Rb}}_{2}$ $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}^{+}$ states are clearly visible. Oscillations in the associated Franck-Condon factors reflect the structure of the triplet ground state wave function. Our results clearly demonstrate the potential of photoassociation spectroscopy as a new probe of molecular structure.

Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators

Abstract: A Lyapunov function for the phase-locked state of the Kuramoto model of non-linearly coupled oscillators is presented. It is also valid for finite-range interactions and allows the introduction of thermodynamic formalism such as ground states and universality classes. For the Kuramoto model, a minimum of the Lyapunov function corresponds to a ground state of a system with frustration: the interaction between the oscillators,XY spins, is ferromagnetic, whereas the random frequencies induce random fields which try to break the ferromagnetic order, i.e., global phase locking. The ensuing arguments imply asymptotic stability of the phase-locked state (up to degeneracy) and hold for any probability distribution of the frequencies. Special attention is given to discrete distribution functions. We argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results, but that a partial locking of some but not all sublattices is not to be expected. The order parameter of the phase-locked state is shown to have a strictly positive lower bound (r ⩾ 1/2), so that a continuous transition to a nonlocked state with vanishing order parameter is to be excluded.

Ultrafast transient-absorption spectroscopy of the aqueous solvated electron

Abstract: We have performed the first direct pump‐probe transient‐absorption measurements on the near‐infrared (IR) band of the equilibrated aqueous solvated electron. The pump pulse was centered at 780 nm. The absorption spectrum of the excited state is observed to be red‐shifted relative to the ground‐state absorption. The radiationless transition from the excited state to the ground state occurs with an average time constant of 550±170 fs. In observing a subpicosecond lifetime and red‐shifted absorption for the excited p‐states, these experiments are in accord with a growing body of experimental and theoretical work, serving to provide a consistent picture of the photophysics of the solvated electron.