Search results for "density [dark matter]"

Integral-geometrical consideration of density matrices

1995

The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators {Theta}{sub {lambda}} are represented using particular values (at specially chosen {Xi} = {Xi}{sub o}) of the Radon transform D{sub N{lambda}} D{sub N{lambda}}({Xi}) of the N-DM spatial parts (or their sums) D{sub N{lambda}}({chi}{prime}{vert_bar}{chi}{double_prime}) (here, {Xi} is a d-plane in the n-space {Re}{double_prime} of {chi} = ({chi}{prime}, {chi}{double_prime}), with n = 6N, d = 3(N - k), {chi}{p…

Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants

1996

A theory for the calculation of nuclear magnetic shielding constants at the coupled‐cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge‐including atomic orbital (GIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H2O,NH3, CH4, N2, CO, HCN, and F2. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the abil…

Effective pseudopotential for energy density functionals with higher-order derivatives

2011

We derive a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, it gives the average energy that corresponds to a quasi-local nuclear Energy Density Functional (EDF) built of derivatives of the one-body density matrix up to sixth order. The direct reference of the EDF to the pseudopotential acts as a constraint that divides the number of independent coupling constants of the EDF by two. This allows, e.g., for expressing the isovector part of the functional in terms of the isoscalar part, or vice versa. We also derive the analogous set of constraints for the coupling constants of the EDF that is restricted by sp…

Electron-transfer dynamics in a donor—acceptor complex

1991

Abstract Density matrix theory is used for the study of the dissipative quantum dynamics of electron transfer in a donor—acceptor complex. The vibrational modes of the complex are divided into a single interaction coordinate coupling to the transferred electron and the remaining modes which form a dissipative environment. With increase of the coupling of the interaction coordinate to the environment and, thus, of the corresponding damping rate of the vibrational quanta, the results of the numerical calculations display a change from the coherent to the incoherent transfer regime. In contrast to the case of small values of the damping, the transfer dynamics become independent of the number o…

Multi-level coupled cluster theory

2014

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and prese…

Many-particle Green's functions

2013

Anomalous d-like surface resonances on Mo(110) analyzed by time-of-flight momentum microscopy.

2015

The electronic surface states on Mo(110) have been investigated using time-of-flight momentum microscopy with synchrotron radiation (hν=35 eV). This novel angle-resolved photoemission approach yields a simultaneous acquisition of the E-vs-k spectral function in the full surface Brillouin zone and several eV energy interval. (kx,ky,EB)-maps with 3.4 A(-1) diameter reveal a rich structure of d-like surface resonances in the spin-orbit induced partial band gap. Calculations using the one-step model in its density matrix formulation predict an anomalous state with Dirac-like signature and Rashba spin texture crossing the bandgap at Γ¯ and EB=1.2 eV. The experiment shows that the linear dispersi…

Backward production of mesons associated with? ++(1232) in? + p interactions at 20 GeV/c

1991

We have analyzed backward meson production inπ + p reactions at 20GeV/c, which were measured in the CERN Ω spectrometer triggered by a fast proton (p f ), in experiment WA56. Production via baryon exchange of quasi-two-body final statesΔ ++ (1232)ρ 0 (770),Δ ++ (1232)f 2 (1270), andΔ ++ (1232)ρ 3 0 (1690) is clearly identified. The density matrix elements of meson resonances and ofΔ ++ (1232) are analyzed. We have observed also the reactionsπ + p→Δ ++ (1232)π 0 andπ + p→Δ ++ (1232)ω in thep f π + π 0 andp f π + π + π − π 0 final states.

Fast noniterative orbital localization for large molecules

2006

We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals ("Cholesky molecular orbitals") demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implem…

Density gradient expansion of correlation functions

2013

We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of density derivatives of arbitrary order. We further derive a consistency condition that is necessary for the existence of the gradient expansion. This condition is used to carry out an infinite summation of terms involving response functions up to infinite order from which it follows that the coefficient functions of the gradient expansion can be expressed in terms the local density profile rather than the background density around which the expansion is ca…