441 research outputs found

### Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an
asymptotic exponential expansion for large values of the coordinate. We test it
on the expansion of the generating functions for the moments and connected
moments of the Hamiltonian operator. In the former case the formula produces
the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We
choose the harmonic oscillator and a strongly anharmonic oscillator as
illustrative examples for numerical test. Our results reveal some features of
the connected-moments expansion that were overlooked in earlier studies and
applications of the approach

### Improved tensor-product expansions for the two-particle density matrix

We present a new density-matrix functional within the recently introduced
framework for tensor-product expansions of the two-particle density matrix. It
performs well both for the homogeneous electron gas as well as atoms. For the
homogeneous electron gas, it performs significantly better than all previous
density-matrix functionals, becoming very accurate for high densities and
outperforming Hartree-Fock at metallic valence electron densities. For isolated
atoms and ions, it is on a par with previous density-matrix functionals and
generalized gradient approximations to density-functional theory. We also
present analytic results for the correlation energy in the low density limit of
the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure

### High--order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion
(CMX) for the Rabi Hamiltonian. To this end we calculate the moments and
connected moments of the Hamiltonian operator to a sufficiently large order.
Our large--order results suggest that the CMX is not reliable for most
practical purposes because the expansion exhibits considerable oscillations.Comment: 12 pages, 5 figures, 1 tabl

### An Approximate Spectral Density for the Estimation of so me Topological Indices of Alternant Systems

A symmetric two-delta-function model spectral density is used
to estimate several topological indices of alternant hydrocarbons,
namely: the total n-electron energy (E.), the modified topological
index (Z), the HOlVIO-LUMO separation (XHL) and the spectral
radius of adjacency matrix (R). It is found, that the invariants defined by integration (like E. and Z) are reproduced much better than the invariants defined as the Iimiting values of the spectral distribution (like XHL and R). The reason for the well known linear dependence between Er. and lnZ, is discussed

### Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local
Hamiltonian are largely determined by the $k$-particle reduced density matrices
($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least
enough for the calculation of the ground state and excited state energies.
Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even
the state itself is completely determined by its $k$-RDMs, and therefore
contains no genuine ${>}k$-particle correlations, as they can be inferred from
$k$-particle correlation functions. It is natural to ask whether a similar
result holds for non-degenerate excited states. In fact, for fermionic systems,
it has been conjectured that any non-degenerate excited state of a 2-local
Hamiltonian is simultaneously a unique ground state of another 2-local
Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version
of this conjecture states that any non-degenerate excited state of a 2-local
Hamiltonian is uniquely determined by its 2-matrix among all the pure
$n$-particle states. We construct explicit counterexamples to show that both
conjectures are false. It means that correlations in excited states of local
Hamiltonians could be dramatically different from those in ground states. We
further show that any non-degenerate excited state of a $k$-local Hamiltonian
is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely
determined by its $2k$-RDMs (or $2k$-matrix)

### Kohn-Sham calculations combined with an average pair-density functional theory

A recently developed formalism in which Kohn-Sham calculations are combined
with an ``average pair density functional theory'' is reviewed, and some new
properties of the effective electron-electron interaction entering in this
formalism are derived. A preliminary construction of a fully self-consitent
scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th
International Workshop on Condensed Matter Theories

### The Compact Nomenclature of the Benzenoid Hydrocarbons: A Short Review

The short review concerning the recently proposed compact narning (CN) of the benzenoid hydrocarbons is presented. Since this nomenclature allows to construct the dualist of a particular hydrocarbon directly from its name, the connections between the structure of the dualist and various properties of hydrocarbon are discussed. In general, these properties faU into three categories according to their local, nodal or global dependence

### Reducible Correlations in Dicke States

We apply a simple observation to show that the generalized Dicke states can
be determined from their reduced subsystems. In this framework, it is
sufficient to calculate the expression for only the diagonal elements of the
reudced density matrices in terms of the state coefficients. We prove that the
correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to
$2\ell$-partite level. Application to the Quantum Marginal Problem is also
discussed.Comment: 12 pages, single column; accepted in J. Phys. A as FT

### W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions

In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120},
4129 (2004)] we consider such refinements as more accurate estimates for the
contribution of connected quadruple excitations ($\hat{T}_4$), inclusion of
connected quintuple excitations ($\hat{T}_5$), diagonal Born-Oppenheimer
corrections (DBOC), and improved basis set extrapolation procedures. Revised
experimental data for validation purposes were obtained from the latest version
of the ATcT (Active Thermochemical Tables) Thermochemical Network. We found
that the CCSDTQ$-$CCSDT(Q) difference converges quite rapidly with the basis
set, and that the formula
1.10[CCSDT(Q)/cc-pVTZ+CCSDTQ/cc-pVDZ$-$CCSDT(Q)/cc-pVDZ] offers a very reliable
as well as fairly cost-effective estimate of the basis set limit $\hat{T}_4$
contribution. The largest $\hat{T}_5$ contribution found in the present work is
on the order of 0.5 kcal/mol (for ozone). DBOC corrections are significant at
the 0.1 kcal/mol level in hydride systems. . Based on the accumulated
experience, a new computational thermochemistry protocol for first-and
second-row main-group systems, to be known as W4 theory, is proposed. Our W4
atomization energies for a number of key species are in excellent agreement
(better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1
kJ/mol) with the latest experimental data obtained from Active Thermochemical
Tables. A simple {\em a priori} estimate for the importance of post-CCSD(T)
correlation contributions (and hence a pessimistic estimate for the error in a
W2-type calculation) is proposed.Comment: J. Chem. Phys., in press; electronic supporting information available
at http://theochem.weizmann.ac.il/web/papers/w4.htm

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