Interpolant polynomial technique applied to the PPP model. I. Asymptotics for excited states of cyclic polyenes in the finite cyclic Hubbard model

Bracken, Paul; Ek, J. van

doi:10.1002/(sici)1097-461x(1996)57:6<1019::aid-qua1>3.0.co;2-w

Cited by 7 publications

(1 citation statement)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method of effective characteristic polynomials has been introduced byČížek and coworkers recently. It has been applied to the summation of the divergent perturbation series of anharmonic oscillators [1] and to correlation energies of model systems [2][3][4][5][6][7][8]. Extensions of the method for the simultaneous treatment of several perturbation series have recently been proposed [9] but this will not be considered in the following.…”

Section: Introductionmentioning

confidence: 99%

The size-extensivity of correlation energy estimators based on effective characteristic polynomials

Homeier

1997

Journal of Molecular Structure: THEOCHEM

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

The size-extensivity of correlation energy estimators based on effective characteristic polynomials

Homeier

1997

Journal of Molecular Structure: THEOCHEM

View full text Add to dashboard Cite

Interpolant polynomial technique applied to the PPP model. II. Testing the interpolant technique on the Hubbard model

Bracken

1996

Int. J. Quantum Chem.

Self Cite

View full text Add to dashboard Cite

rnOne is often led, in quantum mechanics, to a perturbative solution of an eigenvalue problem, which is defined by a given Hamiltonian. The perturbative series for the energy which results will be a function of a coupling constant which appears in the Hamiltonian. In this article, the perturbative series for the energy of a state of a cyclic polyene ring which are valid for the small and large coupling limit of the model are used to construct algebraic functions. These algebraic functions are defined in terms of polynomials which are given as a function of the energy variable and coupling parameter and can be solved to give the energy as a function of coupling. It is found that relatively small polynomials give very good agreement with the exact values and that the accuracy of the results increases rapidly as the degree of the polynomial increases. The final goal of this and subsequent articles is to study energy levels in PPP models of planar conjugated hydrocarbons. In this article, we test an interpolant technique on the case of the one-dimensional Hubbard model, where an exact solution can be obtained by solving a system of nonlinear equations. In the case of the Hubbard model, the correlation effects are overestimated. Therefore, if the technique works for the Hubbard model, it is reasonable to assume that the technique would work even better for the PPP model.

show abstract

Density of states of alternant cyclic polyenes (CH) _N by a direct Lanczos method

Karlsson¹,

Bendazzoli²,

Goscinski³

et al. 1997

Int J of Quantum Chemistry

View full text Add to dashboard Cite

A direct full configuration interaction approach, previously used for studying individual low‐lying eigenvalues, is combined with iterative Lanczos calculations, in order to obtain global properties of large Hermitean Hamiltonian matrices. To this effect systematic generation of random start vectors is used to compute statistical approximations to the density of states (DOS). Applications for cyclic polyenes in order to illustrate the viability of the scheme modeled by correlated, high‐binding Pariser‐Parr‐Pople (PPP) Hamiltonians of increasing complexity are presented. The degree of correlation in the solutions is controlled by the parameter β. Convergence properties of the DOS for N = 10 and N = 14 are studied varying the extent of correlation. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 719–728, 1997

show abstract

Interpolant polynomial technique applied to the PPP model. I. Asymptotics for excited states of cyclic polyenes in the finite cyclic Hubbard model

Cited by 7 publications

References 36 publications

The size-extensivity of correlation energy estimators based on effective characteristic polynomials

The size-extensivity of correlation energy estimators based on effective characteristic polynomials

Interpolant polynomial technique applied to the PPP model. II. Testing the interpolant technique on the Hubbard model

Density of states of alternant cyclic polyenes (CH) _N by a direct Lanczos method

Contact Info

Product

Resources

About

Interpolant polynomial technique applied to the PPP model. I. Asymptotics for excited states of cyclic polyenes in the finite cyclic Hubbard model

Cited by 7 publications

References 36 publications

The size-extensivity of correlation energy estimators based on effective characteristic polynomials

The size-extensivity of correlation energy estimators based on effective characteristic polynomials

Interpolant polynomial technique applied to the PPP model. II. Testing the interpolant technique on the Hubbard model

Density of states of alternant cyclic polyenes (CH) N by a direct Lanczos method

Contact Info

Product

Resources

About

Density of states of alternant cyclic polyenes (CH) _N by a direct Lanczos method