Josef Paldus

Bio: Josef Paldus is an academic researcher from University of Waterloo. The author has contributed to research in topics: Coupled cluster & Unitary group. The author has an hindex of 65, co-authored 300 publications receiving 14872 citations. Previous affiliations of Josef Paldus include University of Guelph & Czechoslovak Academy of Sciences.

Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the B H 3 Molecule

Abstract: The equations of the coupled-pair many-electron theory (CPMET) are extended to incorporate the effect of both unlinked and linked triexcited clusters. The minimal basis correlation energy of the B${\mathrm{H}}_{3}$ molecule in the ground state is calculated using the ordinary as well as extended CPMET in various degrees of approximation, and the relative importance of linked and unlinked triexcited clusters is studied. The results afford an unambiguous conclusion for closed-shell systems that, in contrast to the situation with tetraexcited states, unlinked triexcited clusters are negligible relative to the linked ones. It is shown that the extended CPMET reproduces the full configuration-interaction results to a very high degree of accuracy.

Stability Conditions for the Solutions of the Hartree—Fock Equations for Atomic and Molecular Systems. Application to the Pi‐Electron Model of Cyclic Polyenes

Abstract: The stability conditions which ensure that the Hartree—Fock determinant minimizes the energy expectation value are rederived using the language familiar in quantum chemistry. These stability conditions are then specified for the case of closed‐shell electronic systems which allow additional simplification of the conditions as well as a certain classification of the instabilities.Examples of the instabilities of different types are presented and the case of the so‐called singlet instabilities—most interesting from the physical point of view—is studied in detail for the pi‐electron model of cyclic polyenes.

Correlation problems in atomic and molecular systems III. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methodst

Abstract: The equations of the coupled-pair many-electron theory (CPMET) for the closed shell systems are rederived both in the spin-orbital and orbital forms without the use of second quantization, Wick's theorem or the technique of Feynman-like diagrams Only the Slater rules are used for the calculation of necessary matrix elements A comparison with earlier papers shows clearly the usefulness and conceptual simplicity of the mathematical methods of quantum field theory both in the derivation of the CPMET, in spin-orbital form, and in the process of excluding spin variables

Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems

Abstract: A formalism for an efficient generation of spin‐symmetry adapted configuration interaction (CI) matrices of the N‐electron atomic or molecular systems, described by nonrelativistic spin‐independent Hamiltonians, is presented. The Gelfand and Tsetlin canonical basis for the finite dimensional irreducible representations of the unitary groups is used as an N‐electron CI basis. A simplified Gelfand‐type pattern pertaining to the N‐electron problem is introduced, which considerably simplifies the canonical basis generation and, more importantly, the calculation of representation matrices of the (infinitesimal) generators of the pertinent unitary group in this basis. The calculation of the CI matrices for the above mentioned systems is then straightforward, since any particle number conserving operator may be written as a sum of n‐degree forms in the unitary group generators. The computation of CI matrices for various Hamiltonians as well as the problems of the space‐symmetry adaptation of the Gelfand‐Tsetlin basis and of limited CI calculations are briefly discussed.

Time-Independent Diagrammatic Approach to Perturbation Theory of Fermion Systems

Abstract: Publisher Summary The chapter discusses the time-independent diagrammatic approach to perturbation theory of fermion systems. The chapter explores the perturbation theory for a non-degenerate level. The formulas derived serves as a starting point for the subsequent consideration of the excitation and ionization energies. The advantages of the direct calculation of excitation energies, compared with the approach in which the total energies of the pertinent electronic states are calculated separately for each state and then the excitation energies are obtained by subtracting the appropriate state energies, are quite obvious. The Rayleigh-Schrodinger (RS) perturbation theory (PT) for the case of a non-degenerate level of some Hamiltonian operator is discussed. The chapter discusses that even the Rayleigh-Schrodinger perturbation expressions for the direct calculation of the excitation energies may be obtained in a rather simple way without the involvement of the Green function formalism. On the contrary, our simple approach using the ordinary perturbation theory for separate levels presents certain desirable features of the Green function formalism. The chapter explains the diagrammatic representation of Wick's theorem and resulting diagrams. General explicit formulas for the second- and third-order excitation energy contributions are given in the chapter.

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples

Abstract: The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.

An efficient internally contracted multiconfiguration–reference configuration interaction method

Abstract: A new internally contracted direct multiconfiguration–reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than any previous MRCI method. The configurations with two electrons in the external orbital space are generated by applying pair excitation operators to the reference wave function as a whole, while the singly external and internal configurations are standard uncontracted spin eigenfunctions. A new efficient and simple method for the calculation of the coupling coefficients is used, which is well suited for vector machines, and allows the recalculation of all coupling coefficients each time they are needed. The vector H⋅c is computed partly in a nonorthogonal configuration basis. In order to test the accuracy of the internally contracted wave functions, benchmark calculations have been performed for F−, H2O, NH2, CH2, CH3, OH, NO, N2, and O2 at various geometries. The deviations of the energies obtained with internally contracted and uncontracted MRCI wave functions are mostly smaller than 1 mH and typically 3–5 times smaller than the deviations between the uncontracted MRCI and the full CI. Dipole moments, electric dipole polarizabilities, and electronic dipole transition moments calculated with uncontracted and contracted MRCI wave functions also are found to be in close agreement. The efficiency of the method is demonstrated in large scale calculations for the CN, NH3, CO2, and Cr2 molecules. In these calculations up to 3088 reference configurations and up to 154 orbitals were employed. The biggest calculation is equivalent to an uncontracted MRCI with more than 78 million configurations.