Electronic Fock spaces: Phase prefactors and hidden symmetry

Efficient technique of manipulation with phase prefactors in electronic Fock spaces is developed. Its power is demonstrated on example of both relatively simple classic configuration interaction matrix element evaluation and essentially more complicated coupled cluster case. Interpretation of coupled cluster theory in terms of a certain commutative algebra is given.Comment: LaTex, 31 pages, submitted to Int. J. Quantum Che

Multiple solutions of coupled-cluster equations for PPP model of [10]annulene

Multiple (real) solutions of the CC equations (corresponding to the CCD, ACP and ACPQ methods) are studied for the PPP model of [10]annulene, C_{10}H_{10}. The long-range electrostatic interactions are represented either by the Mataga--Nishimoto potential, or Pople's R^{-1} potential. The multiple solutions are obtained in a quasi-random manner, by generating a pool of starting amplitudes and applying a standard CC iterative procedure combined with Pulay's DIIS method. Several unexpected features of these solutions are uncovered, including the switching between two CCD solutions when moving between the weakly and strongly correlated regime of the PPP model with Pople's potential.Comment: 5 pages, 4 figures, RevTeX

Valence bond approach and Verma bases

The unitary group approach (UGA) to the many-fermion problem is based on the Gel’fand–Tsetlin (G–T) representation theory of the unitary or general linear groups. It exploits the group chain U(n)⊃U(n−1)⊃⋯⊃U(2)⊃U(1) and the associated G–T triangular tableau labeling basis vectors of the relevant irreducible representations (irreps). The general G–T formalism can be drastically simplified in the many-electron case enabling an efficient exploitation in either configuration interaction (CI) or coupled cluster approaches to the molecular electronic structure. However, while the reliance on the G–T chain provides an excellent general formalism from the mathematical point of view, it has no specific physical significance and dictates a fixed Yamanouchi–Kotani coupling scheme, which in turn leads to a rather arbitrary linear combination of distinct components of the same multiplet with a given orbital occupancy. While this is of a minor importance in molecular orbital based CI approaches, it is very inconvenient when relying on the valence bond (VB) scheme, since the G–T states do not correspond to canonical Rumer structures. While this shortcoming can be avoided by relying on the Clifford algebra UGA formalism, which enables an exploitation of a more or less arbitrary coupling scheme, it is worthwhile to point out the suitability of the so-called Verma basis sets for the VB-type approaches

Calculation of the Positions of the α- and β-bands in the Electronic Spectra of Benzenoid Hydrocarbons Using the Method of Limited Configuration Interaction

The positions of the α- and β-bands in the electronic absorption spectra of twenty aromatic benzenoid hydrocarbons were calculated by the semiempirical method of limited configuration interaction in the π-electron approximation using the Huckel molecular orbitals. The agreement of the experimental and calculated values is good for the β-band whereas a systematic deviation is observed for the α-band. This deviation cannot be removed by extending the configuration interaction of the monoexcited states constructed from the molecular orbitals considered. However, the consideration of electronic repulsion enables us to explain the character of the dependences of the experimental excitation energies on the excitation energies obtained by the simple Huckel method of molecular orbitals. Using a suitable choice of semiempirical parameters different for various electronic transitions (showing no large mutual differences) yields semiempirical interpolation formulas for the; p-, α-, and β-bands which give very good agreement with the corresponding experimental excitation energies for the compounds studied

Coupled-Cluster Approach to Electron Correlations in the Two-Dimensional Hubbard Model

We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations actually used in ab-initio band calculations. The double excitation version of the CCM, implemented using the approximate coupled pair (ACP) method, account for most of the correlation energies of the 2D Hubbard model in the weak ($U/t \simeq 1$) and the intermediate $U/t$ regions ($U/t \simeq 4$). The error is always less than 1% there. The ACP approximation gets less accurate for large $U/t$ ($U/t \simeq 8$) and/or near half-filling. Further incorporation of electron correlation effects is necessary in this region. The accuracy does not depend on the system size and the gap between the lowest unoccupied level and the highest occupied level due to the finite size effect. Hence, the CCM may be favorably applied to ab-initio band calculations on metals as well as semiconductors and insulators.Comment: RevTeX3.0, 4 pages, 4 figure

Convergence improvement for coupled cluster calculations

Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also includes a relatively small number of off-diagonal coefficients, selected according to the excitation amplitudes undergoing the largest change in the coupled cluster iteration. A test case shows that the new IPM (inversion of partial matrix) method gives much better convergence than the straightforward Jacobi-type scheme or such well-known convergence aids as the reduced linear equations or direct inversion in iterative subspace methods.Comment: 7 pages, IOPP styl

On the transferability of three water models developed by adaptive force matching

Water is perhaps the most simulated liquid. Recently three water models have been developed following the adaptive force matching (AFM) method that provides excellent predictions of water properties with only electronic structure information as a reference. Compared to many other electronic structure based force fields that rely on fairly sophisticated energy expressions, the AFM water models use point-charge based energy expressions that are supported by most popular molecular dynamics packages. An outstanding question regarding simple force fields is whether such force fields provide reasonable transferability outside of their conditions of parameterization. A survey of three AFM water models, B3LYPD-4F, BLYPSP-4F, and WAIL are provided for simulations under conditions ranging from the melting point up to the critical point. By including ice-Ih configurations in the training set, the WAIL potential predicts the melting temperate, TM, of ice-Ih correctly. Without training for ice, BLYPSP-4F underestimates TM by about 15 K. Interestingly, the B3LYPD-4F model gives a TM 14 K too high. The overestimation of TM by B3LYPD-4F mostly likely reflects a deficiency of the B3LYP reference. The BLYPSP-4F model gives the best estimate of the boiling temperature TB and is arguably the best potential for simulating water in the temperature range from TM to TB. None of the three AFM potentials provides a good description of the critical point. Although the B3LYPD-4F model gives the correct critical temperature TC and critical density, there are good reasons to believe the agreement is reached fortuitously. Links to Gromacs input files for the three water models are provided at the end of the paper.Comment: 25 pages, 2 figure

Coupled cluster calculations of ground and excited states of nuclei

The standard and renormalized coupled cluster methods with singles, doubles, and noniterative triples and their generalizations to excited states, based on the equation of motion coupled cluster approach, are applied to the He-4 and O-16 nuclei. A comparison of coupled cluster results with the results of the exact diagonalization of the Hamiltonian in the same model space shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei. The bulk of the correlation effects is obtained at the coupled cluster singles and doubles level. Triples, treated noniteratively, provide the virtually exact description