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

ZZPolyCalc: An open-source code with fragment caching for determination of Zhang-Zhang polynomials of carbon nanostructures

Determination of topological invariants of graphene flakes, nanotubes, and fullerenes constitutes a challenging task due to its time-intensive nature and exponential scaling. The invariants can be organized in a form of a combinatorial polynomial commonly known as the Zhang-Zhang (ZZ) polynomial or the Clar covering polynomial. We report here a computer program, ZZPolyCalc, specifically designed to compute ZZ polynomials of large carbon nanostructures. The curse of exponential scaling is avoided for a broad class of nanostructures by employing a sophisticated bookkeeping algorithm, in which each fragment appearing in the recursive decomposition is stored in the cache repository of molecular fragments indexed by a hash of the corresponding adjacency matrix. Although exponential scaling persists for the remaining nanostructures, the computational time is reduced by a few orders of magnitude owing to efficient use of hash-based fragment bookkeeping. The provided benchmark timings show that ZZPolyCalc allows for treating much larger carbon nanostructures than previously envisioned.Comment: 8 pages, 7 figures; submitted to "Comput. Phys. Commu

Second-order electronic correlation effects in a one-dimensional metal

The Pariser-Parr-Pople (PPP) model of a single-band one-dimensional (1D) metal is studied at the Hartree-Fock level, and by using the second-order perturbation theory of the electronic correlation. The PPP model provides an extension of the Hubbard model by properly accounting for the long-range character of the electron-electron repulsion. Both finite and infinite version of the 1D-metal model are considered within the PPP and Hubbard approximations. Calculated are the second-order electronic-correlation corrections to the total energy, and to the electronic-energy bands. Our results for the PPP model of 1D metal show qualitative similarity to the coupled-cluster results for the 3D electron-gas model. The picture of the 1D-metal model that emerges from the present study provides a support for the hypothesis that the normal metallic state of the 1D metal is different from the ground state.Comment: 21 pages, 16 figures; v2: small correction in title, added 3 references, extended and reformulated a few paragraphs (detailed information at the end of .tex file); added color to figure

Ab initio potential energy surfaces for NH-NH with analytical long range

We present four-dimensional ab initio potential energy surfaces for the three spin states of the NH-NH complex. The potentials are partially based on the work of Dhont et al. [J. Chem. Phys. 123, 184302 (2005)]. The surface for the quintet state is obtained at the RCCSD(T)/aug-cc-pVTZ level of theory and the energy diferences with the singlet and triplet states are calculated at the CASPTn/aug-cc-pVTZ (n = 2; 3) level of theory. The ab initio potentials are fitted to coupled spherical harmonics in the angular coordinates, and the long range is further expanded as a power series in 1/R. The RCCSD(T) potential is corrected for a size-consistency error prior to fitting. The long-range coeficients obtained from the fit are found to be in good agreement with perturbation theory calculations.Comment: submitted to JCP, supporting information available from authors on reques

Efficient Calculations of Dispersion Energies for Nanoscale Systems from Coupled Density Response Functions

Dispersion energies computed from coupled Kohn–Sham (CKS) dynamic density–density response functions are known to be highly accurate. At the same time, the computational algorithm is of only modest complexity compared to other accurate methods of dispersion energy calculation. We present a new implementation of this algorithm that removes several computational barriers present in current implementations and enables calculations of dispersion energies for systems with more than 200 atoms using more than 5000 basis functions. The improvements were mainly achieved by reorganizing the algorithm to minimize memory and disk usage. We present applications to two systems: the buckycatcher complex with fullerene and the vancomycin complex with a diacetyl-Lys-d-Ala-d-Ala bacterial wall precursor, both calculations performed with triple-ζ-quality basis sets. Our implementation makes it possible to use <i>ab initio</i> computed dispersion energies in popular “density functional theory plus dispersion” approaches

Extension of the Hartree−Fock Plus Dispersion Method by First-Order Correlation Effects

The Hartree−Fock plus dispersion (HFD) method for calculations of intermolecular interaction energies has been extended by the addition of the correlation part of the first-order interaction energy computed from Kohn−Sham determinants of monomers. This extension increases the computational requirements of the HFD approach only insignificantly and at the same time reduces the uncertainties of the interaction energies several times for most of the investigated systems. Thus, the proposed method becomes an attractive computational tool for investigating interactions of very large molecules at the HF-level costs