Ab initio calculations with small ellipsoidal gaussian basis sets. I

The use of ellipsoidal gaussian type orbitals in ab initio calculations on molecular systems of small and intermediate size is demonstrated, in both non-linear and SCF MO schemes. The method is an extension of Frost's Floating Gaussian Orbital Method. Results for conformational properties (barriers to internal rotation in ethane and 1,3-butadiene) are better than those obtained with basis sets containing only spherical gaussians. The usefulness of very small basis sets is discussed.     

Benchmark calculations using the individually selecting configuration interaction method

Further progress is reported on the implementation of the configuration-selecting multi-reference configuration interaction method for massively parallel architectures with distributed memory which allows calculations with Hilbert spaces in excess of 10¹¹ configurations, 2 × 10⁷ of which can now be included in the variational subspace. This code makes it possible to elucidate the importance of the correlated treatment of triple and quadruple excitations into the (3s3p) shell of the oxygen molecule, to account quantitatively for its electron affinity. Also included are extensive calculations to elucidate the reaction pathways of members of the enediyne family.     

Transverse interaction in configuration mixing calculations

An expression of the general matrix element of the transverse interaction appropriate for the Dirac-Fock-Slater formalism is obtained straightforwardly by using the vector-spherical-harmonics expansion technique.     

Benchmark full configuration interaction calculations on N2

Summary Valence Full Configuration Interaction (FCI) calculations are reported for the N₂ molecule with a 4s3p triple-zeta basis set at different distances. The size of the FCI space is more than 225 000 000 symmetry-adapted Slater determinants. The computation requires about 1400 s of c.p.u. time per iteration on a CRAY C90, and is one of the largest FCI calculations ever converged. Our results, as is in general the case for FCI computations, can be used to test the performance of approximated methods used to study electronic correlation in molecules. The authors of this paper have agreed to not receive the proofs for correction.     

Center-of-mass problem in truncated configuration interaction and coupled-cluster calculations

The problem of center-of-mass (CM) contaminations in ab initio nuclear structure calculations using configuration interaction (CI) and coupled-cluster (CC) approaches is analyzed. A rigorous and quantitative scheme for diagnosing the CM contamination of intrinsic observables is proposed and applied to ground-state calculations for ⁴He and ¹⁶O. The CI and CC calculations for ¹⁶O based on model spaces defined via a truncation of the single-particle basis lead to sizable CM contaminations, while the importance-truncated no-core shell model based on the N_maxΩ space is virtually free of CM contaminations.     

Many-body calculations of molecular electric polarizabilities in asymptotically complete basis sets

The static dipole polarizabilities of Ne, CO, N₂, F₂, HF, H₂O, HCN, and C₂H₂ (acetylene) have been determined close to the Full-CI limit along with an asymptotically complete basis set (CBS), according to the principles of a Focal Point Analysis. For this purpose the results of Finite Field calculations up to the level of Coupled Cluster theory including Single, Double, Triple, Quadruple and perturbative Pentuple excitations [CCSDTQ(P)] were used, in conjunction with suited extrapolations of energies obtained using augmented and doubly-augmented Dunning's correlation consistent polarized valence basis sets of improving quality. The polarizability characteristics of C₂H₄ (ethylene) and C₂H₆ (ethane) have been determined on the same grounds at the CCSDTQ level in the CBS limit. Comparison is made with results obtained using lower levels in electronic correlation, or taking into account the relaxation of the molecular structure due to an adiabatic polarization process. Vibrational corrections to electronic polarizabilities have been empirically estimated according to Born–Oppenheimer Molecular Dynamical simulations employing Density Functional Theory. Confrontation with experiment ultimately indicates relative accuracies of the order of 1 to 2%.     

Applicability of medium-size basis sets in calculations of molecular dynamic polarisabilities

Static and dynamic average polarisabilities and polarisability anisotropies of seven linear non-polar and polar molecules are calculated within the CCS, CC2, and CC3 approximations using a range of medium-sized basis sets: the polarised LPol-n (n = ds, dl, fs, fl), the aug-pc-n (n = 1, 2), the def2-SVPD, and -TZVPD basis sets. Reference values are obtained using a hierarchy of Dunning's (d-)aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The results are discussed together with the available CCSD values in terms of basis set and correlation method errors, and their ratio. Detailed analysis shows that already the def2-SVPD basis set can be used in CCS polarisability calculations. When affordable, the slightly larger aug-pc-1 basis set is recommended, as it leads to significant reduction of basis set error. The def2-TZVPD, LPol-ds, and aug-pc-2 basis sets are optimal choice within the CC2 approximation, with the latter allowing to approach the CC2 basis set limit. The LPol-ds, -dl, and def2-TZVPD sets outperform the aug-cc-pVTZ set in average polarisability CCSD calculations, with the def2-TZVPD being competitive to other reduced-size sets also in determination of polarisability anisotropy. The aug-pc-2 basis is a particularly attractive choice for CCSD, giving the accuracy of aug-cc-pVQZ at a significantly reduced computational cost. The polarisability anisotropy is shown to be more computationally demanding than the average polarisability, in particular with respect to the accuracy of the correlation method and an accurate evaluation of this property requires at least the CCSD model.     

Fast convergence in the configuration interaction method

A method is given for finding the value of the internal parameters of each configuration, whose linear combination gives fast convergence. A sample calculation for a three-configuration function of the ground state of the hydrogen molecule is described, which gives 4·555 eV for the binding energy.     

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite c chi N . With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical ( S _cp phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd ( O⁷⁰ morphology, showing that conformational asymmetry has a significant effect on its stability.     

Symplectic shell-model calculations for 20Ne with horizontal configuration mixing

The symplectie shell model, which incorporates vertical $\text{(2n}\text{h}\text{?}\text{ω; n = 1, 2…)}$ major shell configuration mixing as dictated by a quadrupole interaction, is augmented with horizontal (0?ω) mixing induced by realistic single-particle energies and a monopole-pairing interaction. The excitation spectrum and B(E2) rates of the ²⁰Ne ground band are accurately reproduced without the use of an effective charge. The degree of horizontal and vertical mixing is found to be on the order of 20% in the ground state and up to as much as 50% for the 8⁺ level.     

Brueckner calculations in harmonic-oscillator basis I. The method

The problem of solving the reaction matrix equation in harmonic-oscillator basis is studied. A general approximation of the Pauli operator, diagonal with respect to the centre-of-mass quantum numbers, is derived and method for solving the corresponding Bethe-Goldstone equation is proposed and compared with other methods. The accuracy of the approximation is estimated and found to be satisfactory, especially if the method is applied to the⁴He nucleus, in which case the Pauli corrections to the most importantt-matrix elements vanish.     

Analytic variationally optimized internally orthogonalized modified Laguerre orbitals in accurate atomic configuration interaction calculation

An analytic configuration interaction method based on variationally optimized internally orthogonalized modified Laguerre orbitals is presented. We have developed the corresponding computer code. For application, we study the 1s2s $^{1}S$ isoelectronic sequence from helium to neon, and compare with other methods. By taking into account the Eckart upper-bound theorem, we obtained more accurate and more intuitively understandable results than Hartree--Fock and multi-configuration Hartree--Fock reported results.     

"Lagrange functions": a family of powerful basis sets for real-space order-N electronic structure calculations

Plane waves have unparalleled simplicity and systematic convergence by a single monotonic parameter, the energy cutoff, but they are limited to speriodic systems and require Fourier transforms that scale as N(2)logN, where N is the number of atoms. Real-space methods for order-N scaling are computationally complex and convergence depends on several variables. Here we introduce and demonstrate "Lagrange functions" as a family of analytical, complete, and orthonormal basis sets that are suitable for efficient, accurate, real-space, order-N electronic structure calculations. Convergence is controlled by a single monotonic parameter, the dimension of the basis set, and computational complexity is lower than that of plane waves.     

Faddeev calculations in configuration space with Cartesian coordinates

The Faddeev-Noyes equations are solved in their natural Cartesian Jacobi coordinates for scattering below break-up threshold and for bound states. This approach is particularly well adapted to deal with strongly varying interactions. The method is proved to be successful in the three-nucleon system. First results concerning the⁴He trimer in configuration space are presented and further generalizations are suggested.Deceased