Alexander A. Auer

Combined coupled-cluster and many-body perturbation theories.

Various approximations combining coupled-cluster (CC) and many-body perturbation theories have been derived and implemented into the parallel execution programs that take into account the spin, spatial (real Abelian), and permutation symmetries and that are applicable to closed- and open-shell molecules. The implemented models range from the CCSD(T), CCSD[T], CCSD(2)(T), CCSD(2)(TQ), and CCSDT(2)(Q) methods to the completely renormalized (CR) CCSD(T) and CCSD[T] approaches, where CCSD (CCSDT) stands for the CC method with connected single and double (single, double, and triple) cluster operators, and subscripted or parenthesized 2, T, and Q indicate the perturbation order or the excitation ranks of the cluster operators included in the corrections. The derivation and computer implementation have been automated by the algebraic and symbolic manipulation program TENSOR CONTRACTION ENGINE (TCE). The TCE-synthesized subroutines generate the tensors with the highest excitation rank in a blockwise manner so that they need not be stored in their entirety, while enabling the efficient reuse of other precalculated intermediate tensors defined by prioritizing the memory optimization as well as operation minimization. Consequently, the overall storage requirements for the corrections due to connected triple and quadruple cluster operators scale as O(n(4)) and O(n(6)), respectively (n being a measure of the system size). For systems with modest multireference character of their wave functions, we found that the order of accuracy is CCSD<CR-CCSD(T) approximately CCSD(2)(T) approximately CCSD(T)<CCSDT approximately CCSD(2)(TQ)<CCSDT(2)(Q), whereas CR-CCSD(T) is more effective in cases of larger quasidegeneracy. The operation costs of the TCE-generated CCSD(2)(TQ) and CCSDT(2)(Q) codes scale as rather steep O(n(9)), while the TCE-generated CCSD(T), CCSD(2)(T), and CR-CCSD(T) codes are near operation minimum [a noniterative O(n(7))]. The perturbative correction part of the CCSD(T)/cc-pVDZ calculations for azulene exhibited a 45-fold speedup upon a 64-fold increase in the number of processors from 8 to 512.

Synthesis of High-Performance Parallel Programs for a Class of ab Initio Quantum Chemistry Models

This paper provides an overview of a program synthesis system for a class of quantum chemistry computations. These computations are expressible as a set of tensor contractions and arise in electronic structure modeling. The input to the system is a a high-level specification of the computation, from which the system can synthesize high-performance parallel code tailored to the characteristics of the target architecture. Several components of the synthesis system are described, focusing on performance optimization issues that they address.

Automatic code generation for many-body electronic structure methods: the tensor contraction engine‡‡

As both electronic structure methods and the computers on which they are run become increasingly complex, the task of producing robust, reliable, high-performance implementations of methods at a rapid pace becomes increasingly daunting. In this paper we present an overview of the Tensor Contraction Engine (TCE), a unique effort to address issues of both productivity and performance through automatic code generation. The TCE is designed to take equations for many-body methods in a convenient high-level form and acts like an optimizing compiler, producing an implementation tuned to the target computer system and even to the specific chemical problem of interest. We provide examples to illustrate the TCE approach, including the ability to target different parallel programming models, and the effects of particular optimizations.

Optimization of augmentation functions for correlated calculations of spin-spin coupling constants and related properties

A new hierarchy of augmented basis sets optimized for the calculation of molecular properties such as indirect spin-spin coupling constants is presented. Based on the Dunning hierarchy of cc-pVXZ (X = D, T, Q, and 5) basis sets augmentation functions with tight exponents have been optimized for coupled-cluster calculations of indirect spin-spin coupling constants. The optimal exponents for these tight functions have been obtained by optimizing the sum of the absolute values of all contributions to the coupling constant. On the basis of a series of test cases (CO, HF, N(2), F(2), H(2)O, NH(3), and CH(4)) we propose a set of tight s, p, and d functions to be added to the uncontracted Dunning basis sets, and, subsequently, to recontract. The resulting ccJ-pVXZ (X = D, T, Q, and 5) basis sets demonstrate excellent cost efficiency in benchmark calculations. These new basis sets should generally be applicable for the calculation of spin-spin coupling constants and other properties that have a strong dependence on powers of 1r or even contain a delta distribution for correlated ab initio methods.

Synthesis and mesomorphic properties of new V-shaped shape-persistent nematogens containing a thiazole or a thiadiazole bending unit

Two series of new V-shaped molecules, containing a central thiazole or thiadiazole bending unit have been synthesised. The design is based on shape-persistent phenylene ethynylene scaffolds that were attached stepwise with high regioselectivity to a desymmetrised iodo and bromo functionalised bent core with an apex angle of about 160°. Molecular engineering results in materials that exhibit exclusively nematic liquid crystal phases (monotropic or enantiotropic). The phase behaviour was investigated by means of polarised optical microscopy (POM), differential scanning calorimetry (DSC) and X-ray diffraction.

Full configuration-interaction and coupled-cluster calculations of the indirect spin–spin coupling constant of BH

Abstract Full configuration-interaction calculations of the indirect spin–spin coupling constant of the BH molecule have been carried out in order to investigate the performance of various coupled-cluster (CC) methods in the treatment of electron-correlation effects, while the corresponding basis set convergence is analyzed in CC singles and doubles calculations. Assuming additivity of correlation and basis set effects, a theoretical estimate of 50.67 Hz is obtained for the 11 B 1 H spin–spin coupling constant.

Quantitative prediction of gas-phase N15 and P31 nuclear magnetic shielding constants

High-level ab initio benchmark calculations of the (15)N and (31)P NMR chemical shielding constants for a representative set of molecules are presented. The computations have been carried out at the Hartree-Fock self-consistent field (HF-SCF), density functional theory (DFT) (B-P86 and B3-LYP), second-order Moller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), and CCSD augmented by a perturbative treatment of triple excitations [CCSD(T)] level of theory using basis sets of triple zeta quality or better. The influence of the geometry, the treatment of electron correlation, as well as basis set and zero-point vibrational effects on the shielding constants are discussed and the results are compared to gas-phase experimental shifts. As for the first time a study using high-level post-HF methods is carried out for a second-row element, we also propose a family of basis sets suitable for the computation of (31)P shielding constants. The mean deviations observed for (15)N and (31)P are 0.9 [CCSD(T)/13s9p4d3f] and -3.3 ppm [CCSD(T)/15s12p4d3f2g], respectively, when corrected for zero-point vibrational effects. Results obtained at the DFT level of theory are of comparable accuracy to MP2 for (15)N and of comparable accuracy to HF-SCF for (31)P. However, they are not improved by inclusion of zero-point vibrational effects. The PN molecule is an especially interesting case with exceptionally large electron correlation effects on shielding constants beyond MP2 which, therefore, represents an excellent example for further benchmark studies.

Accurate molecular geometries of the protonated water dimer

The n equilibrium geometry of the protonated water dimer, H5O2+, was studied using Moller–Plesset perturbation theory n and coupled-cluster theory. Constrained geometry optimizations were carried out for the C2 and Cs symmetric n structures within the counterpoise framework and near the limit of a complete basis set. In the constrained n optimization, the degrees of freedom of the complex are reduced to an intrafragmental distortion and an interfragmental n coordinate, making the procedure tractable for large basis sets and explicitly correlated linear n r12 methods. The energy of the stationary point n of C2 symmetry n was found to be 1.2 kJ n mol−1 below the energy of the Cs structure.

Basis-Set Completeness Profiles in Two Dimensions

A two‐electron basis‐set completeness profile is proposed by analogy with the one‐electron profile introduced by D. P. Chong (Can J Chem 1995, 73, 79). It is defined as Y(α,β)=∑m∑n〈Gα(1)Gβ(2)∣(1/r12)∣Ψm(1)Ψn(2)〉〈Ψm(1)Ψn(2)∣r12∣Gα(1)Gβ(2)〉 and motivated by the expression for the basis‐set truncation correction that occurs in the framework of explicitly correlated methods (Gα is a scanning Gaussian‐type orbital of exponent α and {Ψm} is the orthonormalized one‐electron basis under study). The two‐electron basis‐set profiles provide a visual assessment of the suitability of basis sets to describe electron‐correlation effects. Furthermore, they provide the opportunity to assess the quality of the basis set as a whole—not only of the individual angular momentum subspaces, as is the case for the one‐electron basis‐set profiles. The two‐electron completeness profiles of the cc‐pVXZ (X=D, T, Q), aug‐cc‐pVTZ, cc‐pCVTZ, and SVP‐auxiliary basis sets for the carbon atom are presented as illustrative examples.

Optimized Basis Sets for Calculating Spin‐Spin Coupling Constants

We propose a series of basis sets for systematically reducing the basis set error for calculating nuclear spin‐spin coupling constants. At the density functional level, the basis sets are derived from the previously proposed polarization consistent basis sets by augmentation with tight s‐, p‐, d‐ and f‐functions. The optimum exponents for the tight functions can be derived by a variational procedure, and the optimum exponents are sufficiently regular that a standard set of tight functions can be derived. Preliminary results at the coupled cluster level suggest that a similar sequence of optimum basis sets can be derived from the correlation consistent basis sets by augmentation with tight functions.