Detection of embedded dynamics in the Györgyi-Field model.

The main aim of this paper is to detect embedded dynamics of the Györgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, an analysis was performed in order to identify different dynamics regimes.

Pipek-Mezey localization of occupied and virtual orbitals.

Recent advances in orbital localization algorithms are used to minimize the Pipek-Mezey localization function for both occupied and virtual Hartree-Fock orbitals. Virtual Pipek-Mezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the Pipek-Mezey (PM) localization function is implemented for both the Mulliken and a Löwdin population analysis.

Local Hartree-Fock orbitals using a three-level optimization strategy for the energy.

Using the three-level energy optimization procedure combined with a refined version of the least-change strategy for the orbitals--where an explicit localization is performed at the valence basis level--it is shown how to more efficiently determine a set of local Hartree-Fock orbitals. Further, a core-valence separation of the least-change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented.

Orbital localization using fourth central moment minimization.

We present a new orbital localization function based on the sum of the fourth central moments of the orbitals. To improve the locality, we impose a power on the fourth central moment to act as a penalty on the least local orbitals. With power two, the occupied and virtual Hartree-Fock orbitals exhibit a more rapid tail decay than orbitals from other localization schemes, making them suitable for use in local correlation methods.

MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme.

Divide-Expand-Consolidate (DEC) is a local correlation method where the inherent locality of the electron correlation problem is used to express the correlated calculation on a large molecular system in terms of small independent fragment calculations employing small subsets of local HF orbitals. A crucial feature of the DEC scheme is that the sizes of the local orbital spaces are determined in a black box manner during the calculation. In this way it is ensured that the correlation energy has been determined to a predefined precision compared to a conventional calculation.

Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme.

We demonstrate that the divide-expand-consolidate (DEC) scheme--which has previously been used to determine the second-order Møller-Plesset (MP2) correlation energy--can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local Hartree-Fock orbitals. All manipulations of four-index quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas two-index quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a black-box manner to ensure that the error in the DEC-MP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT).

Trust Region Minimization of Orbital Localization Functions.

The trust region method has been applied to the minimization of localization functions, and it is shown that both local occupied and local virtual Hartree-Fock (HF) orbitals can be obtained. Because step sizes are size extensive in the trust region method, large steps may be required when the method is applied to large molecular systems. For an exponential parametrization of the localization function only small steps are allowed, and the standard trust radius update therefore has been replaced by a scheme where the direction of the step is determined using a conservative estimate of the trust radius and the length of the step is determined from a line search along the obtained direction.

The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory.

Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals.

A Locality Analysis of the Divide-Expand-Consolidate Coupled Cluster Amplitude Equations.

We present a thorough locality analysis of the divide-expand-consolidate amplitude equations for second-order Møller-Plesset perturbation theory and the coupled cluster singles doubles (CCSD) model, which demonstrates that the amplitude equations are local when expressed in terms of a set of local occupied and local unoccupied Hartree-Fock orbitals, such as the least-change molecular basis. The locality analysis thus shows that a CC calculation on a large molecular system may be carried out in terms of CC calculations on small orbital fragments of the total molecular system, where the sizes of the orbital fragment spaces are determined in a black box manner to ensure that the CC correlation energy is calculated to a preset energy threshold. A practical implementation of the locality analysis is described, and numerical results are presented, which demonstrate that both the orbital fragment sizes and the relative energy error compared to a full CC calculation are independent of the molecular system size.

Local orbitals by minimizing powers of the orbital variance.

It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered.

Linear scaling coupled cluster method with correlation energy based error control.

Coupled cluster calculations can be carried out for large molecular systems via a set of calculations that use small orbital fragments of the full molecular orbital space. The error in the correlation energy of the full molecular system is controlled by the precision in the small fragment calculations. The determination of the orbital spaces for the small orbital fragments is black box in the sense that it does not depend on any user-provided molecular fragmentation, rather orbital spaces are carefully selected and extended during the calculation to give fragment energies of a specified precision.

The CO-Ne van der Waals complex: ab initio intermolecular potential energy, interaction induced electric dipole moment and polarizability surfaces, and second virial coefficients.

The intermolecular potential energy, interaction induced electric dipole moment and polarizability surfaces of the CO-Ne van der Waals complex are calculated using coupled cluster methods and the d-aug-cc-pVTZ basis set extended with a set of 3s3p2d1f1g midbond functions placed in the middle of the van der Waals bond. After fitting the interaction properties to appropriate analytical functions the surfaces are further used in semiclassical calculations of the pressure, the dielectric and the refractivity second virial coefficients of the system. The interaction potential energy surface has a single minimum (-49.

A stepwise atomic, valence-molecular, and full-molecular optimisation of the Hartree-Fock/Kohn-Sham energy.

A hierarchical optimisation strategy has been introduced for minimising the Hartree-Fock/Kohn-Sham energy, consisting of three levels (3L): an atom-in-a-molecule optimisation, a valence-basis molecular optimisation, and a full-basis molecular optimisation. The density matrix formed at one level is used as a starting density matrix at the next level with no loss of information. To ensure a fast and reliable convergence to a minimum, the augmented Roothaan-Hall (ARH) algorithm is used in both the valence-basis and full-basis molecular optimisations.

Maximum locality in occupied and virtual orbital spaces using a least-change strategy.

A new strategy is introduced for obtaining localized orthonormal Hartree-Fock (HF) orbitals where the underlying principle is to minimize the size of the transformation matrix from the atomic orbital basis to the HF optimized orbital basis. The new strategy gives both localized occupied and localized virtual orbital spaces. The locality of the occupied orbital space is similar to one obtained using standard localization schemes.

Robust and Reliable Multilevel Minimization of the Kohn-Sham Energy.

Kohn-Sham density-functional calculations are used in many branches of science to obtain information about the electronic structure of molecular systems and materials. Conventional algorithms for minimization of the Kohn-Sham energy have certain deficiencies, however, that may cause divergence or, worse, convergence to unphysical saddle points. We here present a three-level hierarchical minimization strategy which is both more efficient and robust than the conventional algorithms and which does not suffer from the flaws of these algorithms.

The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices.

We present a novel method for the optimization of Hartree-Fock and Kohn-Sham energies that does not suffer from the flaws of the conventionally used two-step Roothaan-Hall (RH) with direct inversion in iterative subspace (DIIS) acceleration scheme, improving the reliability of the optimization while reducing its cost. The key to its success is the replacement of the two separate steps of each RH/DIIS iteration by a single concerted step that fully exploits the Hessian information available from the previous iterations. It is a trust-region based method and therefore by design converges to an energy minimum.

Variational and robust density fitting of four-center two-electron integrals in local metrics.

Density fitting is an important method for speeding up quantum-chemical calculations. Linear-scaling developments in Hartree-Fock and density-functional theories have highlighted the need for linear-scaling density-fitting schemes. In this paper, we present a robust variational density-fitting scheme that allows for solving the fitting equations in local metrics instead of the traditional Coulomb metric, as required for linear scaling.

A ground-state-directed optimization scheme for the Kohn-Sham energy.

Kohn-Sham density-functional calculations are used in many branches of science to obtain information about the electronic structure of molecular systems and materials. Unfortunately, the traditional method for optimizing the Kohn-Sham energy suffers from fundamental problems that may lead to divergence or, even worse, convergence to an energy saddle point rather than to the ground-state minimum--in particular, for the larger and more complicated electronic systems that are often studied by Kohn-Sham theory nowadays. We here present a novel method for Kohn-Sham energy minimization that does not suffer from the flaws of the conventional approach, combining reliability and efficiency with linear complexity.

Strong Two-Photon Circular Dichroism in Helicenes: A Theoretical Investigation.

Using a recently derived origin-invariant quadratic response approach combined with time-dependent density functional theory, four representative helicenes are shown to present a very strong two-photon circular dichroism (TPCD) response, which makes them candidates for the first experimental observation of a TPCD effect. The large response is attributed to the unique combination of chirality and electron delocalization. Comparison with electronic circular dichroism and two-photon absorption (TPA) shows that the three effects exhibit complementary features for unravelling the molecular structures.

Gauge-origin-independent coupled cluster singles and doubles calculation of magnetic circular dichroism of azabenzenes and phosphabenzene using London orbitals.

A computational study of the Faraday B term of magnetic circular dichroism at the coupled cluster singles and doubles level is presented for pyridine, pyrazine, pyrimidine, and phosphabenzene. Gauge-origin independence is obtained by expressing the B term as a total derivative of the one-photon dipole transition strength and using London orbitals. The high quality of the coupled cluster singles and doubles (CCSD) B terms makes these useful for the assignment of experimental spectra.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution).

Electronic structure of copper phthalocyanine: an experimental and theoretical study of occupied and unoccupied levels.

An experimental and theoretical study of the electronic structure of copper phthalocyanine (CuPc) molecule is presented. We performed x-ray photoemission spectroscopy (XPS) and photoabsorption [x-ray absorption near-edge structure (XANES)] gas phase experiments and we compared the results with self-consistent field, density functional theory (DFT), and static-exchange theoretical calculations. In addition, ultraviolet photoelectron spectra (UPS) allowed disentangling several outer molecular orbitals.

Linear-scaling symmetric square-root decomposition of the overlap matrix.

We present a robust linear-scaling algorithm to compute the symmetric square-root or Lowdin decomposition of the atomic-orbital overlap matrix. The method is based on Newton-Schulz iterations with a new approach to starting matrices. Calculations on 12 chemically and structurally diverse molecules demonstrate the efficiency and reliability of the method.

Linear-scaling implementation of molecular electronic self-consistent field theory.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used.