Hartree-Fock orbitals for complex-scaled configuration interaction calculation of highly excited Feshbach resonances

We examine a complex-scaled configuration interaction [(CS)CI] for highly excited Feshbach resonances, where we study the 2s(2) resonance of helium as a test case. Sizable full-CI calculations are reduced by using a correctly defined minimum active space. We compare the convergence of the minimum active space for conventional Hartree-Fock (HF) orbitals obtained as solutions to Hermitian HF equations, to the convergence of minimum active space for complex orbitals obtained as solutions to complex-scaled HF equations. Ground-state optimized orbitals are compared to a simple modification of the HF method using the excited-state mean-field potential.     

The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations

We apply the multiconfiguration time-dependent Hartree-Fock method to electronic structure calculations and show that quantum chemical information can be obtained with this explicitly time-dependent approach. Different equations of motion are discussed, as well as the numerical cost. The two-electron integrals are calculated using a natural potential expansion, of which we describe the convergence behavior in detail.     

SPOCK.CI: a multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.     

A diagrammatic valence bond method for configuration interaction calculations in atoms and molecules

A diagrammatic valence bond method based on Rumer-Pauling rules for configuration interaction calculations is described. The advantages of this method are that it is simple and flexible and is expected to be computationally efficient as the basis functions can be coded as increasing integers. Evaluation of Hamiltonian matrix elements involves simple bit manipulations and binary searches. The basis, being represented pictorially, should also help in utilizing spatial symmetries for further block-diagonalizing the Hamiltonian matrix. The eigenfunctions of the Hamiltonian can also be used to compute matrix elements between different electronic states.     

Configuration space partitioning and matrix buildup scaling for the vibrational configuration interaction method

The accurate computation of anharmonic vibrational states for medium to large molecules is a requirement for the detailed understanding of nonlinear multidimensional infrared spectra and the dynamical information encoded in them. The vibrational configuration interaction (VCI) method constitutes a particularly promising tool in this respect. It is generally hampered though by its unfavorable scaling with respect to system size. We analyze the scaling behavior of several well‐known as well as some new approximate VCI schemes in detail, which are complementary to the class of configuration selection schemes developed recently. We find that the combination of a configuration space partitioning, possibly based on configuration selection, with energetic thresholding and resonance screening provides an efficient scheme for the reduction of computational effort involved in VCI calculations while at the same time maintaining sufficient accuracy for the vibrational energies. © 2012 Wiley Periodicals, Inc.     

Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,S(R). S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds tao 0 identical with{Tao 0(egy),Tao 0(etc.)}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above tao 1 < or = tao 0. An eigenproblem of dimension d0 + d1 for S0 + S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j > or = 2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {tao j;j = 0,1,2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S0 + S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One mu hartree accuracy is achieved for an eigenproblem of order 24 x 10(6), involving 1.2 x 10(12) nonzero matrix elements, and 8.4 x 10(9) Slater determinants.     

A fragment energy assembler method for Hartree-Fock calculations of large molecules

We present a fragment energy assembler approach for approximate Hartree-Fock (HF) calculations of macromolecules. In this method, a macromolecule is divided into small fragments with appropriate size, and then each fragment is capped by its neighboring fragments to form a subsystem. The total energy of the target system is evaluated as the sum of the fragment energies of all fragments, which are available from conventional HF calculations on all subsystems. By applying the method to a broad range of molecules, we demonstrate that the present approach could yield satisfactory HF energies for all studied systems.     

A programmable spin-free method for configuration interaction

In this note a method is presented for quick implementation of configuration interaction (CI) calculations in molecules. A spin-free Hamiltonian for anN electron system in a spin stateS, expressed in terms of the generators for the unitary group algebra, is diagonalized over orbital configurations forming a basis for the irreducible representation [2^1/2N-S 1^2S ] of the permutation group S _N . It has been found that the basic algebraic expressions necessary for the CI calculation involve a limited category of permutations. These have been displayed explicitly. On leave from the Indian Institute of Technology, Bombay, India.     

Local configuration interaction: An efficient approach for larger molecules

The first full implementation of the localized configuration interaction technique at the variational CI, CEPA-2 and variational CEPA levels is described. Timings are presented for a double-zeta plus polarization calculation on butadiene. The restriction of the correlation space to local basis functions results in a spectacular enhancement of the efficiency of the CI loop. The loss in the correlation energy is only a few percent; we argue that most of the loss is due to the exclusion of intramolecular basis set superposition artifacts.     

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.     

On numerical solution of the integral Hartree-Fock equations for molecules by the method of MO LCAO in the momentum space

To develop a numerical solution of mentioned equations the method of factorized projection of integral operator kernel is applied. All matrix elements of the method are calculated analytically, being expressed in terms of two types of standard integrals: the overlap integrals and one-electron Coulomb integrals. To calculate the integrals we used the O(4)-symmetry of hydrogen-like atomic orbitals as well as operational technique of differentiation with respect to scalar and vector parameters.     

Trajectory-guided configuration interaction simulations of multidimensional quantum dynamics

We propose an approach to modelling multidimensional quantum systems which uses direct-dynamics trajectories to guide wavefunction propagation. First, trajectory simulations are used to generate a sample of dynamically relevant configurations on the potential energy surface (PES). Second, the sampled configurations are used to construct an n-mode representation of the PES using a greedy algorithm. Finally, the time-dependent Schr?dinger equation is solved using a configuration interaction expansion of the wavefunction, with individual basis functions derived directly from the 1-mode contributions to the n-mode PES. This approach is successfully demonstrated by application to a 20-dimensional benchmark problem describing tunnelling in the presence of coupled degrees of freedom.     

Immunoasssay based on the antibody-conjugated PAMAM-dendrimer-gold quantum dot complex

An immunoassay based upon photoluminescent gold quantum dots aimed at detecting human IgG in aqueous solution from micromolar to nanomolar concentrations is described.     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for iterative evaluation of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.     

Electronic states of the NiCu molecule determined byab initio Hartree-Fock and configuration interaction methods

The interaction between a Ni atom and a Cu atom in the configurations (3d)⁹(4s)¹ and (3d)¹⁰(4s)¹, respectively, has been calculated usingab initio Hartree-Fock and configuration interaction methods. The chemical bond between the two atoms is due to a bonding 4sσ molecular orbital. Equilibrium distances, dissociation energies and vibrational frequencies are predicted for the low-lying states. Finally the influence of spin-orbit coupling on the low-lying states is considered.     

Coupled-cluster method tailored by configuration interaction

A method is presented which combines coupled cluster (CC) and configuration interaction (CI) to describe accurately potential-energy surfaces (PESs). We use the cluster amplitudes extracted from the complete active space CI calculation to manipulate nondynamic correlation to tailor a single reference CC theory (TCC). The dynamic correlation is then incorporated through the framework of the CC method. We illustrate the method by describing the PESs for HF, H2O, and N2 molecules which involve single, double, and triple bond-breaking processes. To the dissociation limit, this approach yields far more accurate PESs than those obtained from the conventional CC method and the additional computational cost is negligible compared with the CC calculation steps. We anticipate that TCC offers an effective and generally applicable approach for many problems.     

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the "initiator" adaptation to full configuration interaction quantum Monte Carlo (i-FCIQMC), with a view to accelerating convergence. In particular, we find that the fixed-shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i-FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ≤ r(s) ≤ 5.0 a.u. A single-point extrapolation scheme is introduced to produce complete basis energies for 14, 38, and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed-shift strategy to reduce the computational cost of many i-FCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.     

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.     

An efficient method for large scale configuration interaction calculations

An efficient method of handling large scale configuration interaction calculations is developed and applied to the H₂O molecule as a test case. The method, which is based upon matrix partitioning, is shown to be capable of calculating the ¹B₁ spectrum of H₂O to an accuracy level of 0.1 eV for each state with very moderate computational effort.