RRS-PBC: a molecular approach for periodic systems

Technically, when dealing with a perfect crystal, methods in k-(reciprocal) space that impose periodic boundary conditions(PBC) in conjunction with plane-wave basis sets are widely used. Chemists, however, tend to think of a solid as a giant molecule, which offers a molecular way to describe a solid by using a finite cluster model(FCM). However, FCM may fail to simulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space information of a perfect crystalline solid out of a reduced real space(RRS) of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.     

Implementation of the finite field perturbation method in the CRYSTAL program for calculating the dielectric constant of periodic systems

The finite field approach has been implemented in the periodic ab initio CRYSTAL program and been used for calculating the dielectric constants of crystalline LiF and MgO (FCC structure) and BeO (wurtzite structure). To maintain the periodicity along the applied field direction, a "sawtooth" potential is used in conjunction with a supercell scheme. Supercells four to five times longer than the primitive cell in the direction of the applied field provide well-converged results. The influence of the computational parameters is discussed. An alternative scheme has also been implemented, for inner check, that consists of applying a static electric field to a slab of increasing thickness in the direction orthogonal to the surface; the dielectric response at the center of the slab is shown to converge rapidly to the bulk value evaluated with the sawtooth field. The method is accurate and permits the determination of nonlinear corrections to the dielectric constant. When used in conjunction with the local density approximation (LDA) scheme, it provides for the dielectric constant of the three above-mentioned compounds values close to those recently obtained with a time-dependent density functional theory approach.     

Second-order post-Hartree-Fock perturbation theory for the electron current

Based on the super-fermion representation of quantum kinetic equations we develop nonequilibrium, post-Hartree-Fock many-body perturbation theory for the current through a region of interacting electrons. We apply the theory to out of equilibrium Anderson model and discuss practical implementation of the approach. Our calculations show that nonequilibrium electronic correlations may produce significant quantitative and qualitative corrections to mean-field electronic transport properties.     

Wannier-type atomic orbitals for periodic systems

The results of an application of Wannier-type atomic orbitals for calculations of local properties of electronic structure for periodic systems (atomic charges and covalencies, bond orders and total valencies), published earlier by the authors, are summarized. The numerical results are given for bulk crystals with the perovskite structure ATiO₃, A=Sr,Ba,Pb and LaMnO₃ (the Bloch functions are calculated in LCAO basis), for bulk MgO crystal (the Bloch functions are calculated both in LCAO and PW basis) and for the two periodic slab models of surfaces (001) of MgO and (110) of rutile TiO₂.     

Dressed coupled-electron-pair-approximation methods for periodic systems

 The techniques of matrix dressing for configuration-interaction (CI)-type or coupled-electron-pair-approximation (CEPA)-type correlation treatments are reviewed with respect to the application to periodic systems. All methods ranging from canonical second-order M?ller–Plesset perturbation theory over CI of single and double excitation, CEPA-0 or the averaged-coupled-pair-functional to self-consistent size-consistent CI can be formulated completely equivalently as an eigenvalue problem or as a solution to a system of linear equations. The size consistency of each method is obtained in a natural way, and invariance under orbital rotations is clearly assessible. A remark on the size consistency of the Davidson correction is presented. Additionally, the direct generation of localized Hartree–Fock orbitals as basic ingredients for the correlation calculations are addressed, as well as selected results on ring molecules, polymers, and 3D cubic beryllium as a model crystal. Received: 28 August 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Efficient algorithm of the transcorrelated method for periodic systems

The transcorrelated (TC) method is one of the promising wave-function-based approaches for the first-principles electronic structure calculations. In this method, the many-body wave function is approximated as the Jastrow-Slater type and one-electron orbitals in the Slater determinant are optimized with a one-body self-consistent-field equation such as that in the Hartree-Fock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solid-state calculations, being of order O(N(k)(3)N(b)(3)) with N(k) and N(b) the respective numbers of k-points and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a plane-wave basis that is suited to and widely used in solid-state calculations. In this paper, we present a new efficient algorithm of the TC method for the plane-wave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as O(N(k)(2)N(b) (2)). This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors.     

Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules

Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).     

On the role of symmetry in the ab initio hartree-fock linear-combination-of-atomic-orbitals treatment of periodic systems

The symmetry properties of the mono- and bielectronic terms contributing to the Fock matrix in the ab initio Hartree–Fock treatment of periodic systems are discussed. A computational scheme which takes full advantage of the point symmetry is presented; in this respect, it represents a generalization of the scheme proposed in Int. J. Quantum Chem. 17 , 501 (1980). Computational details and numerical examples are reported; it is shown that with respect to two of the bottlenecks of this kind of calculation, namely, computer time and backing storage required for the bielectronic integrals, it is possible to obtain saving factors as large as h and h², respectively, where h is the order of the point group. Preliminary tests are reported which indicate that the study of relatively complicated systems, like quartz or corundum (9 and 10 atoms in the unit cell, respectively) at an ab initio Hartree–Fock level is now within reach.     

A symbolic algorithm for periodic tridiagonal systems of equations

In the current paper, we present a novel symbolic algorithm for solving periodic tridiagonal linear systems without imposing any restrictive conditions. The computational cost of the algorithm is less than or almost equal to those of three well-known algorithms given by Chawla and Khazal (Int. J. Comput. Math. 79(4):473–484, 2002) and by El-Mikkawy (Appl. Math. Comput. 161:691–696, 2005), respectively. In addition, the solution of periodic anti-tridiagonal linear systems is also discussed. Two numerical experiments are provided in order to illustrate the performance and effectiveness of our algorithm. All of the experiments were performed on a computer with aid of programs written in MATLAB.     

Ewald-type formulas for Gaussian-basis studies of one-dimensionally periodic systems

The history of computations at Namur and elsewhere on the electronic structures of stereoregular polymers is briefly reviewed to place the work reported here in the context of related efforts. Our earlier publications described methods for the formal inclusion of Ewald-type convergence acceleration in band-structure computations based on Gaussian-type orbitals, and that work is here extended to include a discussion of the calculation of total energies. It is noted that the continuous nature of the electronic density leads to different functional forms than are encountered for point-charge lattice sums. Examples are provided to document the correctness and convergence properties of the formulation.     

Coupled perturbed Hartree-Fock for periodic systems: the role of symmetry and related computational aspects

A general and efficient implementation of the coupled perturbed Hartree-Fock (CPHF) scheme in the CRYSTAL06 code that applies to systems periodic in one dimension (polymers), two dimensions (slabs), three dimensions (crystals) and, as a limiting case, zero dimension (molecules) is presented. The dielectric tensor of large unit cell systems such as boehmite (gamma-AlOOH, 8 atoms/cell), calcite (CaCO3, 10 atoms/cell), and pyrope (Mg3Al2Si3O12, 80 atoms/cell) has been computed. Results are well converged with respect to the computational parameters, in particular, to the number of k points in the reciprocal space and tolerances used in the truncation of the Coulomb and exchange series, showing that the same standard computational conditions used for the self-consistent-field (SCF) step can also be used safely in a CPHF calculation. Point symmetry, being so important in determining crystal properties, also reduces dramatically the computational cost both of the preliminary SCF step and the CPHF calculation, so that the dielectric tensor for large unit cell systems such as pyrope can be computed within 2 CPU hours on a single processor PC.     

A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections

We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermolecular C(6) dispersion coefficients [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermolecular interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coefficients C(8) and C(10). The extended model performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.     

Acuchem: A computer program for modeling complex chemical reaction systems

Acuchem is a program for solving the system of differential equations describing the temporal behavior of spatially homogeneous, isothermal, multicomponent chemical reaction systems. It is designed to provide modelers, data evaluators, and laboratory scientists with an easy to use program for modeling complex chemical reactions, and for presenting the results in tabular or graphical form. The program is described and some examples of its application given. Acuchem is designed to operate on the IBM Personal Computer family and other compatible microcomputers, and is available in a compiled version on a floppy disk.     

Efficiency of post-Hartree-Fock force field for the interpretation of vibrational spectra ofN,N-dimethylnitramine

Harmonic force fields for the molecule ofN,N-dimethylnitramine were calculated in the RHF/6-31G^* and MP2/6-31G^** approximations. Scaling of the force fields obtained made it possible to reliably interpret the vibrational spectra of light and perdeuterated compounds reported in the literature. The assignment is confirmed by good reproducibility of experimental isotope shifts upon¹⁵N-amino- and¹⁵N-nitrosubstitution. The frequencies of intramolecular vibrations in far IR and Raman spectra as well as in neutron inelastic scattering spectra for the light and perdeuterated samples of solidN,N-dimethylnitramine were identified using the force field calculated with the inclusion of electron correlation (MP2). Although general structures of the force fields calculated in the RHF and MP2 approximations are similar, considerable differences in the force constants of the NO and NN stretching vibrations and especially in the constants of the NO_str/NO_str and NO_str/NN_str interactions remain even after scaling the force fields.     

Ab initio program for treatment of related molecules. II. Integral transformation in extended systems

An integral transformation procedure is reported as a part of an ab initio program (named SYCETY) developed recently for spatially extended molecules. It is shown that all advantages of the program SYCETY can be kept. The procedure is especially suitable to transform the integrals to a localized basis set. By using the MBPT with localized basis the most important part of the correlation can be calculated even for large (spatially extended) systems.     

Influence of a periodic field on the distant electron transfer in biological systems.

Generalization of the Marcus transfer rate is derived for the case of a dissipative long-range donor-acceptor electron transfer (ET) mediated by specific bridging electron pathways in biological systems and driven by ac-electric field. High-frequency electric field is shown to block and even to invert the transfer if a specific relation between amplitude and frequency of the ac-field is fulfilled.     

The electrostatic surface term: (I) periodic systems

The authors propose a new approach to understand the electrostatic surface contributions to the interactions of large but finite periodic distributions of charges. They present a simple method to derive and interpret the surface contribution to any electrostatic field produced by a periodic distribution of charges. They discuss the physical and mathematical interpretations of this term. They present several examples and physical details associated with the calculation of the surface term. Finally, they provide a simple derivation of the surface contribution to the virial. This term does not disappear even if tinfoil boundary conditions are applied.