Evaluation Of Overlap Integrals Research Articles

Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping.

Direct dynamics by mixed quantum-classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive time steps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature-driven coherent switching with decay of mixing (CSDM) and curvature-driven trajectory surface hopping (TSH). We show how powerful these new methods are in terms of computation time and accuracy as compared to previous mixed quantum-classical nonadiabatic dynamics algorithms. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Use of lined-up auxiliary functions in the evaluation of overlap integrals over integer and non-integer n Slater type orbitals

Abstract A combined theory for the overlap integrals of integer and non-integer n χ -Slater type orbitals ( χ -ISTO and χ -NISTO) is presented. This approach is based on the use of lined-up auxiliary functions introduced by one of the authors. The suggested theory guarantees a highly accurate calculation of the overlap integrals for the arbitrary values of quantum numbers and locations of orbitals.

On Evaluation of Overlap Integrals with Noninteger Principal Quantum Numbers

By use of complete orthonormal sets of Ψα exponential-type orbitals the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals (ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.

On the evaluation of overlap integrals with the same screening parameters of Slater-type orbitals using binomial coefficients

On the evaluation of overlap integrals with the same screening parameters of Slater-type orbitals using binomial coefficients

On the evaluation of overlap integrals with exponential‐type basis functions

AbstractThe numerical properties of a one‐dimensional integral representation [H.P. Trivedi and E. O. Steinborn, Phys. Rev. A 27, 670 (1983)] for the overlap integral of a two‐center product of certain exponential‐type orbitals (ETOs) the B functions [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)], are examined. B functions possess a very simple Fourier transform that results in relatively simple general formulas for molecular integrals derivable using the Fourier transform method. In addition, molecular integrals for other ETOs, like the more common Slater‐type orbitals, can be written as finite linear combinations of integrals with B functions because these functions span the space of ETOs. The integrand of the integral representation mentioned above shows peculiarities requiring special quadrature methods, especially in the case of highly asymmetric charge distributions. It is shown that good results can be obtained using Möbiustransformation‐based quadrature rules well suited for the numerical integration of functions possessing a sharp peak at or near one boundary of integration [H. H. H. Homeier and E. O. Steinborn, J. Comput. Phys. 87, 61 (1990)]. The method based on Möbius‐type quadrature is compared to several other methods — based on other quadrature rules, finite sums, and infinite series representations together with convergence acceleration — to evaluate overlap integrals with B functions. The numerical results indicate that the new quadrature schemes are more efficient than are the other methods.

Scattering at an offset circular hole in a rectangular waveguide

A solution is given for the problem of scattering at an offset circular to rectangular junction and at a thick diaphragm, with an offset circular aperture, in a rectangular waveguide. The method used is mode matching for computing one discontinuity. The difficulty arising from the fact that the eigenmodes of the two waveguides are known in different coordinate systems is overcome by simple transformation for the evaluation of overlap integral between the eigenmodes of each waveguide. Experimental results validate this method. >

Method of recurrent construction of Löwdin spin‐adapted wave functions. III. Löwdin basis and its permutation symmetry: Evaluation of overlap integrals

AbstractThe Löwdin basis functions are introduced and their permutation symmetry is studied in detail. A simple relation between the Löwdin basis and the orthogonal basis constructed by means of Young–Yamanouchi units is established. Both analytical and recurrence formulas for the overlap integrals of the Löwdin and some relevant auxiliary functions are derived. The symmetry of the overlap matrix of the Löwdin basis functions is briefly discussed.

Domain statistics and ferroelectric transients

The statistical problem involved in calculating the ferroelectric polarization and switching current resulting from an arbitrary number and distribution of domains is examined. A general scheme for calculating the polarization based upon the successive evaluation of overlap integrals is proposed and illustrated in detail for a random distribution. Calculation of the polarization and current for different numbers of randomly distributed domains are reported and compared with the prediction of Avrami's relation as well as with relevant experimental results. A brief discussion of Avrami's original statistical derivation is contained in an appendix and a more elegant derivation presented.