ترغب بنشر مسار تعليمي؟ اضغط هنا

Efficient evaluation of two-center Gaussian integrals in periodic systems

103   0   0.0 ( 0 )
 نشر من قبل Sandeep Sharma
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

By using Poissons summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large exponent. We demonstrate that the summation can be performed efficiently to calculate 2-center Gaussian integrals over various kernels including overlap, kinetic, and Coulomb. The summation in real space is performed using an efficient flavor of the McMurchie-Davidson Recurrence Relation (MDRR). The expressions for performing summation in the reciprocal space are also derived and implemented. The algorithm for reciprocal space summation allows us to reuse several terms and leads to significant improvement in efficiency when highly contracted basis functions with large exponents are used. We find that the resulting algorithm is only between a factor of 5 to 15 slower than that for molecular integrals, indicating the very small number of terms needed in both the real and reciprocal space summations. An outline of the algorithm for calculating 3-center Coulomb integrals is also provided.



قيم البحث

اقرأ أيضاً

We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the repres entation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cut-off radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artefacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid and water adsorption on a LiH surface, at the level of second-order M{o}ller--Plesset perturbation theory.
We present an efficient ab initio dynamical mean-field theory (DMFT) implementation for quantitative simulations in solids. Our DMFT scheme employs ab initio Hamiltonians defined for impurities comprising the full unit cell or a supercell of atoms an d for realistic quantum chemical basis sets. We avoid double counting errors by using Hartree-Fock as the low-level theory. Intrinsic and projected atomic orbitals (IAO+PAO) are chosen as the local embedding basis, facilitating numerical bath truncation. Using an efficient integral transformation and coupled-cluster Greens function (CCGF) impurity solvers, we are able to handle embedded impurity problems with several hundred orbitals. We apply our ab initio DMFT approach to study a hexagonal boron nitride monolayer, crystalline silicon, and nickel oxide in the antiferromagnetic phase, with up to 104 and 78 impurity orbitals in spin-restricted and unrestricted cluster DMFT calculations and over 100 bath orbitals. We show that our scheme produces accurate spectral functions compared to both benchmark periodic coupled-cluster computations and experimental spectra.
In order to simulate open quantum systems, many approaches (such as Hamiltonian-based solvers in dynamical mean-field theory) aim for a reproduction of a desired environment spectral density in terms of a discrete set of bath states, mimicking the op en system as a larger closed problem. Existing strategies to find a compressed representation of the environment for this purpose can be numerically demanding, or lack the compactness and systematic improvability required for an accurate description of the system propagator. We propose a method in which bath orbitals are constructed explicitly by an algebraic construction based on the Schmidt-decomposition of response wave functions, efficiently and systematically compressing the description of the full environment. These resulting bath orbitals are designed to directly reproduce the system Greens function, not hybridization, which allows for consideration of the relevant system energy scales to optimally model. This results in an accurate and efficient truncation of the environment, with applications in a wide range of numerical simulations of open quantum systems.
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
368 - B. P. Datta 2011
Any physiochemical variable (Ym) is always determined from certain measured variables {Xi}. The uncertainties {ui} of measuring {Xi} are generally a priori ensured as acceptable. However, there is no general method for assessing uncertainty (em) in t he desired Ym, i.e. irrespective of whatever might be its system-specific-relationship (SSR) with {Xi}, and/ or be the causes of {ui}. We here therefore study the behaviors of different typical SSRs. The study shows that any SSR is characterized by a set of parameters, which govern em. That is, em is shown to represent a net SSR-driven (purely systematic) change in ui(s); and it cannot vary for whether ui(s) be caused by either or both statistical and systematic reasons. We thus present the general relationship of em with ui(s), and discuss how it can be used to predict a priori the requirements for an evaluated Ym to be representative, and hence to set the guidelines for designing experiments and also really appropriate evaluation models. Say: Y_m= f_m ({X_i}_(i=1)^N), then, although: e_m= g_m ({u_i}_(i=1)^N), N is not a key factor in governing em. However, simply for varying fm, the em is demonstrated to be either equaling a ui, or >ui, or even <ui. Further, the limiting error (d_m^(Lim.)) in determining an Ym is also shown to be decided by fm (SSR). Thus, all SSRs are classified into two groups: (I) the SSRs that can never lead d_m^(Lim.) to be zero; and (II) the SSRs that enable d_m^(Lim.) to be zero. In fact, the theoretical-tool (SSR) is by pros and cons no different from any discrete experimental-means of a study, and has resemblance with chemical reactions as well.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا