Efficient evaluation of the Coulomb force in density-functional theory calculations

Abstract

Articles you may be interested inOn the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limitThe Coulomb force in density-functional theory calculations is efficiently evaluated based on a partitioning into near-field ͑NF͒ and far-field ͑FF͒ interactions. For the NF contributions, a J force engine method is developed based on our previous J matrix engine methods, and offers a significant speedup over derivative electron repulsion integral evaluation, without any approximation. In test calculations on water clusters and linear alkanes, the computer time for the NF force is reduced by a factor of 5-7 with a 3-21G basis set and 6-8 with a 6-31G** basis set. The FF force is treated by a generalization of the continuous fast multipole method, and the FF computational cost is found to be comparable to that of an energy evaluation.

Auxiliary basis expansions for large-scale electronic structure calculations

“…With the success of linear scaling methods (4,6,31,32) and local correlation models (33)(34)(35) for reducing the scaling with molecular size, it is desirable to combine them with the reduced prefactors offered by the auxiliary basis approach to produce still more efficient algorithms (22,23). The locality of the coefficients determines the extent to which low-scaling methods involving auxiliary basis expansions are possible without further approximations, such as fitting domains (22,23).…”

Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

“…Its variational parameters are 10's of linear combination of atomic orbitals (LCAO) coefficients rather than 100's of plane-wave coefficients or numerical values at 1000's of points per atom per molecular orbital. A second step forward is to compute the contribution of the local density-of-states to forces not by recursion [5], and xyz-factorization [6] but via the generalized Gaunt coefficients [7]. Due to the present limitations [8] on the functional forms that can be treated in ADFT, however, we need to parameterize it in order to get the correct geometry of the giant fullerenes.…”

“…Efficient computation requires switching from the traditional Cartesian-Gaussian basis [5] to the solid-harmonic-Gaussian basis, which minimally contains all essential chemistry; the latter are eigenstates of angular momentum as are the atomic orbitals that collectively they approximate. The matrix elements corresponding to higher angular momentum are computed by differentiating the s-type matrix elements with respect to the corresponding atomic center [9].…”

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg2+-sensitive dye

“…͑The van der Waals interactions are not included in the total QM/MM Fock or KS matrix, but into the total energy.͒ On the other hand, we have also seen significant development based on a fully QM description for large-scale calculations. [6][7][8][9][10][11][12][13][14][15][16][17][18] One of the authors ͑W.Y.͒ has developed the linear-scaling treatment, the divide-and-conquer ͑DC͒ method. [26][27][28] In this method, the entire system is first divided into several subsystems and their electron densities are calculated separately.…”

“…In this subject, many methods have been proposed so far. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] The most well-known and commonly used approach is the quantum-mechanical/molecularmechanical ͑QM/MM͒ method. [19][20][21][22] In this method, the electronically important part is described by quantum mechanics ͑QM͒, while the rest of the system is described by molecular mechanics ͑MM͒.…”