Biomedical subjects

Joseph E Subotnik

Publications and source records attributed to Joseph E Subotnik.

7 recordsLinked to original sources

PubMed2006

Linear scaling density fitting.

Two modifications of the resolution of the identity (RI)/density fitting (DF) approximations are presented. First, we apply linear scaling and J-engine techniques to speed up traditional DF. Second, we develop an algorithm that produces local, accurate fits with effort that scales linearly with system size. The fits produced are continuous, differentiable, well-defined, and do not require preset fitting domains. This metric-independent technique for producing a priori local fits is shown to be accurate and robust even for large systems. Timings are presented for linear scaling RI/DF calculations on large one-, two-, and three-dimensional carbon systems.

Algorithms↗

PubMed2006

A near linear-scaling smooth local coupled cluster algorithm for electronic structure.

We demonstrate near linear scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems. The theory behind our approach has been described previously, [J. Subotnik and M. Head-Gordon, J. Chem. Phys. 123, 064108 (2005)], and requires appropriately multiplying standard iterative amplitude equations by a bump function, creating local amplitude equations (which are smooth according to the implicit function theorem). Here, we provide an example that this theory works in practice: we show that our algorithm leads to smooth potential energy surfaces and yields large computational savings. As an example, we apply our LCCSD approach to measure the post-MP2 correction to the energetic gap between two different alanine tetrapeptide conformations.

Algorithms↗

PubMed2006

Advances in methods and algorithms in a modern quantum chemistry program package.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Algorithms↗

PubMed2005

Fast localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates.

We present here an algorithm for computing stable, well-defined localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates. The algorithm is very fast, limited only by diagonalization of two matrices with dimension the size of the number of virtual orbitals. Furthermore, we require no more than quadratic (in the number of electrons) storage. The basic premise behind our algorithm is that one can decompose any given atomic-orbital (AO) vector space as a minimal basis space (which includes the occupied and valence virtual spaces) and a hard-virtual (HV) space (which includes everything else). The valence virtual space localizes easily with standard methods, while the hard-virtual space is constructed to be atom centered and automatically local. The orbitals presented here may be computed almost as quickly as projecting the AO basis onto the virtual space and are almost as local (according to orbital variance), while our orbitals are orthonormal (rather than redundant and nonorthogonal). We expect this algorithm to find use in local-correlation methods.

Algorithms↗

PubMed2005

A local correlation model that yields intrinsically smooth potential-energy surfaces.

We demonstrate an algorithm for computing local coupled-cluster doubles (LCCD) energies that form rigorously smooth potential-energy surfaces and which should be fast enough for application to large systems in the future. Like previous LCCD algorithms, our method solves iteratively for only a limited number of correlation amplitudes, treating the remaining amplitudes with second-order perturbation theory. However, by employing bump functions, our method smoothes the transition from iteratively solved amplitude to perturbation-treated amplitude, invoking the implicit function theorem to prove that our LCCD energy is an infinitely differentiable function of nuclear coordinates. We make no explicit amplitude domains nor do we rely on the existence of atom-centered, redundant orbitals in order to get smooth potential-energy curves. In fact, our algorithm employs only localized orthonormal occupied and virtual orbitals. Our approach should be applicable to many other electron correlation methods.

Journal Article↗

PubMed2005

A localized basis that allows fast and accurate second-order Moller-Plesset calculations.

We present a method for computing a basis of localized orthonormal orbitals (both occupied and virtual), in whose representation the Fock matrix is extremely diagonal dominant. The existence of these orbitals is shown empirically to be sufficient for achieving highly accurate second-order Moller-Plesset (MP2) energies, calculated according to Kapuy's method. This method (which we abbreviate KMP2) involves a different partitioning of the n-electron Hamiltonian and scales at most quadratically, with potential for linearity, in the number of electrons. As such, we believe the KMP2 algorithm presented here could be the basis of a viable approach to local-correlation calculations.

Journal Article↗

PubMed2004

An efficient method for calculating maxima of homogeneous functions of orthogonal matrices: applications to localized occupied orbitals.

We present here three new algorithms (one purely iterative and two DIIS-like [Direct Inversion in the Iteractive Subspace]) to compute maxima of homogeneous functions of orthogonal matrices. These algorithms revolve around the mathematical lemma that, given an invertible matrix A, the function f(U)=Tr(AU) has exactly one local (and global) maximum for U special orthogonal [i.e., UU(T)=1 and det(U)=1]. This is proved in the Appendix. One application of these algorithms is the computation of localized orbitals, including, for example, Boys and Edmiston-Ruedenberg (ER) orbitals. The Boys orbitals are defined as the set of orthonormal orbitals which, for a given vector space of orbitals, maximize the sum of the distances between orbital centers. The ER orbitals maximize total self-interaction energy. The algorithm presented here computes Boys orbitals roughly as fast as the traditional method (Jacobi sweeps), while, for large systems, it finds ER orbitals potentially much more quickly than traditional Jacobi sweeps. In fact, the required time for convergence of our algorithm scales quadratically in the region of a few hundred basis functions (though cubicly asymptotically), while Jacobi sweeps for the ER orbitals traditionally scale as the number of occupied orbitals to the fifth power. As an example of the utility of the method, we provide below the ER orbitals of nitrated and nitrosated benzene, and we discuss the chemical implications.

Journal Article↗