Driving forces for transmembrane alpha-helix oligomerization.

We present what we believe to be a novel statistical contact potential based on solved structures of transmembrane (TM) alpha-helical bundles, and we use this contact potential to investigate the amino acid likelihood of stabilizing helix-helix interfaces. To increase statistical significance, we have reduced the full contact energy matrix to a four-flavor alphabet of amino acids, automatically determined by our methodology, in which we find that polarity is a more dominant factor of group identity than is size, with charged or polar groups most often occupying the same face, whereas polar/apolar residue pairs tend to occupy opposite faces. We found that the most polar residues strongly influence interhelical contact formation, although they occur rarely in TM helical bundles. Two-body contact energies in the reduced letter code are capable of determining native structure from a large decoy set for a majority of test TM proteins, at the same time illustrating that certain higher-order sequence correlations are necessary for more accurate structure predictions.

An implicit solvent coarse-grained lipid model with correct stress profile.

We develop a coarse-grained parametrization strategy for lipid membranes that we illustrate for a dipalmitoylphosphatidylcholine bilayer. Our coarse-graining approach eliminates the high cost of explicit solvent but maintains more lipid interaction sites. We use a broad attractive tail-tail potential and extract realistic bonded potentials of mean force from all-atom simulations, resulting in a model with a sharp gel to fluid transition, a correct bending modulus, and overall very reasonable dynamics when compared with experiment. We also determine a quantitative stress profile and correct breakdown of contributions from lipid components when compared with detailed all-atom simulation benchmarks, which has been difficult to achieve for implicit membrane models. Such a coarse-grained lipid model will be necessary for efficiently simulating complex constructs of the membrane, such as protein assembly and lipid raft formation, within these nonaqueous chemical environments.

Predicting accurate electronic excitation transfer rates via marcus theory with Boys or Edmiston-Ruedenberg localized diabatization.

We model the triplet-triplet energy-transfer experiments from the Closs group [ Closs , G. L. ; et al. J. Am. Chem. Soc. 1988 , 110 , 2652. ] using a combination of Marcus theory and either Boys or Edmiston-Ruedenberg localized diabatization, and we show that relative and absolute rates of electronic excitation transfer may be computed successfully. For the case where both the donor and acceptor occupy equatorial positions on a rigid cyclohexane bridge, we find beta(calc) = 2.8 per C-C bond, compared with the experimental value beta(exp) = 2.6. This work highlights the power of using localized diabatization methods as a tool for modeling nonequilibrium processes.

Hartree-Fock exchange computed using the atomic resolution of the identity approximation.

In this work, we apply the atomic resolution of the identity (ARI) fitting approximation to the computation of Hartree-Fock exchange. The ARI approximation is a local modification of the RI approximation that produces an energy which is differentiable with respect to nuclear motion, unlike other local applications of RI. We justify empirically the use of locality and present timing comparisons of ARI, RI, and exact computation for one-, two-, and three-dimensional carbon systems. ARI is found to reduce significantly the cost of RI for large systems, while retaining accuracy.

The limits of local correlation theory: electronic delocalization and chemically smooth potential energy surfaces.

Local coupled-cluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys. 125, 074116 (2006)] that one may construct a local coupled-cluster singles-doubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electron-electron correlation), but also on the two-electron integrals themselves (which measure the bare electron-electron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view.

Localized orbital theory and ammonia triborane.

In a previous paper [J. Subotnik, Y. Shao and W. Liang, and M. Head-Gordon, J. Chem. Phys., 2004, 121, 9220], we proposed a new and efficient method for computing localized Edmiston-Ruedenberg (ER) orbitals, which are those localized orbitals that maximize self-interaction. In this paper, we improve upon our previous algorithm in two ways. First, we incorporate the resolution of the identity (RI) and atomic resolution of the identity (ARI) approximations when generating the relevant integrals, which allows for a drastic reduction in computational cost. Second, after convergence to a stationary point, we efficiently calculate the lowest mode of the Hessian matrix in order to either (i) confirm that we have found a minimum, or if not, (ii) move us away from the current saddle point. This gives our algorithm added stability. As a chemical example, in this paper, we investigate the electronic structure (including the localized orbitals) of ammonia triborane (NH(3)B(3)H(7)). Though ammonia triborane is a very electron-deficient compound, it forms a stable white powder which is now being investigated as a potential hydrogen storage material. In contrast to previous electronic structure predictions, our calculations show that ammonia triborane has one localized molecular orbital in the center of the electron-deficient triborane ring (much like the single molecular orbital in H(3)(+)), which gives the molecule added energetic stability. Furthermore, we believe that NH(3)B(3)H(7) is the smallest stable molecule supporting such a closed, three-center BBB bond.

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.

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.

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.

A Fast Implementation of Perfect Pairing and Imperfect Pairing Using the Resolution of the Identity Approximation.

We present an efficient implementation of the perfect pairing and imperfect pairing coupled-cluster methods, as well as their nuclear gradients, using the resolution of the identity approximation to calculate two-electron integrals. The perfect pairing and imperfect pairing equations may be solved rapidly, making integral evaluation the bottleneck step. The method's efficiency is demonstrated for a series of linear alkanes, for which we show significant speed-ups (of approximately a factor of 10) with negligible error. We also apply the imperfect pairing method to a model of a recently synthesized stable singlet biradicaloid based on a planar Ge-N-Ge-N ring, confirming its biradical character, which appears to be remarkably high.

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field.

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.

Auxiliary basis expansions for large-scale electronic structure calculations.

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.