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Evaluation of the self-consistent polarization energy forms a major computational bottleneck in polarizable force fields. In large systems, the linear polarization equations are typically solved iteratively with techniques based on Jacobi iterations (JI) or preconditioned conjugate gradients (PCG). Two new variants of JI are proposed here that exploit domain decomposition to accelerate the convergence of the induced dipoles. The first, divide-and-conquer JI (DC-JI), is a block Jacobi algorithm which solves the polarization equations within non-overlapping sub-clusters of atoms directly via Cholesky decomposition, and iterates to capture interactions between sub-clusters. The second, fuzzy DC-JI, achieves further acceleration by employing overlapping blocks. Fuzzy DC-JI is analogous to an additive Schwarz method, but with distance-based weighting when averaging the fuzzy dipoles from different blocks. Key to the success of these algorithms is the use of K-means clustering to identify natural atomic sub-clusters automatically for both algorithms and to determine the appropriate weights in fuzzy DC-JI. The algorithm employs knowledge of the 3-D spatial interactions to group important elements in the 2-D polarization matrix. When coupled with direct inversion in the iterative subspace (DIIS) extrapolation, fuzzy DC-JI/DIIS in particular converges in a comparable number of iterations as PCG, but with lower computational cost per iteration. In the end, the new algorithms demonstrated here accelerate the evaluation of the polarization energy by 2-3 fold compared to existing implementations of PCG or JI/DIIS.

We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.

Three-body and higher intermolecular interactions can play an important role in molecular condensed phases. Recent benchmark calculations found problematic behavior for many widely used density functional approximations in treating 3-body intermolecular interactions. Here, we demonstrate that the combination of second-order Møller-Plesset (MP2) perturbation theory plus short-range damped Axilrod-Teller-Muto (ATM) dispersion accurately describes 3-body interactions with reasonable computational cost. The empirical damping function used in the ATM dispersion term compensates both for the absence of higher-order dispersion contributions beyond the triple-dipole ATM term and non-additive short-range exchange terms which arise in third-order perturbation theory and beyond. Empirical damping enables this simple model to out-perform a non-expanded coupled Kohn-Sham dispersion correction for 3-body intermolecular dispersion. The MP2 plus ATM dispersion model approaches the accuracy of O(N(6)) methods like MP2.5 or even spin-component-scaled coupled cluster models for 3-body intermolecular interactions with only O(N(5)) computational cost.

To avoid repeated, computationally expensive QM solute calculations while sampling MM solvent in QM/MM simulations, a new approach for constructing an implicit solvent model by coarse-graining the solvent properties over many explicit solvent configurations is proposed. The solvent is modeled using a polarizable force field that is parameterized in terms of distributed multipoles (electrostatics), polarizabilities (induction), and frequency-dependent polarizabilities (dispersion). The coarse-graining procedure exploits the ability to translate these properties to the center of each coarse-graining cell and average them over many solvent configurations before interacting them with the solute. A single coarse-grained QM/MM calculation of the interaction between a formamide solute and aqueous solvent reproduces the much more expensive average over many explicit QM/MM calculations with kJ/mol accuracy.

The MP2C dispersion correction of Pitonak and Hesselmann [J. Chem. Theory Comput. 6, 168 (2010)] substantially improves the performance of second-order Møller-Plesset perturbation theory for non-covalent interactions, albeit with non-trivial computational cost. Here, the MP2C correction is computed in a monomer-centered basis instead of a dimer-centered one. When applied to a single dimer MP2 calculation, this change accelerates the MP2C dispersion correction several-fold while introducing only trivial new errors. More significantly, in the context of fragment-based molecular crystal studies, combination of the new monomer basis algorithm and the periodic symmetry of the crystal reduces the cost of computing the dispersion correction by two orders of magnitude. This speed-up reduces the MP2C dispersion correction calculation from a significant computational expense to a negligible one in crystals like aspirin or oxalyl dihydrazide, without compromising accuracy.

The fragment-based hybrid many-body interaction (HMBI) model provides a computationally affordable means of applying electronic structure wavefunction methods to molecular crystals. It combines a quantum mechanical treatment of individual molecules in the unit cell and their short-range pairwise interactions with a polarizable molecular mechanics force-field treatment of long-range and many-body interactions. Here, we report the implementation of analytic nuclear gradients for the periodic model to enable full relaxation of both the atomic positions and crystal lattice parameters. Using a set of five, chemically diverse molecular crystals, we compare the quality of the HMBI MP2/aug-cc-pVDZ-level structures with those obtained from dispersion-corrected periodic density functional theory, B3LYP-D*, and from the Amoeba polarizable force field. The MP2-level structures largely agree with the experimental lattice parameters to within 2%, and the root-mean-square deviations in the atomic coordinates are less than 0.2 Å. These MP2 structures are almost as good as those predicted from periodic B3LYP-D*/TZP and are significantly better than those obtained with B3LYP-D*/6-31G(d,p) or with the Amoeba force field.

The recently reported photoswitching of diarylethene derivative molecules bridging carbon nanotube (CNT) contacts is theoretically analyzed. The short lifetime of the lowest unoccupied molecular orbital (LUMO) indicates that neither the open nor closed form of the molecule can be photoexcited into a charge-neutral excited state for any appreciable length of time preventing photochromic ring opening. Analysis of the highest occupied molecular orbital (HOMO) and LUMO lifetimes also suggests that photoexcitation results in oxidation of the molecules. This either reduces the quantum yield of photochromic ring closing, or it gives rise to the possibility of oxidative ring closing. Analysis of the resistance values and energy levels indicates that the HOMO energy levels of the closed isomers relevant for transport must lie within a few k(B)T of the CNT Fermi level. For armchair contacts, the change in resistance with isomer or substituent group is the result of shifts in the energy level of the molecular HOMO. The coupling of the molecular HOMO to the CNT contacts is insensitive to the isomer type or substituent group. For zigzag CNTs, the conductance is dominated by surface states at the Fermi level on the cut ends of the CNTs so that the conductance is relatively insensitive to the isomer type, and the conductance switching ratio is low. Multiple bridging molecules can interact coherently, resulting in energy splitting, shifting, and interference that cause a nonlinear change in conductance with increasing numbers of molecules. Instead of a factor of 3 increase in conductance expected for three independent channels, a factor of 10(3) increase in conductance is obtained for three bridging molecules.

Many-body intermolecular interaction expansions provide a promising avenue for the efficient quantum mechanical treatment of molecular clusters and condensed-phase systems, but the computationally expensive three-body and higher terms are often nontrivial. When polar molecules are involved, these many-body terms are typically dominated by electrostatic induction effects, which can be approximated relatively easily. We demonstrate an accurate and inexpensive hybrid quantum/classical model in which one- and two-body interactions are computed quantum mechanically, while the many-body induction effects are approximated with a simple classical polarizable force field. Whereas typical hybrid quantum/classical models partition a system spatially into distinct quantum and classical regions, the model demonstrated here partitions based on the order in the many-body interaction series. This enables a spatially homogeneous treatment of the entire system, which could prove advantageous in studying a wide range of condensed-phase molecular systems.

The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.

We have formulated a second-order perturbative correction for perfect-pairing wave functions [PP2] based on similarity-transformed perturbation techniques in coupled cluster theory. The perfect-pairing approximation is used to obtain a simple reference wave function which can qualitatively describe bond breaking, diradicals, and other highly correlated systems, and the perturbative correction accounts for the dynamical correlation. An efficient implementation of this correction using the resolution of the identity approximation enables PP2 to be computed at a cost only a few times larger than that of canonical MP2 for systems with hundreds of active electrons and tens of heavy atoms. PP2 significantly improves on MP2 predictions in various systems with a challenging electronic structure.

The singular value decomposition of the n-particle excitation operator as determined by coupled cluster or perturbation theory is used to extract the dominant and interesting electron-electron correlations from complex molecular wave functions. As an example of the very general formalism, the decomposition of the T(2) operator obtained from coupled cluster doubles calculations is used to analyze the strength and character of pair correlations in a variety of molecules with interesting electronic structure. The magnitude of the largest singular value(s) determines the strength of the correlation(s), and the corresponding right- and left-hand singular vectors characterize the physical and spatial nature of the correlations. The primary advantage of this tool over natural orbital analysis is that it provides direct associations between the occupied and virtual geminals involved in the correlations., ((c) 2004 American Institute of Physics.)