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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.

The need for configurational sampling dramatically increases the cost of combined quantum mechanics/molecular mechanics (QM/MM) simulations of chemical processes in solution. We developed an averaged condensed phase environment (ACPE) model that constructs an effective polarizable environment directly from explicitly sampled molecular dynamics configurations via the K-means++ algorithm and a mathematically rigorous translation of the molecular mechanics parameters. The model captures detailed heterogeneous features in the environment that may be difficult to describe using a conventional polarizable continuum model. Instead of performing repeated QM/MM calculations for each new configuration of the environment, the ACPE approach allows one to perform a single QM calculation on an averaged configuration. Here, we demonstrate the model by computing electronic excitation energies for several small molecules in solution. The ACPE model predicts the excitation energies in excellent agreement with conventional configurational averaging yet with orders of magnitude of reduction in the computational cost.

Molecular crystals occur widely in pharmaceuticals, foods, explosives, organic semiconductors, and many other applications. Thanks to substantial progress in electronic structure modeling of molecular crystals, attention is now shifting from basic crystal structure prediction and lattice energy modeling toward the accurate prediction of experimentally observable properties at finite temperatures and pressures. This Account discusses how fragment-based electronic structure methods can be used to model a variety of experimentally relevant molecular crystal properties. First, it describes the coupling of fragment electronic structure models with quasi-harmonic techniques for modeling the thermal expansion of molecular crystals, and what effects this expansion has on thermochemical and mechanical properties. Excellent agreement with experiment is demonstrated for the molar volume, sublimation enthalpy, entropy, and free energy, and the bulk modulus of phase I carbon dioxide when large basis second-order Møller-Plesset perturbation theory (MP2) or coupled cluster theories (CCSD(T)) are used. In addition, physical insight is offered into how neglect of thermal expansion affects these properties. Zero-point vibrational motion leads to an appreciable expansion in the molar volume; in carbon dioxide, it accounts for around 30% of the overall volume expansion between the electronic structure energy minimum and the molar volume at the sublimation point. In addition, because thermal expansion typically weakens the intermolecular interactions, neglecting thermal expansion artificially stabilizes the solid and causes the sublimation enthalpy to be too large at higher temperatures. Thermal expansion also frequently weakens the lower-frequency lattice phonon modes; neglecting thermal expansion causes the entropy of sublimation to be overestimated. Interestingly, the sublimation free energy is less significantly affected by neglecting thermal expansion because the systematic errors in the enthalpy and entropy cancel somewhat. Second, because solid state nuclear magnetic resonance (NMR) plays an increasingly important role in molecular crystal studies, this Account discusses how fragment methods can be used to achieve higher-accuracy chemical shifts in molecular crystals. Whereas widely used plane wave density functional theory models are largely restricted to generalized gradient approximation (GGA) functionals like PBE in practice, fragment methods allow the routine use of hybrid density functionals with only modest increases in computational cost. In extensive molecular crystal benchmarks, hybrid functionals like PBE0 predict chemical shifts with 20-30% higher accuracy than GGAs, particularly for 1 H, 13 C, and 15 N nuclei. Due to their higher sensitivity to polarization effects, 17 O chemical shifts prove slightly harder to predict with fragment methods. Nevertheless, the fragment model results are still competitive with those from GIPAW. The improved accuracy achievable with fragment approaches and hybrid density functionals increases discrimination between different potential assignments of individual shifts or crystal structures, which is critical in NMR crystallography applications. This higher accuracy and greater discrimination are highlighted in application to the solid state NMR of different acetaminophen and testosterone crystal forms.

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state 13 C and 15 N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Molecular crystals expand appreciably upon heating due to both zero-point and thermal vibrational motion, yet this expansion is often neglected in molecular crystal modeling studies. Here, a quasi-harmonic approximation is coupled with fragment-based hybrid many-body interaction calculations to predict thermal expansion and finite-temperature thermochemical properties in crystalline carbon dioxide, ice Ih, acetic acid and imidazole. Fragment-based second-order Möller-Plesset perturbation theory (MP2) and coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)] predict the thermal expansion and the temperature dependence of the enthalpies, entropies and Gibbs free energies of sublimation in good agreement with experiment. The errors introduced by neglecting thermal expansion in the enthalpy and entropy cancel somewhat in the Gibbs free energy. The resulting ∼ 1-2 kJ mol(-1) errors in the free energy near room temperature are comparable to or smaller than the errors expected from the electronic structure treatment, but they may be sufficiently large to affect free-energy rankings among energetically close polymorphs.

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

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.

Many-body noncovalent interactions are increasingly important in large and/or condensed-phase systems, but the current understanding of how well various models predict these interactions is limited. Here, benchmark complete-basis set coupled cluster singles, doubles, and perturbative triples (CCSD(T)) calculations have been performed to generate a new test set for three-body intermolecular interactions. This "3B-69" benchmark set includes three-body interaction energies for 69 total trimer structures, consisting of three structures from each of 23 different molecular crystals. By including structures that exhibit a variety of intermolecular interactions and packing arrangements, this set provides a stringent test for the ability of electronic structure methods to describe the correct physics involved in the interactions. Both MP2.5 (the average of second- and third-order Møller-Plesset perturbation theory) and spin-component-scaled CCSD for noncovalent interactions (SCS-MI-CCSD) perform well. MP2 handles the polarization aspects reasonably well, but it omits three-body dispersion. In contrast, many widely used density functionals corrected with three-body D3 dispersion correction perform comparatively poorly. The primary difficulty stems from the treatment of exchange and polarization in the functionals rather than from the dispersion correction, though the three-body dispersion may also be moderately underestimated by the D3 correction.

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.

From first principles: In recent studies the lattice energy of crystalline benzene was predicted with sub-kilojoule per mole accuracy. Fundamental to this success was the combination of a fragment approach with state-of-the-art electronic structure methods., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Recent developments in fragment-based methods make it increasingly feasible to use high-level ab initio electronic structure techniques to molecular crystals. Such studies remain computationally demanding, however. Here, we describe a straightforward algorithm for exploiting space-group symmetry in fragment-based methods which often provides computational speed-ups of several fold or more. This algorithm does not require a priori specification of the space group or symmetry operators. Rather, the symmetrically equivalent fragments are identified automatically by aligning the individual fragments along their principle axes of inertia and testing for equivalence with other fragments. The symmetry operators relating equivalent fragments can then be worked out easily. Implementation of this algorithm for computing energies, nuclear gradients with respect to both atomic coordinates and lattice parameters, and the nuclear hessian is described., (© 2014 Wiley Periodicals, Inc.)

First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.

Controlling charge transfer at a molecular scale is critical for efficient light harvesting, energy conversion, and nanoelectronics. Dipole-polarization electrets, the electrostatic analogue of magnets, provide a means for "steering" electron transduction via the local electric fields generated by their permanent electric dipoles. Here, we describe the first demonstration of the utility of anthranilamides, moieties with ordered dipoles, for controlling intramolecular charge transfer. Donor-acceptor dyads, each containing a single anthranilamide moiety, distinctly rectify both the forward photoinduced electron transfer and the subsequent charge recombination. Changes in the observed charge-transfer kinetics as a function of media polarity were consistent with the anticipated effects of the anthranilamide molecular dipoles on the rectification. The regioselectivity of electron transfer and the molecular dynamics of the dyads further modulated the observed kinetics, particularly for charge recombination. These findings reveal the underlying complexity of dipole-induced effects on electron transfer and demonstrate unexplored paradigms for molecular rectifiers.

The dispersion-corrected second-order Møller-Plesset perturbation theory (MP2C) approach accurately describes intermolecular interactions in many systems. MP2C, however, expends much computational effort to compute the long-range correlation with MP2, only to discard and replace those contributions with a simpler long-range dispersion correction based on intermolecular perturbation theory. Here, we demonstrate that one can avoid calculating the long-range MP2 correlation by attenuating the Coulomb operator, allowing the dispersion correction to handle the long-range interactions inexpensively. With relatively modest Coulomb attenuation, one obtains results that are very similar to those from conventional MP2C. With more aggressive attenuation, one can remove just enough short-range repulsive exchange-dispersion interactions to compensate for finite basis set errors. Doing so makes it possible to approach complete basis set limit quality results with only an aug-cc-pVTZ basis, resulting in substantial computational savings. Further computational savings could be achieved by reformulating the MP2C algorithm to exploit the increased sparsity of the two-electron integrals.

Accurately modeling molecular crystal polymorphism requires careful treatment of diverse intra- and intermolecular interactions which can be difficult to achieve without the use of high-level ab initio electronic structure techniques. Fragment-based methods like the hybrid many-body interaction QM/MM technique enable the application of accurate electronic structure models to chemically interesting molecular crystals. The theoretical underpinnings of this approach and the practical requirements for the QM and MM contributions are discussed. Benchmark results and representative applications to aspirin and oxalyl dihydrazide crystals are presented.

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.

Crystalline oxalyl dihydrazide has five experimentally known polymorphs whose energetics are governed by subtle balances between intra- and intermolecular interactions, providing a severe challenge for theoretical crystal structure modeling. Previous work has shown that many common density functional methods that neglect van der Waals dispersion cannot correctly describe this system, but it has been argued that empirically dispersion-corrected DFT-D performs much better. Here, we examine these crystals with second-order Møller-Plesset perturbation theory (MP2) and related levels of theory using the fragment-based hybrid many-body interaction method. The energetics prove sensitive to the treatment of electron-electron correlation, the basis set, many-body induction, three-body dispersion, and zero-point contributions. Nevertheless, our best predictions for the polymorph energy ordering based on dispersion-corrected MP2C calculations agree with the available experimental data. In contrast, lower levels of theory, including the common B3LYP-D* and D-PW91 dispersion-corrected density functional approximations, fail to reproduce experimental observations and/or the high-level calculations.

Significant advances in fragment-based electronic structure methods have created a real alternative to force-field and density functional techniques in condensed-phase problems such as molecular crystals. This perspective article highlights some of the important challenges in modeling molecular crystals and discusses techniques for addressing them. First, we survey recent developments in fragment-based methods for molecular crystals. Second, we use examples from our own recent research on a fragment-based QM/MM method, the hybrid many-body interaction (HMBI) model, to analyze the physical requirements for a practical and effective molecular crystal model chemistry. We demonstrate that it is possible to predict molecular crystal lattice energies to within a couple kJ mol(-1) and lattice parameters to within a few percent in small-molecule crystals. Fragment methods provide a systematically improvable approach to making predictions in the condensed phase, which is critical to making robust predictions regarding the subtle energy differences found in molecular crystals.

Vibrational spectra of the conjugate acid of Me(2)NCH(2)CH(2)CH(2)CH(2)NMe(2) (N,N,N',N'-tetramethylputrescine) have been examined in the gaseous and crystalline phases using Infrared Multiple Photon Dissociation (IRMPD) spectroscopy, Inelastic Neutron Scattering (INS), and high pressure Raman spectroscopy. A band observed near 530 cm(-1) is assigned to the asymmetric stretch of the bridging proton between the two nitrogens, based on deuterium substitution and pressure dependence. The NN distance measured by X-ray crystallography gives a good match to DFT calculations, and the experimental band position agrees with the value predicted from theory using a 2-dimensional potential energy surface. The reduced dimensionality potential energy surface, which treats the ion as though it possesses a linear NHN geometry, shows low barriers to proton transit from one nitrogen to the other, with zero point levels close to the barrier tops. In contrast, two other related systems containing strong hydrogen bonds do not exhibit the same spectroscopic signature of a low barrier hydrogen bond (LBHB). On the one hand, the IRMPD spectra of the conjugate acid ions of the amino acid N,N,N',N'-tetramethylornithine (in which the two nitrogens have different basicities) show fewer bands and no comparable isotopic shifts in the low frequency domain. On the other hand, the IRMPD spectrum of the shorter homologue Me(2)NCH(2)CH(2)CH(2)NMe(2) (N,N,N',N'-tetramethyl-1,3-propanediamine), for which the NHN bond angle deviates substantially from linearity, displays more than one band in the 1100-1400 cm(-1) domain, which vanish as a consequence of deuteration.

We combine quantum and classical mechanics in a fragment-based many-body interaction model to predict organic molecular crystal lattice energies. Individual molecules in the central unit cell and their short-range pairwise interactions are modeled quantum mechanically, while long-range pairwise and many-body interactions are approximated classically. The classical contributions are evaluated using an accurate ab initio force field that is constructed on-the-fly from quantum mechanical calculations on the individual molecules in the unit cell. The force field parameters include ab initio distributed multipole moments, distributed polarizabilities, and isotropic two- and three-body atomic dispersion coefficients. This QM/MM fragment model reproduces full periodic MP2 lattice energies to within a couple kJ/mol at substantially reduced cost. When high-level electronic structure methods are coupled with the ab initio force field, molecular crystal lattice energies are predicted to within 2 kJ/mol of their experimental values for six of the seven crystals examined here. Finally, Axilrod-Teller-Muto three-body dispersion energy plays a nontrivial role in several of the molecular crystals studied here.

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.

Quantum and classical mechanics are combined in a hybrid many-body interaction model to enable the computationally affordable study of systems containing many interacting molecules. This model treats intramolecular and pairwise intermolecular interactions quantum mechanically, while many-body electrostatic induction effects are approximated using a polarizable force field. In this paper, we demonstrate that parametrizing the force field with distributed multipoles and atom-centered polarizabilities obtained on-the-fly from ab initio quantum mechanical monomer calculations makes the model very accurate and eliminates nearly all empiricism. Test calculations on water, formamide, hydrogen fluoride, and glycine-water clusters, all of which exhibit strong many-body interactions, are presented. The performance of the hybrid model is competitive with related point-charge embedding models.

Potential biomarkers were identified for in vitro sensitivity to the epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor gefitinib in head and neck cancer. Gefitinib sensitivity was determined in cell lines, followed by transcript profiling coupled with a novel pathway analysis approach. Eleven cell lines were highly sensitive to gefitinib (inhibitor concentration required to give 50% growth inhibition [GI(50)] < 1 microM), three had intermediate sensitivity (GI(50) 1-7 microM), and six were resistant (GI(50) > 7 microM); an exploratory principal component analysis revealed a separation between the genomic profiles of sensitive and resistant cell lines. Subsequently, a hypothesis-driven analysis of Affymetrix data (Affymetrix, Inc., Santa Clara, CA, USA) revealed higher mRNA levels for E-cadherin (CDH1); transforming growth factor, alpha (TGF-alpha); amphiregulin (AREG); FLJ22662; EGFR; p21-activated kinase 6 (PAK6); glutathione S-transferase Pi (GSTP1); and ATP-binding cassette, subfamily C, member 5 (ABCC5) in sensitive versus resistant cell lines. A hypothesis-free analysis identified 46 gene transcripts that were strongly differentiated, seven of which had a known association with EGFR and head and neck cancer (human EGF receptor 3 [HER3], TGF-alpha, CDH1, EGFR, keratin 16 [KRT16], fibroblast growth factor 2 [FGF2], and cortactin [CTTN]). Polymerase chain reaction (PCR) and enzyme-linked immunoabsorbant assay analysis confirmed Affymetrix data, and EGFR gene mutation, amplification, and genomic gain correlated strongly with gefitinib sensitivity. We identified biomarkers that predict for in vitro responsiveness to gefitinib, seven of which have known association with EGFR and head and neck cancer. These in vitro predictive biomarkers may have potential utility in the clinic and warrant further investigation.

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.

Despite the industrial importance of the process, the detailed chemistry of the high-temperature oxidation of titanium tetrachloride (TiCl4) to produce titania (TiO2) nanoparticles remains unknown, partly due to a lack of thermochemical data. This work presents the thermochemistry of many of the intermediates in the early stages of the mechanism, computed using quantum chemistry. The enthalpies of formation and thermochemical data for TiOCl, TiOCl2, TiOCl3, TiO2Cl2, TiO2Cl3, Ti2O2Cl3, Ti2O2Cl4, Ti2O3Cl2, Ti2O3Cl3, Ti3O4Cl4, and Ti5O6Cl8 were calculated using density functional theory (DFT). The use of isodesmic and isogyric reactions was shown to be important for determining standard enthlapy of formation (Delta(f)H(degree)(298K)) values for these transition metal oxychloride species. TiOCl2, of particular importance in this mechanism, was also studied with CCSD(T) and found to have Delta(f)H(degree)(298K) = -598 +/- 20 kJ/mol. Finally, equilibrium calculations were performed to identify which intermediates are likely to be most prevalent in the high temperature industrial process, and as a first attempt to identify the size of the critical nucleus.

Active space coupled cluster methods exhibit unusual, nonsmooth spin symmetry-breaking behavior where the unrestricted minimum lies higher in energy at short bond distances and crosses below the restricted solution at longer distances. The restricted solution is also observed to be a stable minimum slightly beyond the symmetry-breaking point. This behavior arises due to differences in the optimal active spaces defining the restricted and unrestricted wave functions and results in unrestricted wave functions that are not strictly size consistent. We suggest a new, size-consistent model that allows the orbitals to break spin symmetry only within the active space.

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.

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.

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.

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.

Previous work has shown that pentacoordinated bromine compounds have their lowest excited electronic states shifted to the blue relative to monocoordinated bromine molecules, and that this shift may be large enough to render them photostable in the lower stratosphere. Our earlier work has also shown that certain pentacoordinated bromine compounds are thermodynamically stable relative to their mono- or tricoordinated isomers, suggesting that if a bromine stratospheric reservoir species exists, it may be a pentacoordinated compound. In this study we have examined the singlet and triplet excited electronic states of several bromine compounds, using time dependent density functional theory, to assess their photostability under stratospheric conditions and in order to elucidate the nature of lowest excited states in mono-, tri-, and pentacoordinated bromine molecules. The triplet states have been included due to the strong spin-orbit mixing in bromine. We have found several pentacoordinated bromine/oxygen compounds that could be photostable in the lower stratosphere, but we have also found that monovalent bromine compounds where the bromine atom is bonded to an atom with no lone-pair p-electrons is far and away the most photostable. Attachment/detachment electron density plots have been useful in ascertaining the nature of the excited electronic states and their likely path to photodissociation.

Obtaining an accurate theoretical model for the activation of dinitrogen by three-coordinate molybdenum amide complexes (e.g. Mo(NH2)3) is difficult due to the interaction of various high- and low-spin open-shell complexes along the reaction coordinate which must be treated with comparable levels of accuracy in order to obtain reasonable potential energy surfaces. Density functional theory with present-day functionals is a popular choice in this situation; however, the dinitrogen activation reaction energetics vary substantially with the choice of functional. An assessment of the reaction using specialized wave function based methods indicates that although current density functionals in general agree qualitatively on the mechanistic details of the reaction, a variety of high-level electron correlation methods (including CCSD(T), OD(T), CCSD(2), KS-CCSD(T), and spin-flip CCSD) provide a consistent but slightly different representation of the system.

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.)