DRF90: a polarizable force field

Multistate, Polarizable QM/MM Embedding Scheme Based on the Direct Reaction Field Method: Solvatochromic Shifts, Analytical Gradients and Optimizations of Conical Intersections in Solution

We recently introduced a polarizable embedding scheme based on an integral-exact reformulation of the direct reaction field method (IEDRF) that accounts for the differential solvation of ground and excited states in QM/MM simulations. The polarization and dispersion interactions between the quantum-mechanical (QM) and molecular-mechanical (MM) regions are described by the DRF Hamiltonian, while the Pauli repulsion between explicitly treated QM electrons and the implicit electron density around MM atoms is modeled with effective core potentials. A single Hamiltonian is used for all electronic states so that Born-Oppenheimer states belonging to the same geometry are orthogonal and state crossings are well-defined. In this work, we describe the implementation of the method using graphical processing unit acceleration in TeraChem, where it is combined with multiple electronic structure methods, including Hartree-Fock, time-dependent density functional theory, and complete active space self-consistent field. In contrast with older implementations of the DRF method, integrals of the polarization operators are evaluated exactly. Expressions for ingredients needed to construct analytical gradients and nonadiabatic coupling vectors are derived and tested by optimizing a conical intersection between two excited states in the presence of a polarizable solvent shell. The method is applied to estimate the solvent shifts of absorption energies of a series of donor-acceptor dyes having low-lying charge-transfer states. Even for a nonpolar solvent such as n-hexane, the inclusion of its static polarizability leads to non-negligible shifts that improve the agreement to essentially quantitative levels (0.03 eV) with full-system calculations. Good agreement with the positions of the experimental absorption maxima measured in solution is also observed.

A Combined Quantum Mechanics and Molecular Mechanics Approach for Simulating the Optical Properties of DNA-Stabilized Silver Nanoclusters

DNA-stabilized silver nanoclusters have emerged as an intriguing type of nanomaterial due to their unique optical and electronic properties, with potential applications in areas such as biosensing and imaging. The development of efficient methods for modeling these properties is paramount for furthering the understanding and utilization of these clusters. In this study, a hybrid quantum mechanical and molecular mechanical approach for modeling the optical properties of a DNA-templated silver nanocluster is evaluated. The influence of different parameters, including ligand fragmentation, damping, embedding potential, basis set, and density functional, is investigated. The results demonstrate that the most important parameter is the type of atomic properties used to represent the ligands, with isotropic dipole-dipole polarizabilities outperforming the rest. This underscores the importance of an appropriate representation of the ligands, particularly through the selection of the properties used to represent them. Moreover, the results are compared to experimental data, showing that the applied methodology is reliable and effective for the modeling of DNA-stabilized silver nanoclusters. These findings offer valuable insights that may guide future computational efforts to explore and harness the potential of these novel systems.

Solvation Effects on Polarizability of Aromatic Fluids

Elucidating solvation effects on polarizability in condensed phases is important for the description of the optical and dielectric behavior of high-refractive-index molecular materials. We study these effects via the polarizability model combining electronic, solvation, and vibrational contributions. The method is applied to well-characterized highly polarizable liquid precursors: benzene, naphthalene, and phenanthrene. We find that the solvation and vibrational terms are of opposite signs and cancel almost exactly for benzene, but for naphthalene and phenanthrene, a 2.5 and 5.0% decrease relative to the equilibrium electronic polarizability of the respective monomer, α₁^e, is predicted, respectively. The increase in electronic polarizability affects interaction polarizability of all contacts, which is the main reason for the increasing importance of solvation contribution. The calculated refractive indices agree very well with experiment for all three systems.

Theoretical Study on Thermal Structural Fluctuation Effects of Intermolecular Configurations on Singlet Fission in Pentacene Crystal Models

Singlet fission (SF) occurs as a result of complex excited state relaxation dynamics in molecular aggregates, where a singlet exciton (FE) state is converted into a double-triplet exciton (TT) state through the interactions with several other degrees of freedom, such as nuclear motions. In this study, we combined quantum dynamics simulation based on the quantum master equation approach with all-atom-based classical molecular mechanics/molecular dynamics to examine the thermal structural fluctuation (i.e., static disorder) effects of intermolecular configuration on SF in pentacene crystal models. In particular, we considered two types of static-disordered models, in which excited states are assumed to interact with nuclear motions of intermolecular modes in the classical mechanical/statistical manner. We found that the introduction of static disorder effects leads to a faster decay of coherence between the FE and charge transfer (CT) states in the early stage of SF, contributing to the accelerations of several FE → TT relaxation pathways. Such acceleration in these models is shown to be attributed to fluctuations in the energies and electronic coupling of the CT states based on relative relaxation factor analysis. The present study is expected to contribute to further development of bottom-up materials design for efficient SF in condensed phases where the exitonic system interacts with nuclear motions in various coupling strengths.

Comparison of approximate intermolecular potentials for ab initio fragment calculations on medium sized N-heterocycles

The ground state intermolecular potential of bimolecular complexes of N‐heterocycles is analyzed for the impact of individual terms in the interaction energy as provided by various, conceptually different theories. Novel combinations with several formulations of the electrostatic, Pauli repulsion, and dispersion contributions are tested at both short‐ and long‐distance sides of the potential energy surface, for various alignments of the pyrrole dimer as well as the cytosine–uracil complex. The integration of a DFT/CCSD density embedding scheme, with dispersion terms from the effective fragment potential (EFP) method is found to provide good agreement with a reference CCSD(T) potential overall; simultaneously, a quantum mechanics/molecular mechanics approach using CHELPG atomic point charges for the electrostatic interaction, augmented by EFP dispersion and Pauli repulsion, comes also close to the reference result. Both schemes have the advantage of not relying on predefined force fields; rather, the interaction parameters can be determined for the system under study, thus being excellent candidates for ab initio modeling.

Molecular versus Excitonic Disorder in Individual Artificial Light-Harvesting Systems

Natural light-harvesting antennae employ a dense array of chromophores to optimize energy transport via the formation of delocalized excited states (excitons), which are critically sensitive to spatio-energetic variations of the molecular structure. Identifying the origin and impact of such variations is highly desirable for understanding and predicting functional properties yet hard to achieve due to averaging of many overlapping responses from individual systems. Here, we overcome this problem by measuring the heterogeneity of synthetic analogues of natural antennae-self-assembled molecular nanotubes-by two complementary approaches: single-nanotube photoluminescence spectroscopy and ultrafast 2D correlation. We demonstrate remarkable homogeneity of the nanotube ensemble and reveal that ultrafast (∼50 fs) modulation of the exciton frequencies governs spectral broadening. Using multiscale exciton modeling, we show that the dominance of homogeneous broadening at the exciton level results from exchange narrowing of strong static disorder found for individual molecules within the nanotube. The detailed characterization of static and dynamic disorder at the exciton as well as the molecular level presented here opens new avenues in analyzing and predicting dynamic exciton properties, such as excitation energy transport.

Multiscale modeling of molecular structure and optical properties of complex supramolecular aggregates

Supramolecular aggregates of synthetic dye molecules offer great perspectives to prepare biomimetic functional materials for light-harvesting and energy transport. The design is complicated by the fact that structure–property relationships are hard to establish, because the molecular packing results from a delicate balance of interactions and the excitonic properties that dictate the optics and excited state dynamics, in turn sensitively depend on this packing. Here we show how an iterative multiscale approach combining molecular dynamics and quantum mechanical exciton modeling can be used to obtain accurate insight into the packing of thousands of cyanine dye molecules in a complex double-walled tubular aggregate in close interaction with its solvent environment. Our approach allows us to answer open questions not only on the structure of these prototypical aggregates, but also about their molecular-scale structural and energetic heterogeneity, as well as on the microscopic origin of their photophysical properties. This opens the route to accurate predictions of energy transport and other functional properties.

Multiscale modeling resolves the molecular structure of a synthetic light-harvesting complex, unraveling the microscopic origin of its photophysical properties.

Substituent effects on energetics and crystal morphology modulate singlet fission in 9,10-bis(phenylethynyl)anthracenes

Singlet fission (SF) converts a singlet exciton into two triplet excitons in two or more electronically coupled organic chromophores, which may then be used to increase solar cell efficiency. Many known SF chromophores are unsuitable for device applications due to chemical instability or low triplet state energies. The results described here show that efficient SF occurs in derivatives of 9,10-bis(phenylethynyl)anthracene (BPEA), which is a highly robust and tunable chromophore. Fluoro and methoxy substituents at the 4- and 4'-positions of the BPEA phenyl groups control the intermolecular packing in the crystal structure, which alters the interchromophore electronic coupling, while also changing the SF energetics. The lowest excited singlet state (S₁) energy of 4,4'-difluoro-BPEA is higher than that of BPEA so that the increased thermodynamic favorability of SF results in a (16 ± 2 ps)^-1 SF rate and a 180% ± 16% triplet yield, which is about an order of magnitude faster than BPEA with a comparable triplet yield. By contrast, 4-fluoro-4'-methoxy-BPEA and 4,4'-dimethoxy-BPEA have slower SF rates, (90 ± 20 ps)^-1 and (120 ± 10 ps)^-1, and lower triplet yields, (110 ± 4)% and (168 ± 7)%, respectively, than 4,4'-difluoro-BPEA. These differences are attributed to changes in the crystal structure controlling interchromophore electronic coupling as well as SF energetics in these polycrystalline solids.

Theoretical Study of the Charge Transfer Exciton Binding Energy in Semiconductor Materials for Polymer:Fullerene-Based Bulk Heterojunction Solar Cells

Recent efforts and progress in polymer solar cell research have boosted the photovoltaic efficiency of the technology. This efficiency depends not only on the device architecture but also on the material properties. Thus, insight into the design of novel semiconductor materials is vital for the advancement of the field. This paper looks from a theoretical viewpoint into two of the factors for the design of semiconductor materials with applications to bulk heterojunction solar cells: the charge transfer exciton binding energy and the nanoscale arrangement of donor and acceptor molecules in blend systems. Being aware that the exciton dissociation of local excitons in charge transfer states initiates the charge generation process, the excited state properties of four oligomers (one donor-type: PEO-PPV; and three donor-acceptor-types: PTFB, PTB7, and PTB7-Th) and two fullerene derivatives ([60]PCBM and [70]PCBM), previously reported in the literature as having high electrical conductance, are studied. With such a study, the donor molecules, either of donor-type or donor-acceptor type, are screened as candidates for [60]PCBM- and/or [70]PCBM-based bulk heterojunctions. The charge transfer energy and charge transfer exciton binding energy of suitable donor:acceptor bulk heterojunctions, some of them not yet fabricated, are studied. Further, the charge transfer exciton binding energies of [60]PCBM- and [70]PCBM-based blends are compared. A combination of molecular dynamics simulations with calculations based on Kohn-Sham density functional theory (KS-DFT) and its time-dependent extension (KS-TDDFT) is used. An important feature of this work is that it incorporates the effect of the environment of the quantum chemical system in KS-DFT or KS-TDDFT calculations through a polarizable discrete reaction field (DRF). Our predictions in terms of the influence of the nanoscale arrangement of donor and acceptor molecules on the performance of organic solar cells indicate that bulk heterojunction morphologies for donor-acceptor-type oligomers lead to their lowest excited states having charge transfer character. Further, we find that in terms of favorable charge transfer exciton binding energy, the PTB7-Th:[70]PCBM blends outperform the other blends.

Decomposition of molecular properties

We review recent work on property decomposition techniques using quantum chemical methods and discuss some topical applications in terms of quantum mechanics-molecular mechanics calculations and the constructing of properties of large molecules and clusters. Starting out from the so-called LoProp decomposition scheme [Gagliardi et al., J. Chem. Phys., 2004, 121, 4994] for extracting atomic and inter-atomic contributions to molecular properties we show how this method can be generalized to localized frequency-dependent polarizabilities, to localized hyperpolarizabilities and to localized dispersion coefficients. Some applications of the generalized decomposition technique are reviewed - calculations of frequency-dependent polarizabilities, Rayleigh scattering of large clusters, and calculations of hyperpolarizabilities of proteins.

Molecular Dynamics Simulations for Biological Systems

Molecular dynamics simulation is an important tool to capture the dynamicity of biological molecule and the atomistic insights. These insights are helpful to explore biological functions. Molecular dynamics simulation from femto seconds to milli seconds scale give a large ensemble of conformations that can reveal many biological mysteries. The main focus of the chapter is to throw light on theories, requirement of molecular dynamics for biological studies and application of molecular dynamics simulations. Molecular dynamics simulations are widely used to study protein-protein interaction, protein-ligand docking, effects of mutation on interactions, protein folding and flexibility of the biological molecules. This chapter also deals with various methods/algorithms of protein tertiary structure prediction, their strengths and weaknesses.

Singlet Fission via an Excimer-Like Intermediate in 3,6-Bis(thiophen-2-yl)diketopyrrolopyrrole Derivatives

Singlet fission (SF) in polycrystalline thin films of four 3,6-bis(thiophen-2-yl)diketopyrrolopyrrole (TDPP) chromophores with methyl (Me), n-hexyl (C6), triethylene glycol (TEG), and 2-ethylhexyl (EH) substituents at the 2,5-positions is found to involve an intermediate excimer-like state. The four different substituents yield four distinct intermolecular packing geometries, resulting in variable intermolecular charge transfer (CT) interactions in the solid. SF from the excimer state of Me, C6, TEG, and EH takes place in τSF = 22, 336, 195, and 1200 ps, respectively, to give triplet yields of 200%, 110%, 110%, and 70%, respectively. The transient spectra of the excimer-like state and its energetic proximity to the lowest excited singlet state in these derivatives suggests that this state may be the multiexciton (1)(T1T1) state that precedes formation of the uncorrelated triplet excitons. The excimer decay rates correlate well with the SF efficiencies and the degree of intermolecular donor-acceptor interactions resulting from π-stacking of the thiophene donor of one molecule with the DPP core acceptor in another molecule as observed in the crystal structures. Such interactions are found to also increase with the SF coupling energies, as calculated for each derivative. These structural and spectroscopic studies afford a better understanding of the electronic interactions that enhance SF in chromophores having strong intra- and intermolecular CT character.

First Hyperpolarizability of Collagen Using the Point Dipole Approximation

The application of localized hyperpolarizabilities to predict a total protein hyperpolarizability is presented for the first time, using rat-tail collagen as a demonstration example. We employ a model comprising the quadratic Applequist point-dipole approach, the so-called LoProp transformation, and a procedure with molecular fractionation using conjugate caps to determine the atomic and bond contributions to the net β tensor of the collagen [(PPG)10]3 triple-helix. By using Tholes exponential damping modification to the dyadic tensor in the Applequist equations, a correct qualitative agreement with experiment is found. The intensity of the βHRS signal and the depolarization ratios are best reproduced by decomposing the LoProp properties into the atomic positions and using Tholes exponential damping with the original damping parameter. Some ramifications of the model for general protein property optimization are briefly discussed.

Tailoring the properties of quadruplex nucleobases for biological and nanomaterial applications

Guanine DNA quadruplexes are interesting and important biological objects because they represent potential targets for regulatory drugs. Their use as building blocks for biomaterial applications is also being investigated. This contribution reports the in silico design of artificial building blocks derived from xanthine. Methods of quantum chemistry were used to evaluate the properties of xanthine structures relative to those containing guanine, the natural reference used. Tailoring the xanthine core showed that the base stacking and the ion coordination were significantly enhanced in the designed systems, while the ion-transport properties were not affected. Our study suggests that the 9-deaza-8-haloxanthine bases (where the halogen is fluorine or chlorine) are highly promising candidates for the development of artificial quadruplexes and quadruplex-active ligands.

Pointillist rendering of electron charge and spin density suffices to replicate trends in atomic properties

The monotonic and non-monotonic variations of atomic properties within and between the rows of the periodic table underlie our understanding of chemistry and accounting for these variations has been a signature strength of quantum mechanics (QM). However, the computational burden of QM motivates the development of more efficient means of describing electrons and reactivity. The recently developed LEWIS • model incorporates lessons learnt from QM into a force field that includes electrons as explicit pseudo-classical particles. Here, we extend LEWIS • across the 2 p and 3 p elements, and show that it is capable of reproducing both monotonic and non-monotonic variations of chemically important atomic properties in a cost-effective manner. An indicator of the strength of the construct is the ability of pairwise potentials trained on ionization energies and the order of spin configurations to predict atomic polarizabilities. In this manner, some insights of QM are uncoupled from its onerous computational burden.

Designing a New Class of Bases for Nucleic Acid Quadruplexes and Quadruplex-Active Ligands

A new class of quadruplex nucleobases, derived from 3-deazaguanine, has been designed for various applications as smart quadruplex ligands as well as quadruplex-based aptamers, receptors, and sensors. An efficient strategy for modifying the guanine quadruplex core has been developed and tested by using quantum chemistry methods. Several potential guanine derivatives modified at the 3- or 8-position or both are analyzed, and the results compared to reference systems containing natural guanine. Analysis of the formation energies (BLYP-D3(BJ)/def2-TZVPP level of theory, in combination with the COSMO model for water) in model systems consisting of two and three stacked tetrads with Na(+) /K(+) ion(s) inside the internal channel indicates that the formation of structures with 3-halo-3-deazaguanine bases leads to a substantial gain in energy, as compared to the corresponding reference guanine complexes. The results cast light on changes in the noncovalent interactions (hydrogen bonding, stacking, and ion coordination) in a quadruplex stem upon modification of the guanine core. In particular, the enhanced stability of the modified quadruplexes was shown to originate mainly from increased π-π stacking. Our study suggests the 3-halo-3-deazaguanine skeleton as a potential building unit for quadruplex systems and smart G-quadruplex ligands.

Models of charge pair generation in organic solar cells

A critical perspective on modelling of charge generation in organic photovoltaics, focussing on interfacial electronic states, electrostatics, and dynamic processes.

A periodic charge-dipole electrostatic model. II. A kinetic-exchange-correlation correction

We extend the periodic charge-dipole electrostatic model, see I. V. Bodrenko, M. Sierka, E. Fabiano, and F. Della Sala, J. Chem. Phys. 137, 134702 (2012), to include a kinetic-exchange-correlation (KXC) correction. The KXC correction is approximated by means of an extended-Hückel-type formula, it is exact in the infinite jellium model and it is also computationally efficient as it requires only the computation of overlap integrals. Tests on the linear response of silver slabs to an external electrostatic perturbation show that the KXC correction yields a very accurate description of induced dipole and of the whole induced charge density profile. We also show that the KXC parameters are quite transferable and related to the atomic polarizability.

Benchmark study on the smallest bimolecular nucleophilic substitution reaction: H⁻+CH₄-->CH₄+H⁻

We report here a benchmark study on the bimolecular nucleophilic substitution (S(N)2) reaction between hydride and methane, for which we have obtained reference energies at the coupled cluster toward full configuration-interaction limit (CC-cf/CBS). Several wavefunction (HF, MP2, coupled cluster) and density functional methods are compared for their reliability regarding these reference data.

Fluorescence of tryptophan in designed hairpin and Trp-cage miniproteins: measurements of fluorescence yields and calculations by quantum mechanical molecular dynamics simulations

The quantum yield of tryptophan (Trp) fluorescence was measured in 30 designed miniproteins (17 β-hairpins and 13 Trp-cage peptides), each containing a single Trp residue. Measurements were made in D(2)O and H(2)O to distinguish between fluorescence quenching mechanisms involving electron and proton transfer in the hairpin peptides, and at two temperatures to check for effects of partial unfolding of the Trp-cage peptides. The extent of folding of all the peptides also was measured by NMR. The fluorescence yields ranged from 0.01 in some of the Trp-cage peptides to 0.27 in some hairpins. Fluorescence quenching was found to occur by electron transfer from the excited indole ring of the Trp to a backbone amide group or the protonated side chain of a nearby histidine, glutamate, aspartate, tyrosine, or cysteine residue. Ionized tyrosine side chains quenched strongly by resonance energy transfer or electron transfer to the excited indole ring. Hybrid classical/quantum mechanical molecular dynamics simulations were performed by a method that optimized induced electric dipoles separately for the ground and excited states in multiple π-π* and charge-transfer (CT) excitations. Twenty 0.5 ns trajectories in the tryptophan's lowest excited singlet π-π* state were run for each peptide, beginning by projections from trajectories in the ground state. Fluorescence quenching was correlated with the availability of a CT or exciton state that was strongly coupled to the π-π* state and that matched or fell below the π-π* state in energy. The fluorescence yields predicted by summing the calculated rates of charge and energy transfer are in good accord with the measured yields.

A periodic charge-dipole electrostatic model: parametrization for silver slabs

We present an extension of the charge-dipole model for the description of periodic systems. This periodic charge-dipole electrostatic model (PCDEM) allows one to describe the linear response of periodic structures in terms of charge- and dipole-type gaussian basis functions. The long-range electrostatic interaction is efficiently described by means of the continuous fast multipole method. As a first application, the PCDEM method is applied to describe the polarizability of silver slabs. We find that for a correct description of the polarizability of the slabs both charges and dipoles are required. However a continuum set of parametrizations, i.e., different values of the width of charge- and dipole-type gaussians, leads to an equivalent and accurate description of the slabs polarizability but a completely unphysical description of induced charge-density inside the slab. We introduced the integral squared density measure which allows one to obtain a unique parametrization which accurately describes both the polarizability and the induced density profile inside the slab. Finally the limits of the electrostatic approximations are also pointed out.

Off-planar geometry and structural instability of EDO-TTF explained by using the extended debye polarizability model for bond angles

The geometry of ethylenedioxy-tetrathiafulvalene, EDO-TTF, plays an important role in the metal-insulator transition in the charge transfer salt (EDO-TTF)(2)PF(6). The planar and off-planar geometrical conformations of the EDO-TTF molecules are explained using an extended Debye polarizability model for the bond angle. The geometrical structure of EDO-TTF is dictated by its four sulfur bond angles and these are, in turn, determined by the polarizability of the sulfur atoms. With Hartree-Fock and second-order Møller-Plesset perturbation theory calculations on EDO-TTF, TTF, H(2)S, and their oxygen and selenium substituted counterparts we confirm this hypothesis. The Debye polarizability model for bond angles relates directly the optimum bond angle with the polarizability of the center atom. Considering the (EDO-TTF)(2)PF(6) material in this light proves to be very fruitful.

Current status of the AMOEBA polarizable force field

Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with AMOEBA for demanding problems such as relative conformational energies of the alanine tetrapeptide and isomers of water sulfate complexes. AMOEBA is shown to be especially successful on protein-ligand binding and computational X-ray crystallography where polarization and accurate electrostatics are critical.

Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability. Theory and applications

A current emphasis in empirical force fields is on the development of potential functions that explicitly treat electronic polarizability. In the present article, the commonly used methodologies for modelling electronic polarization are presented along with an overview of selected application studies. Models presented include induced point-dipoles, classical Drude oscillators, and fluctuating charge methods. The theoretical background of each method is followed by an introduction to extended Langrangian integrators required for computationally tractable molecular dynamics simulations using polarizable force fields. The remainder of the review focuses on application studies using these methods. Emphasis is placed on water models, for which numerous examples exist, with a more thorough discussion presented on the recently published models associated with the Drude-based CHARMM and the AMOEBA force fields. The utility of polarizable models for the study of ion solvation is then presented followed by an overview of studies of small molecules (e.g. CCl(4), alkanes, etc) and macromolecule (proteins, nucleic acids and lipid bilayers) application studies. The review is written with the goal of providing a general overview of the current status of the field and to facilitate future application and developments.

Trypsin-ligand binding free energies from explicit and implicit solvent simulations with polarizable potential

We have calculated the binding free energies of a series of benzamidine-like inhibitors to trypsin with a polarizable force field using both explicit and implicit solvent approaches. Free energy perturbation has been performed for the ligands in bulk water and in protein complex with molecular dynamics simulations. The binding free energies calculated from explicit solvent simulations are well within the accuracy of experimental measurement and the direction of change is predicted correctly in all cases. We analyzed the molecular dipole moments of the ligands in gas, water and protein environments. Neither binding affinity nor ligand solvation free energy in bulk water shows much dependence on the molecular dipole moments of the ligands. Substitution of the aromatic or the charged group in the ligand results in considerable change in the solvation energy in bulk water and protein whereas the binding affinity varies insignificantly due to cancellation. The effect of chemical modification on ligand charge distribution is mostly local. Replacing benzene with diazine has minimal impact on the atomic multipoles at the amidinium group. We have also utilized an implicit solvent based end-state approach to evaluate the binding free energies of these inhibitors. In this approach, the polarizable multipole model combined with Poisson-Boltzmann/surface area (PMPB/SA) provides the electrostatic interaction energy and the polar solvation free energy. Overall the relative binding free energies obtained from the MM-PMPB/SA model are in good agreement with the experimental data.

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.

QUILD: QUantum-regions interconnected by local descriptions

A new program for multilevel (QM/QM and/or QM/MM) approaches is presented that is able to combine different computational descriptions for different regions in a transparent and flexible manner. This program, designated QUILD (for QUantum-regions Interconnected by Local Descriptions), uses adapted delocalized coordinates (Int J Quantum Chem 2006, 106, 2536) for efficient geometry optimizations of equilibrium and transition-state structures, where both weak and strong coordinates may be present. The Amsterdam Density Functional (ADF) program is used for providing density functional theory and MM energies and gradients, while an interface to the ORCA program is available for including RHF, MP2, or semiempirical descriptions. The QUILD optimization setup reduces the number of geometry steps needed for the Baker test-set of 30 organic molecules by approximately 30% and for a weakly-bound test-set of 18 molecules by approximately 75% compared with the old-style optimizer in ADF, i.e., a speedup of roughly a factor four. We report two examples of using geometry optimizations with numerical gradients, for spin-orbit relativistic ZORA and for excited-state geometries. Finally, we show examples of its multilevel capabilities for a number of systems, including the multilevel boundary region of amino acid residues, an S(N)2 reaction in the gas-phase and in solvent, and a DNA duplex.

Time-dependent density functional theory/discrete reaction field spectra of open shell systems: The visual spectrum of [FeIII(PyPepS)2]− in aqueous solution

We report the calculated visible spectrum of [FeIII(PyPepS)2]- in aqueous solution. From all-classical molecular dynamics simulations on the solute and 200 water molecules with a polarizable force field, 25 solute/solvent configurations were chosen at random from a 50 ps production run and subjected the systems to calculations using time-dependent density functional theory (TD-DFT) for the solute, combined with a solvation model in which the water molecules carry charges and polarizabilities. In each calculation the first 60 excited states were collected in order to span the experimental spectrum. Since the solute has a doublet ground state several excitations to states are of type "three electrons in three orbitals," each of which gives rise to a manifold of a quartet and two doublet states which cannot properly be represented by single Slater determinants. We applied a tentative scheme to analyze this type of spin contamination in terms of Delta and Delta transitions between the same orbital pairs. Assuming the associated states as pure single determinants obtained from restricted calculations, we construct conformation state functions (CFSs), i.e., eigenfunctions of the Hamiltonian Sz and S2, for the two doublets and the quartet for each Delta,Delta pair, the necessary parameters coming from regular and spin-flip calculations. It appears that the lower final states remain where they were originally calculated, while the higher states move up by some tenths of an eV. In this case filtering out these higher states gives a spectrum that compares very well with experiment, but nevertheless we suggest investigating a possible (re)formulation of TD-DFT in terms of CFSs rather than determinants.

Acyl chain order parameter profiles in phospholipid bilayers: computation from molecular dynamics simulations and comparison with 2H NMR experiments

Order parameters from deuterium NMR are often used to validate or calibrate molecular dynamics simulations. This paper gives a short overview of the literature in which experimental order parameters from (2)H NMR are compared to those calculated from MD simulations. The different ways in which order parameters from experiment are used to calibrate and validate simulations are reviewed. In the second part of this review, a case study of cholesterol in a DMPC bilayer is presented. It is concluded that the agreement between experimental data and simulation is favorable in the hydrophobic region of the membrane, for both the phospholipids and cholesterol. In the interfacial region the agreement is less satisfactory, probably because of the high polarity of this region which makes the correct computation of the electrostatics more complex.