Ruiqin ZHANG
City University of Hong Kong

As is well known, ab initio calculations have been used for a long time in determining the structures and properties of molecular systems. With a good quality basis set, satisfactory agreements with experiments or predictions have been achieved based on ab initio calculations for many small or medium size molecular systems in terms of their energetic, spectroscopic, and other properties. However, the computational requirement inherent in conventional ab initio methods precludes their applications in very large molecular systems, especially when coupling with large and complicated systems in materials science, clusters, solvents, and biology, which need urgent understanding or interpretation by means of theoretical studies. It would be desirable if the use of basis functions could be minimized so that large systems could be studied using ab initio methods. Toward the goal, we have proposed a scheme of efficiently using basis sets in ab initio calculations and demonstrated its efficiencies in a number of representative systems over the years. 
In this presentation, I will oultline the practical and effective scheme for choosing basis sets for ab initio calculations and the application of the economic basis sets. In the economical basis sets, we consider the different roles of the different basis functions, including the polarization and diffuse functions, adopted in the basis set, and the nature and the environment of the atom. With the scheme, the number and level of basis functions to describe an atom should be increased in the order from left to right of its appearance in the periodic table. For a negatively charged atom, larger basis functions including polarization functions and diffuse functions should be used; while the basis functions for positively charged atoms are reduced and may not adopt any polarization or diffuse functions. For the systems involving hydrogen-bonding, weak interactions, functional groups, metallic bonding with zero valence or low positive valence, and other sensitive interactions, the polarization and diffuse functions must be used. The economic composite basis sets have been applied to a variety of systems, from small molecules to very large compounds, even in excited states. Compared with the calculations by conventional basis sets at different levels, the economic composite basis set can accurately predict the structures and properties of compounds with much reduced CPU time.

Wei WU
Xiamen University

The n-body reduced density matrix (RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. A more generalized Wick’s theorem is proved, which is an extension of generalized Wick’s theorem to the case of nonorthogonal basis set and to the products of any number of reduced density operators. Using tensor analysis tool for nonorthogonal basis functions, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly expressed in terms of tensor contractions of electronic integrals and n-body RDMs of the reference VBSCF wave function. An automatic formula/code generator (AFCG) for nonorthogonal orbital-based many-electronic theory will be developed. By using AFCG, a new Hessian-based algorithm for VBSCF method is implemented. The benchmark VBSCF calculations up to 24 active electrons in 24 active orbitals are preformed. 

Reference
1.    Chen, Z.; Chen, X.; Wu, W., J. Chem. Phys., 2013, 138, 164119.
2.   Chen, Z.; Chen, X.; Wu, W., J. Chem. Phys., 2013, 138, 164120.

Donghui ZHANG
Dalian Institute of Chemical Physics, CAS

In this talk, I will present some of our recent work on theoretical studies of the H/F/O(1D)+CH4 and H+SiH4 reactions. For the H/F+CH4 and H+SiH4 reactions, accurate potential energy surfaces for these systems are constructed using neural network fitting method. They are found to be considerably more accurate than existing potential energy surfaces fitted by using permutation invariant polynomials. High dimensional quantum reactive scattering calculations were performed to obtain final state resolved integral and differential cross sections for these reactions. Comparisons between theory and experiment reveal that theory now is capable of producing dynamical information for these polyatomic reactions rather reliably. While for the O(1D)+CH4 reaction, a global full dimensional potential energy surface was constructed using permutation invariant polynomial fitting due to huge number of ab initio energies included. The deep well in the system and multiple channel nature of the reaction make quantum dynamics calculations, even under reduced dimensionality approximation, infeasible. Consequently, we carried out extensive quasiclassical trajectory calculations on the reaction which revealed a new reaction mechanism for this reaction.

Zexing CAO
Xiamen University

Enzymatic catalysis and photoinduced excited-state dynamics of DNA nucleobases have attracted considerable interest over the past decades. Using ab initio QM/MM MD simulations, we have investigated the structural features of zinc enzymes, nucleoside hydrolases, and deaminases and plausible enzymatic mechanisms. Theoretically, the electronic structure calculations on the decay channels and conical intersections in DNA nucleobases and their analogues have identified the main internal conversion pathways, and further dynamics simulations may provide information about the relative efficiency of related decay channels. Here we performed a series of QM and QM/MM simulations on the excited-state dynamics of three organic conjugated molecules including two base analogues in the gas phase and in solution. At the ab initio level of theory, their excited-state lifetimes and possible decay pathways were explored in detail. Based on the hybrid QM/MM MD simulations with surface hopping, the influence of solvent on their nonadiabatic dynamics properties was also discussed. This talk will cover our recent studies of the catalytic ring-opening of GlcN6P by SmuNagB and the ultrafast nonadiabatic decay of the nucleobase-related systems in the gas phase and in water.

Kenneth Merz 
Michigan State University

Docking (posing) calculations coupled with binding free energy estimates (scoring) are a mainstay of structure-based drug design. Docking and scoring methods have steadily improved over the years, but remain challenging because of the extensive sampling that is required, the need for accurate scoring functions and challenges encountered in accurately estimating entropy effects. This talk addresses the use of ensemble principles to directly address these issues and, thereby, accurately estimate protein-ligand binding free energies. In particular, we analytically demonstrate that sampling reduces computed binding free energy uncertainties and then highlight several methods that incorporate these concepts. For example, the moveable type method, employs an elegant approach to generate the necessary ensembles by using a “binned” pairwise knowledge-based potential combined with atom pair probabilities extracted from known protein-ligand complexes. This allows us to rapidly compute the ligand, protein and protein-ligand (inclusive of solvation effects) ensembles which then can be used to directly estimate protein-ligand binding free energies using basic statistical mechanical principles. This approach improves the quality of the potential (scoring) function by reducing computational uncertainty, sampling phase space in one shot and accurately incorporating entropy effects. This allows us to compute binding free energies rapidly, accurately and yields molecular poses at a minimal computational cost relative to currently available methods based on statistical mechanics.  

Jiali GAO
University of Minnesota

Atomistic simulation and modeling of biomolecular systems and quantitative analysis of protein-ligand interactions are generally performed with the use of molecular mechanical potentials, or force fields.  Although the current force fields have been very successful thanks to the parameterization by many groups around the world in the past half a century, the formalisms and the functional terms have hardly changed. To increase the accuracy and predictability in biomolecular simulation, and ultimately in drug discovery, we have developed a novel theoretical framework for a quantum force field, in which the functional form is based on electronic structural theory explicitly. In this talk, I will present the explicit polarization (X-Pol) theory, which relies on block-localization of molecular fragments, by separating a large molecular system such as a fully solvated protein into subsystem molecular or group fragments. In X-Pol, the total molecular wave function is approximated as a Hartree product of the antisymmetric wave functions of individual fragments. The exchange repulsion, dispersion and charge transfer effects are approximated empirically, or can be determined ab initio. Some recent development and applications are illustrated including the XP3P model for water.

Pengyu REN
The University of Texas at Austin

Molecular recognition between biomolecules such as ligand-receptor, protein-DNA and antigen-antibody is essential for many biological processes and biomedical applications from drug discovery to biosensor design. Multiple factors, including shape complementary, electrostatic interaction, solvent effect and protein dynamics, are responsible for the specificity and selectivity in molecular recognition. While computer simulations are routinely utilized in the study of biomolecular structure and interactions, accurate evaluation of binding free energy and thermodynamics for ligand-protein or host-guest systems in general remains elusive due to the lack of adequate potential energy models and difficulty in statistical sampling of dynamic events. To address these challenges, we have been developing a next-generation physical model with improved electrostatic representation based on atomic multipoles and explicit many-body polarization. The AMOEBA polarizable force field has shown encouraging accuracy for a range of molecular systems including ions, small organics and proteins, from gas-phase to liquid and crystal properties. Using this model, we have evaluated binding thermodynamics of several protein-ligand with encouraging successes and demonstrated the importance of accurate modeling of short-ranged electrostatic forces in molecular recognition. I will present these results along with the development of AMOEBA polarizable force field model as well as discussion on the effectiveness of free energy simulation methods.

Yingkai ZHANG
New York University

Reliable molecular modeling of complex systems is critically dependent on the accuracy of the employed molecular mechanical force field. The present chapter describes our recent efforts to elucidate origin of one key limitation of current force fields, and thus to facilitate the development of a new generation of ab initio quantum mechanics based force fields. Our theoretical approaches center on a recently developed density-based energy decomposition analysis (DEDA) method [J. Chem. Phys., 131, 164112 (2009)]. This new advance allows an unprecedented clean separation of intermolecular interactions into very meaningful individual terms for force field analysis and development. Here we first employed the DEDA approach to tackle one well-known challenge for widely used biomolecular force fields, which is the description of hydrogen bonding directionality at the receptor atom. Contrary to the conventional wisdom, we find that the sum of electrostatic and van der Waals interaction components is the dominant factor in determining directional dependence of hydrogen bonding, while the density relaxation term, including both polarization and charge-transfer contributions, plays a very minor role. Then using the DEDA results as reference, we demonstrate that the main failure coming from the atomic point charge model can be overcome largely by introducing extra charge sites or higher order multipole moments. Among all the electrostatic models explored, the smeared charge distributed multipole model (up to quadrupole), which also takes account of charge penetration effects, gives the best agreement with the corresponding DEDA results. Finally, we found that a B3LYP-D3 dispersion term, which is screened at short-range and has a correct long-rang behavior, plus a Born-Mayer exponential function for repulsion is an excellent function form to model vdW interactions. In combination with a smeared charge multipole model for electrostatics interactions, the resulted force field is found to yield excellent results in reproducing rare gas interaction energies calculated at the CCSD(T)/CBS level. These progresses have set a solid foundation for systematic force field development based on first principal quantum mechanical calculations.

Changge JI
East China Normal University

A major challenge in the present force field development is how to accurately describe electrostatic interaction in biomolecular systems, in particular, how to properly include the polarization effect in MD simulation. We have developed a practical polarizable model, termed Effective Polarizable Bond method (EPB), to include polarization effects efficiently in biomolecular simulation. The EPB model keeps the “effective charge” character of the classical force field and provides a good correction to the traditional force field for MD simulation by introducing “fluctuating" character for atomic charges of polarizable groups. Different from other polarizable models, the dynamic effect polarization cost energy is implicitly included in the present method.

Ray LUO
University of California, Irvine

Atomistic simulations of biomolecules provide a detailed view of structure and dynamics that complement experiments. Increased conformational sampling, enabled by new algorithms and growth in computer power, now allows a much broader range of events to be observed, providing critical insights, largely inaccessible to experiments, such as characterization of the unfolded state or the transiently populated intermediates that occur during complex binding and recognition events. The Amber force field consortium have made significant inroads towards accurately representing the energetic surfaces relevant to both the native and non-native states of proteins and nucleic acids. In this talk, I will provide an overview of our latest efforts in protein force field and solvent model developments, in both atomistic and continuum representations that are widely used in bimolecular simulations.

Yundong WU
Peking University

Despite several decades’ intensive efforts, the development of accurate protein force fields remains as a major challenge. There are two key issues: (1) How to obtain intrinsic conformational potentials of each amino acid residue; (2) How to effectively incorporate these conformational potentials into a force field. We have developed novel strategies to address the above two issues. Namely, intrinsic conformational potentials can be obtained by the statistical analysis of protein coil library, and these conformational features can be effectively incorporated into a force field by using residue specific torsional functions. Using these strategies, we can easily develop much improved protein force fields.  These force fields can better reproduce experimental NMR J coupling constants of short peptides and full length amyloid-β peptides Aβ40 and Aβ42. They can fold a series of proteins.  Preliminary applications of the force fields in protein structure refinement are also presented. 

Acknowledgement: Financial support from the National Science Foundation of China (21133002, 21232001, 21302006), the Shenzhen Science and Technology Innovation Committee (KQTD201103) are acknowledged.