# Highly Accurate and Efficient Quantum Chemical Method Based on Non-Orthogonal Localized Molecular Orbitals

By Fenglong Gu*South China Normal University*

The elongation method was proposed in the early 1990’s as an effective method to achieving linear scaling for large system calculations. The elongation method works in the orthogonal localized molecular orbital (OLMO) basis. The key point of the elongation method is to neglect the contributions from frozen orbitals but the tailing of OLMOs makes it difficult. The non-orthogonal localized molecular orbital (NOLMO) is the most localized representation of electronic degrees of freedom. As such, NOLMOs are thus potentially the most efficient for linear scaling calculations of electronic structures for large systems. In this talk, direct ab initio calculations with NOLMO will be presented by solving its slow convergence in the optimization of NOLMO. An effective preconditioning approach by taking into account the diagonal elements of the second order derivatives has been proposed and it is shown that the convergence of the energy optimization is very much significantly improved. For the studies on nonlinear optical properties, we have derived the corresponding CPHF equations based on NOLMOs up to the third order, which are significantly different from those of a conventional CPHF method because of the release of the orthogonal restrictions on MOs. This work represents the first step towards efficient calculations of molecular response and excitation properties with NOLMOs. Quantum chemical methods based on NOLMOs are potentially ideal for investigating large systems, not only for energies but also for other properties.

# Seniority Number in Valence Bond Theory

By Wei Wu*The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry& College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China*

A hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, will be presented in this talk. It is found from several test examples that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller non-parallelity errors than its molecular orbital (MO) theory based analogue.

# Quantitative Prediction of Charge Mobilities of π-stacked Systems by First-principles Simulation

By Keli Han*State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, P. R .China*

This work is intended to provide chemists and physicists with a tool for predicting the charge carrier mobilities of pi-stacked systems such as organic semiconductors and the DNA double helix. An experimentally determined crystal structure is required as a starting point. The simulation involves the following steps: (i) searching the crystal structure; (ii) selecting molecular monomers and dimers from the crystal structure; (iii) using density function theory (DFT) calculations to determine electronic coupling for dimers; (iv) using DFT calculations to determine self-reorganization energy for monomers; and (v) using a numerical calculation to determine charge carrier mobility. For a single crystal structure consisting of medium-sized molecules, this protocol can be completed in ~ 4 h. To validate the approach, we have selected two case studies (a rubrene crystal and a DNA segment). The protocol is presented in a style to be understandable by ones who have engaged in simple computational work.

# Fractional Perspectives of DFT and Local Scaling Corrections

By Weitao Yang*Department of Chemistry and Physics, Duke University, Durham, N.C. 27708, U.S.A. Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China*

Fractional fractional charges and fractional spins provide a clear analysis of the errors of commonly used functionals. For an effective and universal alleviation of the delocalization error, we develop a local scaling correction scheme by imposing the Perdew-Parr-Levy- Balduz linearity condition to local regions of a system. Our novel scheme is applicable to various mainstream density functional approximations. It substantially reduces the delocalization error, as exemplified by the significantly improved description of dissociating molecules, transition-state species, and charge-transfer systems. The usefulness of our novel scheme affirms that the explicit treatment of fractional electron distributions is essentially important for reducing the intrinsic delocalization error associated with approximate density functionals.

Progress with many-body theory approach will be also be presented. We have formulated the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations, opening new a channel for density functional approximations. This method has many highly desirable properties. It has minimal delocalization error with a nearly linear energy behavior for systems with fractional charges, describes van der Waals interactions similarly and thermodynamic properties significantly better than the conventional RPA, and eliminates static correlation error for single bond systems. It is the first known functional with closed-form dependence on orbitals, which captures the energy derivative discontinuity in strongly correlated systems. We also adopted pp-RPA to approximate the pairing matrix fluctuation and then determine excitation energies by the differences of two-electron addition/removal energies. This approach captures all types of interesting excitations: single and double excitations are described accurately, Rydberg excitations are in good agreement with experimental data and CT excitations display correct 1/R dependence.

References

*A.J. Cohen, P. Mori-Sanchez, and W. T. Yang. Challenges for Density Functional Theory. Chem. Rev. 112:289, 2012**X. Zheng, A. J. Cohen, P. Mori-Sanchez, X. Q. Hu, and W. T. Yang. Improving band gap prediction in density functional theory from molecules to solids. Physical Review Letters, 107(2):026403, 2011.**Chen Li,1 Xiao Zheng, Aron J. Cohen, Paula Mori-Sánchez, and Weitao Yang, Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations Physical Review Letters 114, 053001.2015**H. van Aggelen, Y. Yang, and W. T. Yang. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation. Physical Review A, 88(3):030501, 2013.**Y. Yang, H. van Aggelen, and W. T. Yang. Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation. Journal of Chemical Physics, 139:224105, 2013.**Y. Yang, D. G. Peng, J. F. Lu, and W. T. Yang. Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies. Journal of Chemical Physics, 141:124104, 2014.*

# Substrate Translocation and Extrusion through Multidrug Transporter AcrB: Energetics and Conformational Changes

By Wenning Wang*Department of Chemistry, Fudan University*

AcrB is the inner membrane transporter of the tripartite multidrug efflux pump AcrAB-TolC in Gram-negative bacteria, which poses a major obstacle to the treatment of bacterial infections. X-ray structures have identified two types of substrate-binding pockets in the porter domains of AcrB trimer: the proximal binding pocket (PBP) and the distal binding pocket (DBP), and suggest a functional rotating mechanism in which each protomer cycles consecutively through three distinct conformational states (access, binding and extrusion). However, the details of substrate binding and translocation between the binding pockets remain elusive. In the first part of this work, we performed atomic simulations to obtain the free energy profile of the translocation of an antibiotic drug doxorubicin (DOX) inside AcrB. Our simulation indicates that DOX binds at the PBP and DBP with comparable affinities in the binding state protomer, and overcomes a 3 kcal/mol energy barrier to transit between them. Obvious conformational changes including closing of the PC1/PC2 cleft and shrinking of the DBP were observed upon DOX binding in the PBP, resulting in an intermediate state between the access and binding states. Taken together, the simulation results reveal a detailed stepwise substrate binding and translocation process in the framework of functional rotating mechanism. We next combined targeted MD, Steered MD simulations and MM-GBSA method to compare the binding and extrusion of DOX and inhibitor molecule ABI in AcrB. Targeted MD simulations show that DOX dissociates from the DBP earlier than ABI, and this is mainly due to the binding of ABI in the hydrophobic trap of the DBP. Consistently, MM-GBSA calculations gave higher binding free energy of ABI than that of DOX in the DBP of the binding monomer, while the binding free energies of the two molecules in the extrusion monomer are nearly equivalent. The PMF profiles of DOX/ABI extrusion from AcrB based on steered MD simulations demonstrate that the extrusion of ABI has to overcome higher energy barrier due to the more evident conformational changes at the exit gate as ABI was exported. Therefore, the inhibitory mechanism of ABI can be ascribed to two aspects: the stronger binding affinity in the DBP and the higher energy barrier required to pass through the exit gate.

# Exploring Long Timescale Biomolecular Events: Orthogonal Space Sampling Theory and Algorithms

By Wei Yang*Florida State University*

The "slow configuration response" problem has been the bottleneck issue in the field of advanced molecular simulation sampling. This issue has significantly limited actual sampling capability of the entire enhanced sampling scheme. To systematically tackle this challenge, the orthogonal sampling theory and methods were developed. With the maturity of this algorithm framework, substantial sampling accelerations can be readily gained. The orthogonal sampling methods and applications will be presented in this talk.

# A Mechanistic Structural View of Ras Biology

By Ruth Nussinov*Cancer and Inflammation Program, National Cancer Institute& Medical School, Tel Aviv University*

Ras proteins are small GTPases that act as signal transducers between cell surface receptors and several intracellular signaling cascades. KRas4B is among the frequently mutated oncogenes in human tumors. Ras proteins consist of highly homologous catalytic domains, and flexible C-terminal hypervariable regions (HVRs) that differ significantly across Ras isoforms. We have been focusing on key mechanistic questions in Ras biology from the structural standpoint. These include whether Ras forms dimers, and if so what is their structural landscape; how do Ras dimers activate Raf, a key Ras effector in a major signaling pathway; how calmodulin temporally inhibit Raf signaling, and the potential role of the hypervariable region and its membrane anchoring regulation. We believe that structural biology, computations and experiment, are uniquely able to tackle these fascinating questions.

# The Big Picture of Relativistic Molecular Quantum Mechanics

By Wenjian Liu*Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China*

Relativistic Molecular Quantum Mechanics (RMQM), defined as the union of Relativistic Quantum Chemistry (RQC) and Quantum Electrodynamics (QED), consists of three components (i.e., Hamiltonian, wave function, and property), each of which is confronted with some fundamental issues, including, e.g., 'What is the appropriate relativistic many-electron Hamiltonian?', 'How to make explicit and/or local representations of relativistic wave functions?', 'How to formulate relativistic properties?', 'How to interface RQC and QED?', etc. In this lecture I shall try to address these fundamental issues from both conceptual and methodological standpoints, so as to establish the big picture of RMQM.

References

*W. Liu, Ideas of relativistic quantum chemistry, Mol. Phys. 108 (2010) 1679.**W. Liu, Perspectives of relativistic quantum chemistry: The negative energy cat smiles, Phys. Chem. Chem. Phys. 14 (2012) 35.**W. Liu and I. Lindgren, Going beyond `no-pair relativistic quantum chemistry', J. Chem. Phys. 139 (2013) 014108.**W. Liu, Advances in Relativistic Molecular Quantum Mechanics, Phys. Rep. 537 (2014) 59.**W. Liu, Effective Quantum Electrodynamics Hamiltonians: A Tutorial Review, Int. J. Quantum Chem. 115 (2015) 631.**Z. Li, S. Shao, and W. Liu, Relativistic explicit correlation: Coalescence conditions and practical suggestions, J. Chem. Phys. 136 (2012) 144117.**Z. Li, H. Li, B. Suo, and W. Liu, Localization of molecular orbitals: from fragments to molecule, Acc. Chem. Res. 47 (2014) 2758.**Y. Xiao, Q. Sun, and W. Liu, Fully relativistic theories and methods for NMR parameters, Theor. Chem. Acc. 131 (2012) 1080.**Y. Xiao and W. Liu, Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor, J. Chem. Phys. 138 (2013) 134104.**Y. Xiao and W. Liu, Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor: Linear molecules, J. Chem. Phys. 139 (2013) 034113.**Y. Xiao, Y. Zhang, and W. Liu, New experimental NMR shielding scales mapped relativistically from NSR: Theory and application, J. Chem. Theory Comput. 10 (2014) 600.**W. Liu, The big picture of relativistic molecular quantum mechanics in Theory and Application in Computational Chemistry. The First Decade of the Second Millennium, AIP Conf. Proc. 156 (2012) 62.*

# Generalized Energy-based Fragmentation Approach for Electronic Structure Calculations of Large Molecules and Molecules in Condensed Phases

By Shuhua Li*School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, 210093, P. R. China*

In this talk, I will present our recent advances in developing the generalized energy-based fragmentation approach for large molecules and molecules in condensed phases. The generalized energy-based fragmentation (GEBF) approach is a linear scaling technique that can extend ab initio calculations to very large systems. Within this approach, the ground-state energy of a large molecule can be evaluated directly from energies of various small “embedded” subsystems.1 The GEBF approach has been employed to investigate relative energies of different conformers, optimized structures, vibrational spectra for a wide variety of complex systems.2-5 Recently, the GEBF approach was extended to molecular crystals with periodic boundary conditions (PBC).6 In the PBC-GEBF approach, geometry optimizations6 and vibrational frequencies of molecular crystals7 have been implemented. Our applications demonstrate that the PBC-GEBF method with molecular quantum chemistry methods is capable of providing satisfactory descriptions on the lattice energies, structures, and vibrational spectra for various types of molecular crystals. By combining the PBC-GEBF approach and molecular dynamics simulations, we can now compute the radial distribution functions, vibration spectra (IR and Raman) for molecules in solution with full quantum mechanical calculations. 8 A direct comparison between the calculation results and related experimental results allows us to gain a deeper understanding of structures and spectra of molecules in condensed phases.

References

*W. Li, S. Li, Y. Jiang J. Phys. Chem. A 2007, 111, 2193.**W. Hua, T. Fang, W. Li, J.-G. Yu, and S. Li, J. Phys. Chem. A 2008, 112, 10864.**S. Hua; W. Hua, S. Li J. Phys. Chem. A 2010, 114, 8126.**S. Hua; W. Li, S. Li ChemPhysChem. 2013, 14, 108.**S. Li, W. Li, J. Ma, Acc. Chem. Res. 2014, 47, 2712.**T. Fang; W. Li; F. Gu; S. Li J. Chem. Theory Comput. 2015, 11, 91**T. Fang; S. Li, to be submitted, 2015**8. D. Yuan; S. Li, to be submitted, 2015*

# Ab Initio Energies and Molecular Properties by Systematic Molecular Fragmentation

By Michael Collins*Research School of Chemistry, Australian National University*

Systematic molecular fragmentation describes a molecule in terms of a set of small molecular fragments. A systematic rule provides a hierarchy of estimates for the energy, structure, vibrational frequencies and other properties, of large molecules in terms of the corresponding quantities for the small fragments. The approach requires a computation time that scales linearly with the size of the molecule, or is independent of molecular size if sufficient processors are available. The method can be efficiently applied to molecules (large or small), to molecular clusters, and to non-conducting crystals. Here, the method is illustrated using a number of examples: the energies and vibrational frequencies of molecules containing explicit charges; the NMR shielding constants for proteins of thousands of atoms; and energies of small absorbate molecules in porous materials.

# Alternative Approach to Chemical Accuracy: Neural Network Based Density-Functional Theory

By Guanhua Chen*Department of Chemistry, The University of Hong Kong*

The neural network correction approach that was previously proposed to achieve the chemical accuracy for first-principles methods is further developed by a combination of the Kennard–Stone sampling and Bootstrapping methods. As a result, the accuracy of the calculated heat of formation is improved further, and moreover, the error bar of each calculated result can be determined. An enlarged database (Chen/13), which contains a total of 539 molecules made of the common elements H, C, N, O, F, S, and Cl, is constructed and is divided into the training (449 molecules) and testing (90 molecules) data sets with the Kennard–Stone sampling method. Upon the neural network correction, the mean absolute deviation (MAD) of the B3LYP/6-311+G(3df,2p) calculated heat of formation is reduced from 10.92 to 1.47 kcal mol–1 and 14.95 to 1.31 kcal mol–1 for the training and testing data sets, respectively. Furthermore, the Bootstrapping method, a broadly used statistical method, is employed to assess the accuracy of each neural-network prediction by determining its error bar. The average error bar for the testing data set is 1.05 kcal mol–1, therefore achieving the chemical accuracy. When a testing molecule falls into the regions of the “Chemical Space” where the distribution density of the training molecules is high, its predicted error bar is comparatively small, and thus, the predicted value is accurate as it should be. As a challenge, the resulting neural-network is employed to discern the discrepancy among the existing experimental data.

# The Integration Approach at the Second-order Perturbation Theory: Applications to Ionization Potential and Electron Affinity Calculations

By Xin Xu*Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China**E-mail: xxchem@fudan.edu.cn*

An integration approach is developed to calculate ionization potentials (IPs), and electron affinities (EAs), which is an extension of the D-∆MBPT(2) method [1]. The latter is an extension of the single-point method of Cohen et al. [2] from the perspective of fractional charges. While relaxation effects were included only at the Hartree-Fock (HF) level in the previous methods, such effects are fully taken into account in the present method up to the second-order Møller-Plesset (MP2) level. This is made possible by deriving the full MP2 energy gradient with respect to the orbital occupation numbers, which is solved through the coupled-perturbed HF (CP-HF) equations.

Figure 1. Comparison of the MP2 correlation energy derivatives with respect to the orbital occupation number at different levels of approximations for *L* = I (as in Ref. 2), II (as in Ref. 1), and III(i.e., the present work). (a) The initial derivatives corresponding to HOMO of the *N*0-electron system, (b) the final derivatives corresponding to LUMO of the (*N*0‒1)-electron system, (c) the initial derivatives corresponding to LUMO of the *N*0-electron system; (d) The final derivatives corresponding to HOMO of the (*N*0+1)-electron system.

*This research was sponsored by the Ministry of Science and Technology of China (2013CB834606, 2011CB808505), and National Natural Science Foundation of China (21133004, 91427301).*

*[1] A. Beste, A. Vazquez-Mayagoitia, and J. V. Ortiz, J. Chem. Phys. 138, 074101(2013).[2] A. J. Cohen, P. Mori-Sánchez, and W. Yang, J. Chem. Theory Comput. 5, 786 (2009).[3] N. Q. Su and Xin Xu, J. Chem. Theory Comput., in revision.*

# Survival of the Most Transferable: New Semi-empirical Density Functionals from a Combinatorial Design Strategy

By Martin Head-Gordon*Department of Chemistry, University of California& Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley CA 94720, USA.*

I shall discuss progress in the design of a next generation of density functional theories [1,2]. In contrast to most approaches to functional design, we have adopted a combinatorial approach, in which we have trained a huge number of functionals (over 100,000 in the case of the generalized gradient approximation models [1], and over 1010 in the case of meta GGA functionals [2]). The functional from each class that performs best on independent test data (survival of the most transferable) is self-consistently trained to yield a new generation functional that seems very promising for application purposes. The resulting functionals involve significantly fewer parameters than many of the best functionals of recent years.

References

*“ωB97X-V: A 10 parameter range separated hybrid density functional including non-local correlation, designed by a survival of the fittest strategy”, N. Mardirossian and M. Head-Gordon, Phys. Chem. Chem. Phys. 16, 9904-9924 (2014).**“Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V”, N. Mardirossian and M. Head-Gordon, J. Chem. Phys. 142, 074111 (2015).*