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Viquez Rojas CI, Slipchenko LV. Exchange Repulsion in Quantum Mechanical/Effective Fragment Potential Excitation Energies: Beyond Polarizable Embedding. J Chem Theory Comput 2020; 16:6408-6417. [PMID: 32786899 DOI: 10.1021/acs.jctc.9b01156] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Hybrid quantum mechanical and molecular mechanical (QM/MM) approaches facilitate computational modeling of large biological and materials systems. Typically, in QM/MM, a small region of the system is modeled with an accurate quantum mechanical method and its surroundings with a more efficient alternative, such as a classical force field or the effective fragment potential (EFP). The reliability of QM/MM calculations depends largely on the treatment of interactions between the two subregions, also known as embedding. The polarizable embedding, which allows mutual polarization between solvent and solute, is considered to be essential for describing electronic excitations in polar solvents. In this work, we employ the QM/EFP model and extend the polarizable embedding by incorporating two short-range terms-a charge penetration correction to the electrostatic term and the exchange-repulsion term-both of which are modeled with one-electron contributions to the quantum Hamiltonian. We evaluate the accuracy of these terms by computing excitation energies across 37 molecular clusters consisting of biologically relevant chromophores surrounded by polar solvent molecules. QM/EFP excitation energies are compared to the fully quantum mechanical calculations with the configuration interaction singles (CIS) method. We find that the charge penetration correction diminishes the accuracy of the QM/EFP calculations. On the other hand, while the effect of exchange-repulsion is negligible for most ππ* transitions, the exchange-repulsion significantly improves description of nπ* transitions with blue solvatochromic shifts. As a result, addition of the exchange-repulsion term improves the overall accuracy of QM/EFP. Performances of QM/EFP models remain similar when excitation energies are modeled with cc-pVDZ and aug-cc-pVDZ basis sets.
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Affiliation(s)
- Claudia I Viquez Rojas
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47906, United States
| | - Lyudmila V Slipchenko
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47906, United States
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Abstract
The dispersion energy term between quantum-mechanical (QM) and classical (represented by effective fragment potentials, EFP) subsystems is developed and implemented. A new formulation is based on long-range perturbation theory and uses dynamic polarizability tensors of the effective fragments and electric field integrals and orbital energies of the quantum-mechanical subsystem. No parametrization is involved. The accuracy of the QM-EFP dispersion energy is tested on a number of model systems; the average mean unsigned error is 0.8 kcal/mol or 13% with respect to the symmetry adapted perturbation theory on the S22 data set of noncovalent interactions. The computational cost of the dispersion energy computation is low compared to the self-consistent field calculation of the QM subsystem. The dispersion energy is sensitive to the level of theory employed for the QM part and to the electrostatic interactions in the system. The latter means that the dispersion interactions in the QM/EFP method are not purely two-body but have more complex many-body behavior.
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Affiliation(s)
- Lyudmila V Slipchenko
- Department of Chemistry, Purdue University , West Lafayette, Indiana 47907, United States
| | - Mark S Gordon
- Department of Chemistry and Ames Laboratory, Iowa State University , Ames, Iowa 50011, United States
| | - Klaus Ruedenberg
- Department of Chemistry and Ames Laboratory, Iowa State University , Ames, Iowa 50011, United States
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Chaudret R, Gresh N, Narth C, Lagardère L, Darden TA, Cisneros GA, Piquemal JP. S/G-1: an ab initio force-field blending frozen Hermite Gaussian densities and distributed multipoles. Proof of concept and first applications to metal cations. J Phys Chem A 2014; 118:7598-612. [PMID: 24878003 DOI: 10.1021/jp5051657] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.
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Affiliation(s)
- Robin Chaudret
- Sorbonne Universités , UPMC, Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, case courrier 137, 4 place Jussieu, F-75005 Paris, France
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Fang D, Piquemal JP, Liu S, Cisneros GA. DFT-steric-based energy decomposition analysis of intermolecular interactions. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1484-7] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Gourlaouen C, Clavaguéra C, Marjolin A, Piquemal JP, Dognon JP. Understanding the structure and electronic properties of Th4+-water complexes. CAN J CHEM 2013. [DOI: 10.1139/cjc-2012-0546] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
We present a systematic quantum chemistry study of the [Th(H2O)n]4+ (n = 1 to 10) complexes to gain insight into their electronic structure and properties: the effect of the ligand distribution on the valence shells of the thorium(IV) ion is studied by means of the electron localization function (ELF) topological analysis. Particular care is given to the study of the mono-aqua complex both at its equilibrium geometry, using various tools such as energy decomposition analyses (EDA), and along its dissociation pathway. Indeed, as several electronic states cross the Th4 +-H2O0 ground state along the minimum energy path, we demonstrate that the diabatic representation implemented in MOLPRO is able to generate reference potential energy surfaces that will lead to the evaluation of diabatic dissociation curves. The calculated diabatic interaction energy curve will allow for a consistent parameterization of new generation force fields dedicated to heavy metals based on quantum chemistry.
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Affiliation(s)
- Christophe Gourlaouen
- CEA/Saclay, UMR 3299 CEA/CNRS SIS2M, Laboratoire de Chimie de coordination des éléments f, 91191 Gif-sur-Yvette, France
- Laboratoire de Chimie Quantique, ICS, UMR 7177, Université de Strasbourg, 4, rue Blaise Pascal, 67081 Strasbourg Cedex, France
| | - Carine Clavaguéra
- Laboratoire des mécanismes réactionnels, Département de chimie, Ecole polytechnique, CNRS, 91128 Palaiseau cedex, France
| | - Aude Marjolin
- CEA/Saclay, UMR 3299 CEA/CNRS SIS2M, Laboratoire de Chimie de coordination des éléments f, 91191 Gif-sur-Yvette, France
- UPMC, Univ. Paris 6, UMR 7616, Laboratoire de Chimie Théorique, case courrier 137, 4 place Jussieu, F-75005 Paris, France
| | - Jean-Philip Piquemal
- UPMC, Univ. Paris 6, UMR 7616, Laboratoire de Chimie Théorique, case courrier 137, 4 place Jussieu, F-75005 Paris, France
| | - Jean-Pierre Dognon
- CEA/Saclay, UMR 3299 CEA/CNRS SIS2M, Laboratoire de Chimie de coordination des éléments f, 91191 Gif-sur-Yvette, France
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Burger SK, Cisneros GA. Efficient optimization of van der Waals parameters from bulk properties. J Comput Chem 2013; 34:2313-9. [PMID: 23828265 DOI: 10.1002/jcc.23376] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2013] [Revised: 05/10/2013] [Accepted: 06/16/2013] [Indexed: 01/06/2023]
Abstract
Due to the computational cost involved, when developing a force field for new compounds, one often avoids fitting van der Waals (vdW) terms, instead relying on a general force field based on the atom type. Here, we provide a novel approach to efficiently optimize vdW terms, based on both ab initio dimer energies and condensed phase properties. The approach avoids the computational challenges of searching the parameter space by using an extrapolation method to obtain a reliable difference quotient for the parameter derivatives based on the central difference. The derivatives are then used in an active-space optimization method which convergences quadratically. This method is applicable to polarizable and nonpolarizable force fields, although we focus on the parameterization of the AMBER force field. The scaling of the electrostatic potential (ESP) of the compounds is also studied. The algorithm is tested on 12 compounds, reducing the root mean squared error (RMSE) of the density from 0.061 g/cm(3) with GAFF parameters to 0.004 g/cm(3) , and the heat of vaporization from 1.13 to 0.05 kcal/mol. This is done with only four iterations of molecular dynamic runs. Using the optimized vdW parameters, the RMSE of the self-diffusion (Dself ) was reduced from 1.22 × 10(-9) to 0.78 × 10(-9) m(2) s(-1) and the RMSE of the hydration free energies (ΔGsolv ) was reduced from 0.30 to 0.26 kcal/mol. Scaling the ESP to improve dimer energies resulted in the Dself RMSE improving to 0.77× 10(-9) m(2) s(-1) , but the ΔGsolv worsened to 0.33 kcal/mol.
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Affiliation(s)
- Steven K Burger
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan, 48202
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Giese TJ, Chen H, Dissanayake T, Giambaşu GM, Heldenbrand H, Huang M, Kuechler ER, Lee TS, Panteva MT, Radak BK, York DM. A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields. J Chem Theory Comput 2013; 9:1417-1427. [PMID: 23814506 DOI: 10.1021/ct3010134] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.
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Affiliation(s)
- Timothy J Giese
- BioMaPS Institute and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854-8087 USA
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Gordon MS, Fedorov DG, Pruitt SR, Slipchenko LV. Fragmentation Methods: A Route to Accurate Calculations on Large Systems. Chem Rev 2011; 112:632-72. [DOI: 10.1021/cr200093j] [Citation(s) in RCA: 836] [Impact Index Per Article: 64.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Mark S. Gordon
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States
| | - Dmitri G. Fedorov
- Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
| | - Spencer R. Pruitt
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States
| | - Lyudmila V. Slipchenko
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
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Chaudret R, Gresh N, Parisel O, Piquemal JP. Many-body exchange-repulsion in polarizable molecular mechanics. I. Orbital-based approximations and applications to hydrated metal cation complexes. J Comput Chem 2011; 32:2949-57. [PMID: 21793002 DOI: 10.1002/jcc.21865] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2010] [Revised: 03/22/2011] [Accepted: 05/15/2011] [Indexed: 01/22/2023]
Abstract
We have quantified the extent of the nonadditivity of the short-range exchange-repulsion energy, E(exch-rep), in several polycoordinated complexes of alkali, alkaline-earth, transition, and metal cations. This was done by performing ab initio energy decomposition analyses of interaction energies in these complexes. The magnitude of E(exch-rep(n-body, n > 2)) was found to be strongly cation-dependent, ranging from close to zero for some alkali metal complexes to about 6 kcal/mol for the hexahydrated Zn(2+) complex. In all cases, the cation-water molecules, E(exch-rep(three-body)), has been found to be the dominant contribution to many-body exchange-repulsion effects, higher order terms being negligible. As the physical basis of this effect is discussed, a three-center exponential term was introduced in the SIBFA (Sum of Interactions Between Fragments Ab initio computed) polarizable molecular mechanics procedure to model such effects. The three-body correction is added to the two-center (two-body) overlap-like formulation of the short-range repulsion contribution, E(rep), which is grounded on simplified integrals obtained from localized molecular orbital theory. The present term is computed on using mostly precomputed two-body terms and, therefore, does not increase significantly the computational cost of the method. It was shown to match closely E(three-body) in a series of test cases bearing on the complexes of Ca(2+), Zn(2+), and Hg(2+). For example, its introduction enabled to restore the correct tetrahedral versus square planar preference found from quantum chemistry calculations on the tetrahydrate of Hg(2+) and [Hg(H(2)O)(4)](2+).
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Affiliation(s)
- Robin Chaudret
- UPMC Paris 06, UMR 7616, Laboratoire de Chimie Théorique, case courrier 137, 4 place Jussieu, F-75005 Paris, France
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10
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Connecting the virtual world of computers to the real world of medicinal chemistry. Future Med Chem 2011; 3:399-403. [PMID: 21452976 DOI: 10.4155/fmc.11.16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Drug discovery involves the simultaneous optimization of chemical and biological properties, usually in a single small molecule, which modulates one of nature's most complex systems: the balance between human health and disease. The increased use of computer-aided methods is having a significant impact on all aspects of the drug-discovery and development process and with improved methods and ever faster computers, computer-aided molecular design will be ever more central to the discovery process.
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11
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Gourlaouen C, Parisel O, Piquemal JP. Importance of backdonation in [M–(CO)]p+ complexes isoelectronic to [Au–(CO)]+. J Chem Phys 2010; 133:124310. [DOI: 10.1063/1.3491266] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wu JC, Piquemal JP, Chaudret R, Reinhardt P, Ren P. Polarizable molecular dynamics simulation of Zn(II) in water using the AMOEBA force field. J Chem Theory Comput 2010; 6:2059-2070. [PMID: 21116445 DOI: 10.1021/ct100091j] [Citation(s) in RCA: 125] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
The hydration free energy, structure, and dynamics of the zinc divalent cation are studied using a polarizable force field in molecular dynamics simulations. Parameters for the Zn(2+) are derived from gas-phase ab initio calculation of Zn(2+)-water dimer. The Thole-based dipole polarization is adjusted based on the Constrained Space Orbital Variations (CSOV) calculation while the Symmetry Adapted Perturbation Theory (SAPT) approach is also discussed. The vdW parameters of Zn(2+) have been obtained by comparing the AMOEBA Zn(2+)-water dimerization energy with results from several theory levels and basis sets over a range of distances. Molecular dynamics simulations of Zn(2+) solvation in bulk water are subsequently performed with the polarizable force field. The calculated first-shell water coordination number, water residence time and free energy of hydration are consistent with experimental and previous theoretical values. The study is supplemented with extensive Reduced Variational Space (RVS) and Electron Localization Function (ELF) computations in order to unravel the nature of the bonding in Zn(2+)(H(2)O)(n) (n=1,6) complexes and to analyze the charge transfer contribution to the complexes. Results show that the importance of charge transfer decreases as the size of Zn-water cluster grows due to anticooperativity and to changes in the nature of the metal-ligand bonds. Induction could be dominated by polarization when the system approaches condensed-phase and the covelant effects are eliminated from the Zn(II)-water interaction. To construct an "effective" classical polarizable potential for Zn(2+) in bulk water, one should therefore avoid over-fitting to the ab initio charge transfer energy of Zn(2+)-water dimer. Indeed, in order to avoid overestimation of condensed-phase many-body effects, which is crucial to the transferability of polarizable molecular dynamics, charge transfer should not be included within the classical polarization contribution and should preferably be either incorporated in to the pairwise van der Waals contribution or treated explicitly.
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Affiliation(s)
- Johnny C Wu
- Department of Biomedical Engineering, University of Texas at Austin, Austin, Texas 78712-1062, USA
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Sebetci A, Beran GJO. Spatially Homogeneous QM/MM for Systems of Interacting Molecules with on-the-Fly ab Initio Force-Field Parametrization. J Chem Theory Comput 2009; 6:155-67. [DOI: 10.1021/ct900545v] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ali Sebetci
- Department of Chemistry, University of California, Riverside, California 92521
| | - Gregory J. O. Beran
- Department of Chemistry, University of California, Riverside, California 92521
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Wu Q, Ayers PW, Zhang Y. Density-based energy decomposition analysis for intermolecular interactions with variationally determined intermediate state energies. J Chem Phys 2009; 131:164112. [DOI: 10.1063/1.3253797] [Citation(s) in RCA: 106] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
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