A Machine Learning Force Field for Bio-Macromolecular Modeling Based on Quantum Chemistry-Calculated Interaction Energy Datasets.

Accurate energy data from noncovalent interactions are essential for constructing force fields for molecular dynamics simulations of bio-macromolecular systems. There are two important practical issues in the construction of a reliable force field with the hope of balancing the desired chemical accuracy and working efficiency. One is to determine a suitable quantum chemistry level of theory for calculating interaction energies. The other is to use a suitable continuous energy function to model the quantum chemical energy data. For the first issue, we have recently calculated the intermolecular interaction energies using the SAPT0 level of theory, and we have systematically organized these energies into the ab initio SOFG-31 (homodimer) and SOFG-31-heterodimer datasets. In this work, we re-calculate these interaction energies by using the more advanced SAPT2 level of theory with a wider series of basis sets. Our purpose is to determine the SAPT level of theory proper for interaction energies with respect to the CCSD(T)/CBS benchmark chemical accuracy. Next, to utilize these energy datasets, we employ one of the well-developed machine learning techniques, called the CLIFF scheme, to construct a general-purpose force field for biomolecular dynamics simulations. Here we use the SOFG-31 dataset and the SOFG-31-heterodimer dataset as the training and test sets, respectively. Our results demonstrate that using the CLIFF scheme can reproduce a diverse range of dimeric interaction energy patterns with only a small training set. The overall errors for each SAPT energy component, as well as the SAPT total energy, are all well below the desired chemical accuracy of ~1 kcal/mol.

Intermolecular Non-Bonded Interactions from Machine Learning Datasets.

Accurate determination of intermolecular non-covalent-bonded or non-bonded interactions is the key to potentially useful molecular dynamics simulations of polymer systems. However, it is challenging to balance both the accuracy and computational cost in force field modelling. One of the main difficulties is properly representing the calculated energy data as a continuous force function. In this paper, we employ well-developed machine learning techniques to construct a general purpose intermolecular non-bonded interaction force field for organic polymers. The original ab initio dataset SOFG-31 was calculated by us and has been well documented, and here we use it as our training set. The CLIFF kernel type machine learning scheme is used for predicting the interaction energies of heterodimers selected from the SOFG-31 dataset. Our test results show that the overall errors are well below the chemical accuracy of about 1 kcal/mol, thus demonstrating the promising feasibility of machine learning techniques in force field modelling.

A Minimum Quantum Chemistry CCSD(T)/CBS Data Set of Dimeric Interaction Energies for Small Organic Functional Groups: Heterodimers.

We extend our previous quantum chemistry calculations of interaction energies for 31 homodimers of small organic functional groups (the SOFG-31 data set) by including 239 heterodimers with monomers selected within the SOFG-31 data set, thus resulting in the SOFG-31+239 data set. The minimum-level theoretical scheme contains (1) the basis set superposition error corrected supermolecule (BSSE-SM) approach for intermolecular interactions; (2) the second-order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets for the geometry optimization and correlation energy calculations; and (3) the single-point energy calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods for the MP2 energy calibrations. In addition, we have performed a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT) in order to gain chemical insights. That the above procedure cannot be further reduced has been proven to be very crucial for constructing reliable data sets of interaction energies. The calculated CCSD(T)/CBS interaction energy data can serve as a benchmark for testing or training less accurate but more efficient calculation methods, such as the electronic density functional theory. As an application, we employ a segmental SAPT model previously developed for the SOFG-31 data set to predict binding energies of large heterodimer complexes. These model energy "quanta" can be used in coarse-grained molecular dynamics simulations by avoiding large-scale calculations.

A minimum quantum chemistry CCSD(T)/CBS dataset of dimeric interaction energies for small organic functional groups.

We have performed a quantum chemistry study on the bonding patterns and interaction energies for 31 dimers of small organic functional groups (dubbed the SOFG-31 dataset), including the alkane-alkene-alkyne (6 + 4 + 4 = 14, AAA) groups, alcohol-aldehyde-ketone (4 + 4 + 3 = 11, AAK) groups, and carboxylic acid-amide (3 + 3 = 6, CAA) groups. The basis set superposition error corrected super-molecule approach using the second order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets has been employed in the geometry optimization and energy calculations. To calibrate the MP2 calculated interaction energies for these dimeric complexes, we perform single-point calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods. In order to gain more physical insights, we also perform a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT). The collection of these CCSD(T)/CBS interaction energy values can serve as a minimum quantum chemistry dataset for testing or training less accurate but more efficient calculation methods. As an application, we further propose a segmental SAPT model based on chemically recognizable segments in a specific functional group. These model interactions can be used to construct coarse-grained force fields for larger molecular systems.

Coarse-Grained Simulations Using a Multipolar Force Field Model.

This paper presents a coarse-grained molecular simulation for fullerenes based on a multipolar expansion method developed previously. The method is enabled by the construction of transferable united atoms potentials that approximate the full atomistic intermolecular interactions, as obtained from ab initio electronic structure calculations supplemented by empirical force fields and experimental data, or any combination of the above. The resultant series contains controllable moment tensors that allow to estimate the errors, and approaches the all-atom intermolecular potential as the expansion order increases. We can compute the united atoms potentials very efficiently with a few interaction moment tensors, in order to implement a parallel algorithm on molecular interactions. Our simulations describe the mechanism for the condensation of fullerenes, and they produce excellent agreement with benchmark fully atomistic molecular dynamics simulations.

Molecular dynamics simulations of fluid cyclopropane with MP2/CBS-fitted intermolecular interaction potentials.

Modeling fluid cycloalkanes with molecular dynamics simulations has proven to be a very challenging task partly because of lacking a reliable force field based on quantum chemistry calculations. In this paper, we construct an ab initio force field for fluid cyclopropane using the second-order Møller-Plesset perturbation theory. We consider 15 conformers of the cyclopropane dimer for the orientation sampling. Single-point energies at important geometries are calibrated by the coupled cluster with single, double, and perturbative triple excitation method. Dunning's correlation consistent basis sets (up to aug-cc-pVTZ) are used in extrapolating the interaction energies at the complete basis set limit. The force field parameters in a 9-site Lennard-Jones model are regressed by the calculated interaction energies without using empirical data. With this ab initio force field, we perform molecular dynamics simulations of fluid cyclopropane and calculate both the structural and dynamical properties. We compare the simulation results with those using an empirical force field and obtain a quantitative agreement for the detailed atom-wise radial distribution functions. The experimentally observed gross radial distribution function (extracted from the neutron scattering measurements) is well reproduced in our simulation. Moreover, the calculated self-diffusion coefficients and shear viscosities are in good agreement with the experimental data over a wide range of thermodynamic conditions. To the best of our knowledge, this is the first ab initio force field which is capable of competing with empirical force fields for simulating fluid cyclopropane.

Kinetic energy partition method applied to ground state helium-like atoms.

We have used the recently developed kinetic energy partition (KEP) method to solve the quantum eigenvalue problems for helium-like atoms and obtain precise ground state energies and wave-functions. The key to treating properly the electron-electron (repulsive) Coulomb potential energies for the KEP method to be applied is to introduce a "negative mass" term into the partitioned kinetic energy. A Hartree-like product wave-function from the subsystem wave-functions is used to form the initial trial function, and the variational search for the optimized adiabatic parameters leads to a precise ground state energy. This new approach sheds new light on the all-important problem of solving many-electron Schrödinger equations and hopefully opens a new way to predictive quantum chemistry. The results presented here give very promising evidence that an effective one-electron model can be used to represent a many-electron system, in the spirit of density functional theory.

Improving the binding efficiency of quartz crystal microbalance biosensors by applying the electrothermal effect.

A quartz crystal microbalance (QCM) serving as a biosensor to detect the target biomolecules (analytes) often suffers from the time consuming process, especially in the case of diffusion-limited reaction. In this experimental work, we modify the reaction chamber of a conventional QCM by integrating into the multi-microelectrodes to produce electrothermal vortex flow which can efficiently drive the analytes moving toward the sensor surface, where the analytes were captured by the immobilized ligands. The microelectrodes are placed on the top surface of the chamber opposite to the sensor, which is located on the bottom of the chamber. Besides, the height of reaction chamber is reduced to assure that the suspended analytes in the fluid can be effectively drived to the sensor surface by induced electrothermal vortex flow, and also the sample costs are saved. A series of frequency shift measurements associated with the adding mass due to the specific binding of the analytes in the fluid flow and the immobilized ligands on the QCM sensor surface are performed with or without applying electrothermal effect (ETE). The experimental results show that electrothermal vortex flow does effectively accelerate the specific binding and make the frequency shift measurement more sensible. In addition, the images of the binding surfaces of the sensors with or without applying electrothermal effect are taken through the scanning electron microscopy. By comparing the images, it also clearly indicates that ETE does raise the specific binding of the analytes and ligands and efficiently improves the performance of the QCM sensor.

Intermolecular interactions of trifluorohalomethanes with Lewis bases in the gas phase: an ab initio study.

We perform an ab initio computational study of molecular complexes with the general formula CF3X-B that involve one trifluorohalomethane CF3X (X = Cl or Br) and one of a series of Lewis bases B in the gas phase. The Lewis bases are so chosen that they provide a range of electron-donating abilities for comparison. Based on the characteristics of their electron pairs, we consider the Lewis bases with a single n-pair (NH3 and PH3), two n-pairs (H2O and H2S), two n-pairs with an unsaturated bond (H2CO and H2CS), and a single π-pair (C2H4) and two π-pairs (C2H2). The aim is to systematically investigate the influence of the electron pair characteristics and the central atom substitution effects on the geometries and energetics of the formed complexes. The counterpoise-corrected supermolecule MP2 and coupled-cluster single double with perturbative triple [CCSD(T)] levels of theory have been employed, together with a series of basis sets up to aug-cc-pVTZ. The angular and radial configurations, the binding energies, and the electrostatic potentials of the stable complexes have been compared and discussed as the Lewis base varies. For those complexes where halogen bonding plays a significant role, the calculated geometries and energetics are consistent with the σ-hole model. Upon formation of stable complexes, the C-X bond lengths shorten, while the C-X vibrational frequencies increase, thus rendering blueshifting halogen bonds. The central atom substitution usually enlarges the intermolecular bond distances while it reduces the net charge transfers, thus weakening the bond strengths. The analysis based on the σ-hole model is grossly reliable but requires suitable modifications incorporating the central atom substitution effects, in particular, when interaction components other than electrostatic contributions are involved.

Liquid chloroform structure from computer simulation with a full ab initio intermolecular interaction potential.

We have calculated the intermolecular interaction energies of the chloroform dimer in 12 orientations using the second-order Møller-Plesset perturbation theory. Single point energies of important geometries were calibrated by the coupled cluster with single and double and perturbative triple excitation method. Dunning's correlation consistent basis sets up to aug-cc-pVQZ have been employed in extrapolating the interaction energies to the complete basis set limit values. With the ab initio potential data we constructed a 5-site force field model for molecular dynamics simulations. We compared the simulation results with recent experiments and obtained quantitative agreements for the detailed atomwise radial distribution functions. Our results were also consistent with previous results using empirical force fields with polarization effects. Moreover, the calculated diffusion coefficients reproduced the experimental data over a wide range of thermodynamic conditions. To the best of our knowledge, this is the first ab initio force field which is capable of competing with existing empirical force fields for liquid chloroform.

Liquid properties of dimethyl ether from molecular dynamics simulations using ab initio force fields.

We have used molecular dynamic simulations to study the structural and dynamical properties of liquid dimethyl ether (DME) with a newly constructed ab initio force field in this article. The ab initio potential energy data were calculated at the second order Møller-Plesset (MP2) perturbation theory with Dunning's correlation consistent basis sets (up to aug-cc-pVQZ). We considered 17 configurations of the DME dime for the orientation sampling. The calculated MP2 potential data were used to construct a 3-site united atom force field model. The simulation results are compared with those using the empirical force field of Jorgensen and Ibrahim (Jorgensen and Ibrahim, J Am Chem Soc 1981, 103, 3976) and with available experimental measurements. We obtain quantitative agreements for the atom-wise radial distribution functions, the self-diffusion coefficients, and the shear viscosities over a wide range of experimental conditions. This force field thus provides a suitable starting point to predict liquid properties of DME from first principles intermolecular interactions with no empirical data input a priori.

Computer simulation of trifluoromethane properties with ab initio force field.

Intermolecular interaction potentials of the trifluoromethane dimer in 15 orientations have been calculated using the Hartree-Fock (HF) self-consistent theory and the second-order Møller-Plesset (MP2) perturbation theory. Single point energies at important geometries were also calibrated by the coupled cluster with single and double and perturbative triple excitation [CCSD(T)] calculations. We have employed Pople's medium size basis sets [up to 6-311++G(3df,3pd)] and Dunning's correlation consistent basis sets (up to aug-cc-pVQZ). Basis set limit potential values were obtained through well-studied extrapolation methods. The calculated MP2 potential data were employed to parameterize a 5-site force field for molecular simulations. We performed molecular dynamics simulations using the constructed ab initio force field and compared the simulation results with experiments. Quantitative agreements for the atom-wise radial distribution functions and the self-diffusion coefficients over a wide range of experimental conditions can be obtained, thus validating the ab initio force field without using experimental data a priori.

Structures and energetics of neutral and ionic silicon-germanium clusters: density functional theory and coupled cluster studies.

We have calculated the structural and energetic properties of neutral and ionic (singly charged anionic and cationic) semiconductor binary silicon-germanium clusters Si(m)Ge(n) for s = m + n ≤ 12 using the density functional theory (DFT-B3LYP) and coupled cluster [CCSD(T)] methods with Pople's 6-311++G(3df, 3pd) basis set. Neutral and anionic clusters share similar ground state structures for s = 3-7, independent of the stoichiometry and atom locations, but start to deviate at s = 8. The relative energetic stability of the calculated ground state structures among possible isomers has been analyzed through a bond strength propensity model where the pair interactions of Si-Si, Si-Ge, and Ge-Ge are competing. Electron affinities, ionization potentials, energy gaps between the highest and lowest occupied molecular orbitals (HOMO-LUMO gaps), and cluster mixing energies were calculated and analyzed. Overall, for a fixed s, the vertical ionization potential increases as the number of silicon atoms m increases, while the vertical electron affinity shows a dip at m = 2. As s increases, the ionization potentials increase from s = 2 to s = 3 and then decrease slowly to s = 8. The mixing energies for neutral and ionic clusters are all negative, indicating that the binary clusters are more stable than pure elemental clusters. Except for s = 4 and 8, cationic clusters are more stable than anionic ones and, thus, are more likely to be observed in experiments.

Molecular dynamics simulation of liquid carbon tetrachloride using ab initio force field.

Intermolecular interaction potentials of the carbon tetrachloride dimer in 12 orientations have been calculated using the Hartree-Fock self-consistent theory and the second-order Moller-Plesset (MP2) perturbation theory. We have employed basis sets from Pople's medium size basis sets [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets (up to aug-cc-pVQZ). The calculated MP2 potential data were employed to parametrize a four-site force field for molecular simulations. We performed molecular dynamics simulations using the ab initio force field and compared the simulation results to experiments. Quantitative agreements for the atomwise radial distribution functions, the self-diffusion coefficients, and the neutron and x-ray diffraction scattering functions over a wide range of experimental conditions can be obtained, thus validating the ab initio force field without using experimental data a priori.

A combined experimental and theoretical study on the immunoassay of human immunoglobulin using a quartz crystal microbalance.

We investigate a immunoassay biosensor that employs a Quartz Crystal Microbalance (QCM) to detect the specific binding reaction of the (Human IgG1)-(Anti-Human IgG1) protein pair under physiological conditions. In addition to experiments, a three dimensional time domain finite element method (FEM) was used to perform simulations for the biomolecular binding reaction in microfluidic channels. In particular, we discuss the unsteady convective diffusion in the transportation tube, which conveys the buffer solution containing the analyte molecules into the micro-channel where the QCM sensor lies. It is found that the distribution of the analyte concentration in the tube is strongly affected by the flow field, yielding large discrepancies between the simulations and experimental results. Our analysis shows that the conventional assumption of the analyte concentration in the inlet of the micro-channel being uniform and constant in time is inadequate. In addition, we also show that the commonly used procedure in kinetic analysis for estimating binding rate constants from the experimental data would underestimate these rate constants due to neglected diffusion processes from the inlet to the reaction surface. A calibration procedure is proposed to supplement the basic kinetic analysis, thus yielding better consistency with experiments.

Molecular dynamics simulations of fluid methane properties using ab initio intermolecular interaction potentials.

Intermolecular interaction energy data for the methane dimer have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of fluid methane properties. The full potential curves of the methane dimer at 12 symmetric conformations were calculated by the supermolecule counterpoise-corrected second-order Møller-Plesset (MP2) perturbation theory. Single-point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople's medium size basis sets [up to 6-311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). For each conformer, the intermolecular carbon-carbon separation was sampled in a step 0.1 A for a range of 3-9 A, resulting in a total of 732 configuration points calculated. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well-established analytical extrapolation schemes. A 4-site potential model with sites located at the hydrogen atoms was used to fit the ab initio potential data. This model stems from a hydrogen-hydrogen repulsion mechanism to explain the stability of the dimer structure. MD simulations using the ab initio PES show quantitative agreements on both the atom-wise radial distribution functions and the self-diffusion coefficients over a wide range of experimental conditions.

Optimal higher-lying band gaps for photonic crystals with large dielectric contrast.

We investigate the characteristics of higher-lying band gaps for two-dimensional photonic crystals with large dielectric contrast. An optimal common band gap is attained on a hexagonal lattice of circular dielectric cylinders at relatively higher bands. The corresponding TM and TE modes exhibit simultaneous band edges, around which the frequency branches tend to be dispersionless. Unlike the fundamental band gap which usually appears between the dielectric and air bands, the optimal higher-lying gap in the present study occurs between two consecutive dielectric-like bands with high energy fill factors. The underlying mechanism is illustrated with the apparent change of eigenmode patterns inside the dielectric regions for both polarizations. In particular, the common gap region is bounded by two successive orders of Mie resonance frequencies on a single dielectric cylinder with the same geometry and material, where the Mie resonance modes show similar internal fields with the respective eigenmodes for the photonic crystal.

Intermolecular potentials of the silane dimer calculated with Hartree-Fock theory, Møller-Plesset perturbation theory, and density functional theory.

We have calculated the intermolecular interaction potentials of the silane dimer at the D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order Møller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with 108 functionals chosen from the combinations of 9 exchange and 12 correlation functionals. Single-point coupled cluster [CCSD(T)] calculations have also been carried out to calibrate the correlation effect. The HF calculations yield unbound potentials largely because of the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater type orbitals fitted with Gaussian functions (STO-nG, n = 3 approximately 6), Pople's medium size basis sets [up to 6-311++G(3df,3pd)], to Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(3d,3p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy ( approximately 0.05 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the expected C6 value from molecular polarizability calculations. We attribute the slow convergence partly to the inefficacy of using the MP2 calculations with Gaussian type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the expected potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energies calculated using the OPTXHCTH147, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals and the equilibrium bond lengths calculated using the MPWHCTH93, TPSSHCTH, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals are close to the MP2 results using the 6-311++G(3df,3pd) basis set. A correlation between the calculated DFT potentials and the exchange and correlation enhancement factors at the low-density region has been elucidated. The asymptotic behaviors of the DFT potentials are also analyzed.

Comparative performance of exchange and correlation density functionals in determining intermolecular interaction potentials of the methane dimer.

We have calculated the interaction potentials of the methane dimer for the minimum-energy D(3d) conformation using the density functional theory (DFT) with 90 density functionals chosen from the combinations of nine exchange and 10 correlation functionals. Several hybrid functionals are also considered. While the performance of an exchange functional is related to the large reduced density gradient of the exchange enhancement factor, the correlation energy is determined by the low-density behavior of a correlation enhancement factor. Our calculations demonstrate that the correlation counterpart plays an equally important role as the exchange functional in determining the van der Waals interactions of the methane dimer. These observations can be utilized to better understand the seemingly unsystematic DFT interaction potentials for weakly bound systems.

Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory.

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order Møller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.