Conformational Analysis of Free and Bound Retinoic Acid

The conformational profiles of unbound all-trans and 9-cis retinoic acid (RA) have been determined using classical and quantum mechanical calculations. Sixty-six all-trans-RA (ATRA) and forty-eight 9-cis-RA energy minimum conformers were identified via HF/6-31G* geometry optimizations in vacuo. Their relative conformational energies were estimated utilizing the M06, M06-2x and MP2 methods combined with the 6-311+G(d,p), aug-cc-pVDZ and aug-cc-pVTZ basis sets, as well as complete basis set MP2 extrapolations using the latter two basis sets. Single-point energy calculations performed with the M06-2x density functional were found to yield similar results to MP2/CBS for the low-energy retinoic acid conformations. Not unexpectedly, the conformational propensities of retinoic acid were governed by the orientation and arrangement of the torsion angles associated with the polyene tail. We also used previously reported QM/MM X-ray refinement results on four ATRA-protein crystal structures plus one newly refined 9-cis-RA complex (PDB ID 1XDK) in order to investigate the conformational preferences of bound retinoic acid. In the re-refined RA conformers the conjugated double bonds are nearly coplanar, which is consistent with the global minimum identified by the Omega/QM method rather than the corresponding crystallographically determined conformations given in the PDB. Consequently, a 91.3% average reduction of the local strain energy in the gas phase, as well as 92.1% in PCM solvent, was observed using the QM/MM refined structures versus the PDB deposited RA conformations. These results thus demonstrate that our QM/MM X-ray refinement approach can significantly enhance the quality of X-ray crystal structures refined by conventional refinement protocols, thereby providing reliable drug-target structural information for use in structure-based drug discovery applications.     

Comparative study on formamide–water complex

The hydrogen bonding of 1:1 complexes formed between formamide and water molecule have been investigated systematically using Hartree–Fock (HF), hybrid density functional theory (B3LYP), and post‐Hartree–Fock (MP2 and CCSD(T)) methods with range of basis sets 6‐31G(d), cc‐pVXZ (X = D, T, Q) and aug‐cc‐pVYZ (Y = D, T). Three stable structures are considered on the potential energy surface of formamide and water system. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The IR frequencies, intensities, and frequency shifts are reported. This study shows that B3LYP/aug‐cc‐pVDZ method gives better performance for formamide‐water complexes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010.     

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 Å for a range of 3–9 Å, 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. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals for noncovalent interactions: Basis set effects and tentative applications to large noncovalent systems

Basis set effects on the DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals for noncovalent interactions have been extensively studied in this work. The cc‐pVXZ (X = D, T, Q, 5, 6) and augmented aug‐cc‐pVXZ (X = D, T, Q) basis sets are systematically tested without counterpoise (CP) corrections against the well‐known S66 database. Additionally, the basis sets of def2‐TZVPP and def2‐TZVPPD are also examined. Based on our computations, the performances of the aug‐cc‐pVQZ, cc‐pV5Z, and cc‐pV6Z basis sets are very approximate to those obtained with the def2‐QZVP basis set for both the DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals. Note that the short‐range attenuation parameters for these two functionals were directly optimized using the def2‐QZVP basis set without CP corrections against the S66 database. Generally speaking, the cc‐pVXZ (X = D, T, Q), aug‐cc‐pVXZ (X = D, T, Q), def2‐TZVPP, and def2‐TZVPPD basis sets favor half CP correction for these two functionals. Nevertheless, the aug‐cc‐pVQZ basis set already performs well without any CP correction, especially for the DOD‐PBEP86‐NL functional. With respect to accuracy and computational cost, the cc‐pVTZ and def2‐TZVPP basis sets with half CP corrections are recommended for these two functionals to evaluate interaction energies of large noncovalent complexes.     

A Refined Intermolecular Interaction Potential for Methane: Spectral Analysis and Molecular Dynamics Simulations

The previously constructed methane interaction potential energy surface calculated at the second‐order Møller‐Plesset (MP2) perturbation theory has been significantly improved in two aspects. First, all ab initio potential energy data are calculated by the supermolecule counterpoise corrected coupled cluster with single and double and perturbative triple excitations [CCSD(T)] method with Dunning’s correlation‐consistent aug‐cc‐pVXZ, X=D, T, Q, 5, basis sets and extrapolated to the complete basis set (CBS) limits with a convergence precision of 0.01 kcal/mol. Second, instead of the simple 4‐site model proposed in the previous study, a 5‐site model has been used to represent the ab initio potential data. The simulated infrared spectrum using the potential energy surface seems to be broadly in line with the spectral features observed in experiments. Molecular dynamics simulations using the ab initio force field show quantitative agreements with experiments. The properties examined in this paper include the atom‐to‐atom radial distribution functions in liquid and supercritical phases and the self‐diffusion coefficients over a wide range of thermodynamic conditions. It is shown that the refined ab initio force field can be applied to study fluid properties in different phases.     

A Comparative Study of Hydrogen Bonding Using Density Functional Theory

The hydrogen‐bond energies of water dimer and water‐formaldehyde complexes have been studied using density functional theory (DFT). Basis sets up to aug‐cc‐pVXZ (X=D, T, Q) were used. It was found that counterpoise corrected binding energies using the aug‐cc‐pVDZ basis set are very close to those predicted with the aug‐cc‐pVQZ set. Comparative studies using various DFT functionals on these two systems show that results from B3LYP, mPW1PW91 and PW91PW91 functionals are in better agreements with those predicted using high‐level ab initio methods. These functionals were applied to the study of hydrogen bonding between guanine (G) and cytosine (C), and between adenine (A) and thy mine (T) base pairs. With the aug‐cc‐pVDZ basis set, the predicted binding energies of base pairs are in good agreement with the most elaborate ab initio results.     

Many‐body interactions of carbon monoxide cyclic oligomers: A computational study

Structural properties and energetics for the optimized carbon monoxide cyclic oligomers are analyzed at the correlated ab initio second‐order Møller–Plesset (MP2) and density functional methods (B3LYP and mPW1PW), using Dunning's cc‐pVXZ (X = D, T, Q) basis set, augmented with diffuse functions. Many‐body interactions of the stable carbon monoxide cyclic oligomers, (CO)₄ and (CO)₅ are computed at the MP2/aug‐cc‐pVTZ level. Contributions of two‐ to five‐body terms to each of these oligomers for their interaction energies, including corrections for basis set superposition error (BSSE) are investigated by using function counterpoise and its generalized version. It has been found that three‐body terms are attractive in nature and essential in order to describe the cooperative effects in the stable cyclic CO oligomers. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

IR Low‐Temperature Matrix and ab Initio Study on β‐Alanine Conformers

For the first time the argon‐matrix low‐temperature FTIR spectra of β‐alanine are recorded. They reveal a quite complicated spectral pattern which suggests the presence of several β‐alanine conformers in the matrix. To interpret the spectra, the eighteen β‐alanine conformers, stable in the gas phase, are estimated at the B3LYP and MP2 levels combined with the aug‐cc‐pVDZ. Ten low‐energy structures are reoptimized at the QCISD/aug‐cc‐pVDZ and B3LYP and MP2 levels by using the aug‐cc‐pVTZ basis sets. Assignment of the experimental spectra is undertaken on the basis of the calculated B3LYP/aug‐cc‐pVDZ anharmonic IR frequencies as well as careful estimation of the conformer population. The presence of at least three β‐alanine conformers is demonstrated. The detailed analysis of IR spectra points to the possible presence of five additional β‐alanine conformers.     

Intermolecular bond lengths: extrapolation to the basis set limit on uncorrected and BSSE‐corrected potential energy hypersurfaces

Geometry optimizations were carried out for the (HF)₂, (H₂O)₂, and HF–H₂O intermolecular complexes using the MP2/aug‐cc‐pVXZ {X=2, 3, 4, and 5} theoretical models on both the uncorrected and counterpoise (CP) corrected potential energy hypersurfaces (PES). Our results and the available literature data clearly show that extrapolation of intermolecular distances to the complete basis set (CBS) limit is satisfactory on PESs corrected for BSSE. On the other hand, one should avoid such extrapolations using data obtained from uncorrected PESs. Also, fixing intramolecular parameters at their experimental values could cause difficulties during the extrapolation. As the available literature data and our results clearly show, the MP2/aug‐cc‐pVXZ {X=2, 3, 4} data series of intermolecular distances obtained from the CP‐corrected surfaces can be safely used for the purpose of CBS extrapolations. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 196–207, 2001     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

A theoretical study on three conformational structures of 2,6‐distyrylpyridine

Ab initio methods at the levels HF/cc‐pVDZ, HF/6‐31G(d,p), MP2/cc‐pVDZ, and MP2/6‐31G(d,p), as well as methods based on density functional theory (DFT) employing the hybrid functional B3LYP with the basis sets cc‐pVDZ and 6‐31G(d,p), have been applied to study the conformers of 2,6‐distyrylpyridine. Bond distances, bond angles, and dihedral angles have been calculated at the B3LYP level. The calculated values were in good agreement with those measured by X‐ray diffraction analysis of 2,6‐distyrylpyridine. The values calculated using the Hartree‐Fock method and second‐order perturbation theory (MP2) were inconsistent. The optimized lowest‐energy geometries were calculated from the reported X‐ray structural data by the B3LYP/cc‐pVDZ method. Three conformations, A, B, and C, were proposed for 2,6‐distyrylpyridine. Calculations at the three levels of theory indicated that conformation A was the most stable structure, with conformations C and B being higher in energy by 1.10 and 2.57 kcal/mol, respectively, using the same method and basis function. The same trend in the relative energies of the three possible conformations was observed at the two levels of theory and with the different basis sets employed. The reported X‐ray data were utilized to optimize total molecular energy of conformation A at the different calculation levels. The bond lengths, bond angles, and dihedral angles were then obtained from the optimized geometries by ab initio methods and by applying DFT using the two basis functions cc‐pVDZ and 6‐31G(d,p). The values were analyzed and compared. The calculated total energies, the relative energies of the molecular orbitals, the gap between them, and the dipole moment for each conformational structure proposed for 2,6‐distyrylpyridine are also reported. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Analytic energy gradient in combined second-order Møller-Plesset perturbation theory and polarizable force field calculation

Second-order M?ller-Plesset perturbation theory (MP2) is used to describe electronic correlation on the basis of Hartree-Fock (HF) variational calculations that incorporate induced dipole polarizable force fields (i.e., QM/MMpol style HF and MP2). The Z-vector equations for regular closed shell and open shell MP2 methods (RMP2, ZAPT2, and UMP2) are extended to include induced dipole contributions to determine the MP2 response density so that nuclear gradient and other properties can be efficiently evaluated. A better estimation of the induced dipole polarization energy can be obtained using the MP2 relaxed density. QM/MMpol style MP2 molecular dynamics simulations are performed for the ground state and first triplet state of acetone solvated by 1024 polarizable water molecules. A switching function is used to ensure energy conservation in QM/MM simulation under periodic boundary condition.     

Ab initio calculations of the Ar–ethane intermolecular potential energy surface using bond function basis sets

The intermolecular potential energy surface (PES) of argon with ethane has been studied by ab initio calculations at the levels of second‐order Møller–Plesset perturbation (MP2) theory and coupled‐cluster theory with single, double, and noniterative triple configurations (CCSD(T)) using a series of augmented correlation‐consistent basis sets. Two sets of bond functions, bf1 (3s3p2d) and bf2 (6s6p4d2f), have been added to the basis sets to show a dramatic and systematic improvement in the convergence of the entire PES. The PES of Ar–ethane is characterized by a global minimum at a near T‐shaped configuration with a well depth of 0.611 kcal mol^?1, a second minimum at a collinear configuration with a well depth of 0.456 kcal mol^?1, and a saddle point connecting the two minima. It is shown that an augmented correlation‐consistent basis set with a set of bond functions, either bf1 or bf2, can effectively produce results equivalent to the next larger augmented correlation‐consistent basis set, that is, aug‐cc‐pVDZ‐bf1 ≈ aug‐cc‐pVTZ, aug‐cc‐pVTZ‐bf1 ≈ aug‐cc‐pVQZ. Very importantly, the use of bond functions improves the PES globally, resulting accurate potential anisotropy. Finally, MP2 method is inadequate for accurate calculations, because it gives a potentially overestimated well depth and, more seriously, a poor potential anisotropy. © 2012 Wiley Periodicals, Inc.     

Study of conformational and optical rotation for the alaninamide

Six stationary points of alaninamide have been located on the potential surface energy (PES) at the B3LYP/6‐311++G(2d,2p) level of theory both in the gas phase and in aqueous solution. In the aqueous solution, to take the water solvent effect into account, the polarizable continuum model (PCM) method has been used. Accurate geometric structures and their relative stabilities have been investigated. The results show that the intramolecular hydrogen bond plays a very important role in stabilizing the global minimum of the alaninamide. Moreover, the consistent result in relative energy using high‐level computations, including the MP2 and MP3 methods with the same basis set [6‐311++G(2d,2p)], indicates that the B3LYP/6‐311++G(d,p) level may be applied to the analogue system. More importantly, the optical rotation of the optimized conformers (both in the gas phase and in aqueous solution) of alaninamide have been calculated using the density functional theory (DFT) and Hartree–Fock (HF) method at various basis sets (6‐31+G*, 6‐311++G(d,p), 6‐311++G(2d,2p) and aug‐cc‐pvdz). The results show that the selection of the computation method and the basis set in calculation has great influence on the results of the optical rotations. The reliability of the HF method is less than that of DFT, and selecting the basis set of 6‐311++G(2d,2p) and aug‐cc‐pvDZ produces relative reliable results. Analysis of the computational results of the structure parameters and the optical rotations yields the conclusion that just the helixes in molecules caused the chiral molecules to be optical active. The Boltzmann equilibrium distributions for the six conformers (both in the gas phase and in the aqueous solution) are also carried out. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Analysis of the nitrile and methyl torsional vibrations of n‐propyl cyanide in its S0 electronic state

This work presents a structural and vibrational theoretical study of n‐propyl cyanide as a function of the nitrile and methyl torsional modes. A potential energy hypersurface is built at the MP4(SDQ)/aug‐cc‐pVTZ//MP2/aug‐cc‐pVTZ theory level. The equilibrium structure is found in a gauche conformation. Another minimum is found for the trans form. The maximum appears in a cis conformation. For the first time, the interconversion barriers between the different forms are calculated. A two‐dimensional anharmonic vibrational Hamiltonian is built for the nitrile and methyl torsional modes. We find the vibrational energy levels to organize in two stacks associated to the gauche and trans forms. Fundamental frequencies of 113.12 and 220.54 cm^?1 are predicted for the nitrile and methyl torsions in the equilibrium, gauche, conformer. In addition, we find symmetry allowed transitions between the gauche and trans energy levels stacks. The lowest transition is predicted to appear at 24.49 cm^?1. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Development of massive multilevel molecular dynamics simulation program,platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

A massively parallel program for quantum mechanical‐molecular mechanical (QM/MM) molecular dynamics simulation, called Platypus (PLATform for dYnamic Protein Unified Simulation), was developed to elucidate protein functions. The speedup and the parallelization ratio of Platypus in the QM and QM/MM calculations were assessed for a bacteriochlorophyll dimer in the photosynthetic reaction center (DIMER) on the K computer, a massively parallel computer achieving 10 PetaFLOPs with 705,024 cores. Platypus exhibited the increase in speedup up to 20,000 core processors at the HF/cc‐pVDZ and B3LYP/cc‐pVDZ, and up to 10,000 core processors by the CASCI(16,16)/6‐31G** calculations. We also performed excited QM/MM‐MD simulations on the chromophore of Sirius (SIRIUS) in water. Sirius is a pH‐insensitive and photo‐stable ultramarine fluorescent protein. Platypus accelerated on‐the‐fly excited‐state QM/MM‐MD simulations for SIRIUS in water, using over 4000 core processors. In addition, it also succeeded in 50‐ps (200,000‐step) on‐the‐fly excited‐state QM/MM‐MD simulations for the SIRIUS in water. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Structure,properties, and nature of the BrF‐HX complexes: An Ab initio study

Structure and properties of complexes (energies and charge transfer) of complexes BrF‐HX (X = F, Cl, Br, I) have been investigated at the MP2/aug‐cc‐pVDZ (aug‐cc‐pVDZ‐pp basis sets for I) level. Two types of geometries (hydrogen‐bonded and halogen‐bonded) are observed. The calculated interaction energies show that the halogen bonded structures are more stable than the corresponding hydrogen‐bonded structures. To study the nature of the intermolecular interactions, symmetry‐adapted perturbation theory (SAPT) energy decomposition analysis reveals that the BrF‐HX complexes are dominantly electrostatic in nature. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011