Effects of different basis sets and donor‐acceptor groups on linear and second‐order nonlinear optical properties and molecular frontier orbital energies

The calculation of molecular hyperpolarizability, molecular frontier orbital energies of some donor‐acceptor oxadiazoles ( 5a – f , 8a – f , and 9a – f ) have been investigated using ab initio methods and different basis sets. Ab initio optimizations were performed at the Hartree–Fock (HF) and density functional (Beckee‐3–Lee–Yang–Parr; B3LYP) levels of theory with 6‐31G basis set. The polarizability (<α>), anisotropy of polarizability (Δα), and ground‐state dipole moment (μ), first hyperpolarizability (β), and molecular frontier orbital (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) energies of 5a – f , 8a – f , and 9a – f have been calculated at the HF and B3LYP methods with 6‐31G, 6‐31G(d), 6‐31+G(d), 6‐31++G(d,p), 6‐311G, 6‐311G(d), 6‐311+G(d), and 6‐311++G(d,p) basis sets. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained using molecular frontier orbital energies. The <α>, Δα, μ, β, HOMO, LUMO energies, η and χ parameters have been investigated as dependence on the choice of method and basis set. The variation graphics of <α>, Δα, μ, β, η, and χ parameters using HF and B3LYP methods with different basis sets are presented. We have examined the frontier molecular orbital pictures of 5a – f , 8a – f , and 9a – f using B3LYP/6‐31++G(d,p) level. The 5a – f , 8a – f , and 9a – f display significant linear, second‐order molecular nonlinearity, and molecular parameters and provide the basis for future design of efficient nonlinear optical materials having the 1,3,4‐oxadiazole core. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A Theoretical Study of the Kinetics of the Hydrogen Atom Abstraction Reactions from Cyclopropane by H,O (3P), and Cl (2P3/2) Atoms and OH Radicals

The rate constants of the H‐abstraction reactions from cyclopropane by H, O (³P), Cl (²P_3/2), and OH radicals have been calculated over the temperature range of 250?2500 K using two different levels of theory. Calculations of optimized geometrical parameters and vibrational frequencies are performed using the MP2 method combined with the cc‐pVTZ basis set and the 6–311++G(d,p) basis set. Single‐point energy calculations have been carried out with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (perturbatively) electron excitations CCSD(T) using either the cc‐pVTZ, aug‐cc‐pVTZ, and aug‐cc‐pVQZ basis sets or the 6–311++G(3df,3pd) basis set. The CCSD(T) calculated potential energies have been extrapolated to the complete basis limit (CBS) limit. The Full Configuration Interaction (FCI) energies have been also estimated using the continued‐fraction approximation as proposed by Goodson (J. Chem. Phys., 2002, 116, 6948–6956). Canonical transition‐state theory combined with an Eckart tunneling correction has been used to predict the rate constants as a function of temperature using two kinetic models (direct abstraction or complex mechanism) at two levels of theory (CCSD(T)‐cf/CBS//MP2/cc‐pVTZ and CCSD(T)‐cf/6–311++G(3df,3pd)//MP2/6–311++G(d,p)). The calculated kinetic parameters are in reasonable agreement with their literature counterparts for all reactions. In the light of these trends, the use of the Pople‐style basis sets for studying the reactivity of other systems such as larger cycloalkanes or halogenated cycloalkanes is recommended because the 6–311++G(3df,3pd) basis set is less time consuming than the aug‐cc‐pVQZ basis set. Based on our calculations performed at the CCSD(T)‐cf/CBS//MP2/cc‐pVTZ level of theory, the standard enthalpy of formation at 298 K for the cyclopropyl radical has been reassessed and its value is (290.5 ± 1.6) kJ mol^?1.     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Calculation of dissociation constants and chemical hardness of some biologically important molecules: A theoretical study

The gas‐phase geometries of neutral, protonated, and deprotonated forms of some biologically important molecules, alanine (Ala), glycine (Gly), phenylalanine (Phe), and tyrosine (Tyr), were optimized using density functional theory at B3LYP/6‐311++G(d) and the ab initio HF/6‐311++G(d) level of theories. The neutral and different stable ionic states of Ala, Gly, Phe, and Tyr have also been solvated in aqueous medium using polarizable continuum model for the determination of solvation free energies in the aqueous solution. The gas‐phase acidity constants of above four molecules have been also calculated at both levels of theories and found that the values calculated at HF/6‐311++G(d) method are in good agreement with experimental results. A thermodynamic cycle was used to determine the solvation free energies for the proton dissociation process in aqueous solution and the corresponding pK_a values of these molecules. The pK_a values calculated at B3LYP/6‐311++G(d) method are well supported by the experimental data with a mean absolute deviation 0.12 pK_a units. Additionally, the chemical hardness and the ionization potential (IP) for these molecules have been also explored at both the level of theories. The Tyr has less value of chemical hardness and IP at both levels of theories compared with other three molecules, Ala, Gly, and Phe. The calculated values of chemical hardness and IP are decreasing gradually with the substitution of the various functional groups in the side chain of the amino acids. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum study on the electrocyclic reactions of CH2CHCHCHX (XH,F, Cl)

The microscopic mechanisms of the electrocyclic reactions for cis‐1,3‐butadiene and its monofluoro‐, monochloroderivatives have been studied by density functional theory (DFT), using the B3LYP method and 6‐311++G** basis sets. We optimized the geometric configurations of reactants, transition states, and products; verified all the probable transition states through vibrational analysis; and calculated the relative single‐point energies at the QCISD(T)/6‐311++G**//B3LYP/6‐311++G**. The results show that the monofluoro‐, monochloroderivatives of cis‐1,3‐butadiene both have two conformers; the reactant favors the electrocyclic reaction when one outboard hydrogen atom of the CH₂ groups is substituted by the fluorine or chlorine atom. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Rapid evaluation of the binding energies between peptide amide and DNA base

The binding energies and the equilibrium hydrogen bond distances as well as the potential energy curves of 20 hydrogen‐bonded amide–base dimers are evaluated from the analytic potential energy function established in our laboratory recently. The analytic potential energy function is used to calculate the N? H···N, N? H···O?C, C? H···N, and C? H···O?C dipole–dipole attractive interaction energies and C?O···O?C, N? H···H? N, and N? H···H? C dipole–dipole repulsive interaction energies in the 20 dimers composed of DNA bases adenine, guanine, cytosine, or thymine and peptide amide. The calculation results show that the potential energy curves obtained from the analytic potential energy function are in good agreement with those obtained from MP2/6‐311+G** calculations by including the basis set superposition error (BSSE) correction. For all the 20 dimers, the analytic potential energy function yields the binding energies of the MP2/6‐311+G** with BSSE correction within the error limits of 0.50 kcal/mol for 19 dimers, only one difference is larger than 0.50 kcal/mol and the difference is only 0.61 kcal/mol. The analytic potential energy function produces the equilibrium hydrogen bond distances of the MP2/6‐311+G** with BSSE correction within the error limits of 0.030 Å for all the 20 dimers. The analytic potential energy function is further applied to four more complicated DNA base‐peptide amide systems involving amino acid side chain and β‐sheet. The values of the binding energies and equilibrium hydrogen bond distances obtained from the analytic potential energy function are also in good agreement with those obtained from MP2 calculations with the BSSE correction. These results demonstrate that the analytic potential energy function can be used to evaluate the binding energies in hydrogen‐bonded peptide amide–DNA base dimers quickly and accurately. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

The influence of formamide (model of protein unit) on the intramolecular proton transfer in the DNA simple base guanine: A density functional theory study

For the purpose of investigating the influence of protein unit on the intramolecular proton transfer (IPT) reactions in the simple base guanine, a simple model (formamide) of peptides is designed to biological system investigations, and five complexes of formamide–guanine (FG1, FG2, FG3, FG4, and FG5) are determined at the B3LYP/6‐311++G(d,p) level of theory. For comparison, HF and MP2 methods are also used in this paper. The proton transfer (PT) reaction processes of guanine and FGs have been investigated employing the B3LYP/6‐311++G(d,p) level of theory. The selected thermodynamic and kinetic parameters, such as the activation energies (E_a), changes of enthalpy (ΔH) and changes of free energies (ΔG), as well as the equilibrium constants (K_p) for those reaction processes, have also been obtained by calculational means. The calculated results indicate that the assisted and protected effects of formamide on IPT in guanine are site‐dependent. CH1 is the lowest activation energy needed PT process no matter where the formamide molecule is located in. The activation energy of CH1 with formamide in S2 is the lowest one (153.3 KJ/mol), whereas the one of CH5 with formamide in S5 is the highest (318.3 KJ/mol). © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

乙烯、乙炔和苯与氨基锂间的π型锂键相互作用

分别在DFT-B3LYP和MP2/6-311++G**水平上求得乙烯、乙炔和苯与氨基锂锂键复合物势能面上的3个几何构型. 频率分析表明,3个构型均为稳定构型. 计算结果表明,形成锂键复合物后,质子供体N(2)- Li(4)的键长明显增大,且其伸缩振动的频率发生了不同程度的红移. 分别在乙烯…氨基锂、乙炔…氨基锂和苯…氨基锂三种复合物中,经MP2/6-311++G**水平计算的同时含基组重叠误差(BSSE)和零点振动能校正的单体间锂键相互作用能分别为-26.04、-24.86 和 -30.02 kJ·mol-1. 自然键轨道理论（NBO）分析表明单体间的弱相互作用属于π-s型锂键.     

Many-body interaction in glycine-(water)3 complex using density functional theory method

Various configurations were investigated to find the most stable structures of glycine-(water)3 complex. Five different optimized conformers of glycine-(water)3 complex are obtained from density functional theory calculations using 6-311++G* basis set. Relaxation energy and many body interaction energies (two, three, and four body) are also calculated for these conformers. Out of the five conformers, the most stable conformer has the BSSE corrected total energy -513.917 967 7 Hartree and binding energy -27.28 Kcal/mol. It has been found that the relaxation energies, two body energies and three body energies have significant contribution to the total binding energy whereas four body energies are very small. The chemical hardness and chemical potential also confirmed the stability of the conformer having lowest total energy.     

Theoretical study of hydrogen bonds between acetylene and selected proton donor systems

The equilibrium structures, the binding energies, and the second‐order energy components of a series of hydrogen‐bonded complexes involving acetylene are studied. The strength of the binding energy of the selected systems (HF … HCCH, HCl … HCCH, HCN … HCCH, and HCCH … HCCH) was different, ranging from a very weak interaction to a strong interaction. Calculations have been carried out at both the Hartree–Fock and correlated (second‐order Møller–Plesset perturbation theory) levels of theory, using several different basis sets [6‐31G(d,p), 6‐311G(d,p), 6‐31G++(d,p), 6‐311G++(d,p), 6‐31++G(2d,2p) and 6‐311++G(2d,2p)]. The widely used a posteriori Boys–Bernardi counterpoise (CP) correction scheme has been compared with the a priori CHA/CE, CHA–MP2, and CHA–PT2 methods, using the chemical Hamiltonian approach (CHA). The results show that at both levels the CP and the appropriate CHA results are very close to each other. Only the monomer‐based CHA‐PT2 theory gives slightly overcorrected results, reflecting that the charge transfer and polarization effects are not taken into account in this method up to second order. We have also applied our earlier developed energy decomposition scheme in order to decompose the second‐order energy contribution into different physically meaningful components. The results show that at large and intermediate intermolecular distances, the second‐order intermolecular contribution is almost equal to the sum of different physically meaningful components (e.g., polarization, charge transfer, dispersion), while at shorter distances the slightly strong overlap effects fairly disturb this simple additivity. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 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     

A theoretical study of inversion barriers and NMR chemical shifts of 3-pyrazolines (2,3-dihydro-1H-pyrazoles)

A rather neglected family of heterocyclic compounds, the 3-pyrazolines or 2,3-dihydro-1H-pyrazoles, has been studied theoretically at the B3LYP/6–311++G(d,p) level to obtain geometries and energies and at the GIAO/B3LYP/6–311++G(d,p) level for NMR chemical shifts. The calculated barriers of inversion of the N-substituents reproduce adequately the scarce experimental data. The calculated ¹H and ¹³C chemical shifts are consistent with those reported in the literature. A combination of both results, geometries, and ¹³C chemical shifts, shed light on the conformation of N-phenyl groups.     

硝酸乙酯分子间相互作用的ab initio研究

在abinitio-HF/6-31G水平上求得硝酸乙酯二聚体势能面上的四种优化构型和电子结构。经MP2电子相关校正和基组叠加误差(BSSE)以及零点能(ZPE)校正，求得二聚体的最大结合能为11.46kJ.mol^-^1，还进行HF/6-311G和HF/6-311++G水平的总能量比较计算，发现6-31G基组对计算结合能比较适合，二子体系间的电荷转移很少，对优化构型进行振动分析，并基于统计热力学求得从单体形成二聚体的热力学性质变化。     

Peptide models XXXI. Conformational properties of hydrophobic residues shaping the core of proteins. An ab initio study of N‐formyl‐L‐valinamide and N‐formyl‐L‐phenylalaninamide

Employing introductory (3‐21G RHF) and medium‐size (6‐311++G** B3LYP) ab initio calculations, complete conformational libraries, containing as many as 27 conformers, have been determined for diamide model systems incorporating the amino acids valine (Val) and phenylalanine (Phe). Conformational and energetic properties of these libraries were analyzed. For example, significant correlation was found between relative energies from 6‐311++G** B3LYP and single‐point B3LYP/6‐311++G**//RHF/3‐21G calculations. Comparison of populations of molecular conformations of hydrophobic aromatic and nonaromatic residues, based on their ab initiorelative energies, with their natural abundance indicates that, at least for the hydrophobic core of proteins, the conformations of Val (Ile, Leu) and Phe (Tyr, Trp) are controlled by the local energetic preferences of the respective amino acids. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 732–751, 2001     

Complexation of Phenol and Thiophenol by Amine N‐Oxides: Isothermal Titration Calorimetry and ab Initio Calculations

To develop a new solvent‐impregnated resin (SIR) system for removal of phenols from water, the complex formation of dimethyldodecylamine N‐oxide (DMDAO), trioctylamine N‐oxide (TOAO), and tris(2‐ethylhexyl)amine N‐oxide (TEHAO) with phenol (PhOH) and thiophenol (PhSH) is studied. To this end we use isothermal titration calorimetry (ITC) and quantum chemical modeling (on B3LYP/6‐311G(d,p)‐optimized geometries: B3LYP/6‐311+G(d,p), B3LYP/6‐311++G(2d,2p), MP2/6‐311+G(d,p), and spin component scaled (SCS) MP2/6‐311+G(d,p); M06‐2X/6‐311+G(d,p)//M06‐2X/6‐311G(d,p), MP2 with an extrapolation to the complete basis set limit (MP2/CBS), as well as CBS‐Q). The complexes are analyzed in terms of structural (e.g., bond lengths) and electronic elements (e.g., charges). Furthermore, complexation and solvent effects (in benzene, toluene, and mesitylene) are investigated by ITC measurements, yielding binding constants K, enthalpies ΔH⁰, Gibbs fre energies ΔG⁰, and entropies ΔS⁰ of complex formation, and stoichiometry N. The ITC measurements revealed strong 1:1 complex formation between both DMDAO–PhOH and TOAO–PhOH. The binding constant (K=1.7–5.7×10⁴ M ^?1) drops markedly when water‐saturated toluene was used (K=5.8×10³ M ^?1), and π–π interaction with the solvent is shown to be relevant. Quantum mechanical modeling confirms formation of stable 1:1 complexes with linear hydrogen bonds that weaken on attachment of electron‐withdrawing groups to the amine N‐oxide moiety. Modeling also showed that complexes with PhSH are much weaker than those with PhOH, and in fact too weak for ITC determination. CBS‐Q incorrectly predicts equal or even higher binding enthalpies for PhSH than for PhOH, which invalidates it as a benchmark for other calculations. Data from the straightforward SCS‐MP2 method without counterpoise correction show very good agreement with the MP2/CBS values.     

DFT computational studies on rotation barriers,tautomerism, intramolecular hydrogen bond,and solvent effects in 8‐hydroxyquinoline

Intramolecular hydrogen binding interactions in 8‐hydroxyquinoline, both in its zwitterionic tautomer and in the rotamer without the intramolecular hydrogen bond (IHB), have been computed using the B3LYP and MPW1K density functionals. The rotation of the O? H bond and intramolecular proton transfer reactions were studied theoretically. The following theory levels have been applied: B3LYP/6‐31G(d,p), B3LYP/6‐311++G(d,p), MPW1K/6‐311++G(d,p), and MPW1K/6‐311++G(2d,3p)//MPW1K/6‐311++G(d,p). Natural bond orbital (NBO) analysis has also been carried out. The effect of medium (benzene, chloroform, tetrahydrofuran, 1,2‐dichloroethane, acetone, water) was simulated using the self‐consistent reaction field (SCRF) method within the framework of the polarizable continuum model (PCM), at the MPW1K/6‐311++G(d,p) level. The evolution of geometry, relative energies, heights of rotation (around the O? H bond) and tautomerization barriers, IHB energies, and ΔG(solv) have been systematically investigated. The results obtained have shown the failure to neglect some changes of the above characteristics in polar media with respect to the gaseous phase. The series of stability of the forms under study in the gaseous phase remains the same in solution. Thus, in spite of the important role of the solvent electrostatic effects, the intrinsic stability of those species overcomes the solvent effects. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Contemplation on Some Prismatic Polynitrogen Structures – A DFT Treatment

Polynitrogen compounds, are rare molecules having only nitrogen atoms. In recent years, they have been considered as promising candidates of clean (green) high energy density materials. They possess high energy content and their sole decomposition product is N₂. Presently some prismatic polynitrogen structures (N₆ – N₁₄) are considered within the limitations of density functional theory at the levels of B3LYP/6‐311++G(d,p) and B3LYP/cc‐PVTZ. The calculations reveal that they are all highly endothermic but stable. Certain quantum chemical properties, IR and UV/Vis spectra are reported. Homolytic bond cleavage of top rings are considered. Then, the transition state and activation energies, and also homolytic bond dissociation energies for the top rings have been calculated at the level of UB3LYP/6‐311++G(d,p). Also NICS(0) values have been calculated at the level of B3LYP/6‐311++G(d,p). The results indicate that N₆ and N₁₀ have aromatic and nonaromatic top (and also base) rings, respectively. All the rest of the structures have antiaromatic rings (all the structures have antiaromatic N₄ rings).     

Anharmonic Effect of the Unimolecular Isomerization/Decomposition of Benzyne

The anharmonic and harmonic rate constants were calculated for the unimolecular decomposition of o‐benzyne, the isomerization of o‐benzyne to m‐benzyne, the isomerization of m‐benzyne to p‐benzyne and unimolecular decomposition of p‐benzyne by using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory respectively, in the canonical and microcanonical systems. The geometry and the vibrational frequencies were calculated by MP2 and B3LYP methods with 6‐311G(d,p) basis set and the barrier energies were corrected using CBS‐QB3 theory. The anharmonic effect on the reactions was also examined. Comparison of results for the decompositions of benzyne indicate that both in microcanonical and canonical cases, the anharmonic effect on the decomposition of the o‐C₆H₄ and p‐C₆H₄ are significant, while the anharmonic effect on the two isomerizations are not pronounced.