Theoretical studies of uracil–(H2O)n (n = 1–7) clusters by ab initio and ABEEMσπ/MM fluctuating charge model

Uracil–(H₂O)_n (n = 1–7) clusters were systemically investigated by ab initio methods and the newly constructed ABEEMσπ/MM fluctuating charge model. Water molecules have been gradually placed in an average plane containing uracil. The geometries of 38 uracil–water complexes were obtained using B3LYP/6-311++G** level optimizations, and the energies were determined at the MP2/6-311++G** level with BSSE corrections. The ABEEMσπ/MM potential model gives reasonable properties of these clusters when comparing with the present ab initio data. For interaction energies, the root mean square deviation is 0.96 kcal/mol, and the linear coefficient reaches 0.997. Furthermore, the ABEEMσπ charges changed when H₂O interacted with the uracil molecule, especially at the sites where the hydrogen bond form. These results show that the ABEEMσπ/MM model is fine giving the overall characteristic hydration properties of uracil–water systems in good agreement with the high-level ab initio calculations.     

The impact of basis set superposition error on the structure of π?π dimers

The effect of basis set superposition error (BSSE) on the structure and energy of benzene, naphthalene, corannulene, and sumanene dimer has been analyzed. MP2 method was chosen and the effect is estimated using 6‐31G, 6‐31G(d), 6‐311+G(d), cc‐pVDZ, and cc‐pVTZ basis sets. The model calculations on benzene dimer indicate that the impact of BSSE on the equilibrium geometry of π‐stacked dimers appears to be quite significant. Calculations on larger molecular dimers such as the dimers of naphthalene, corannulene, and sumanene are also studied. The practical implication of the current observation on modeling the macromolecular structure is discussed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Coupling characteristics and proton transfer mechanisms of guanine–Na monohydrate

The coupling characteristics and the proton transfer mechanisms of guanine–Na⁺ monohydrate are determined in this investigation after the implementation of the geometry optimization and the harmonic vibrational frequency calculations. There are two elementary coupling modes: the interaction of monohydrated sodium ion with two heteroatoms which form a ringed coupling, and hydrogen-bond involved coupling mode. Two potential reaction pathways, coupling mode and hydration have been taken into account, and the accurate values of binding energy are corrected for basis set superposition error (BSSE) and zero-point vibrational energy (ZPVE). Relative energies of the hydrated guanine–sodium ion complexes indicate that the ringed-coupling complexes are predominant geometries with much lower energies. Monohydrated sodium ion coupling with O6 and N7 generates the most stable geometry with a five-member cycle. Sodium ion plays an important role in the tautomerization for guanine–sodium ion complexes. This investigation indicates that the stable cation-π complexes cannot be optimized for guanine–sodium ion monohydrate. Amino-involved coupling often gives rise to a twisted four-membered cycle with unrealistic distribution of positive charge and higher energies. The rotation of amino group is likely to lead to the redistribution of the base pair hydration bonding. Effective distribution of the positive charge is an important factor in the stabilization of biological systems and binding energies for the monohydrated guanine–sodium ion complexes. The enolic coupling complex has the higher energy than the keto type due to the hindrance for the positive charge.     

A theoretical study of the C–HN hydrogen bond in the methane–ammonia complex

The C–HN hydrogen bond in the methane–ammonia complex is studied by determining its bond dissociation energy (BDE) and the n(N)→σ^*(C–H) interaction. At the MP2(Full)/6-311++G(3df,2p) level of theory with basis set superposition error (BSSE) correction, the BDE was determined to be 2.5 kJ mol⁻¹. The n(N)→σ^*(C–H) interaction at this level of theory was found to be 3.7 kJ mol⁻¹ by natural bond orbital (NBO) analysis. It was also found that the NBO values are in general higher than the BDE values with BSSE correction when they are compared at the same level of theory.     

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.     

Conformational dependence of the second hyperpolarizability of quadrupolar molecules

Hatree–Fock calculations at ab initio and semiempirical levels were carried out for the averaged polarizability α and second hyperpolarizability γ of two pairs of quadrupolar isomers with different donor and acceptor groups. These properties were correlated with the antibonding/bonding π occupation number (π*/π ratio). It was found that isomers with extended π systems had low π*/π ratios and high α and γ values, while low α and γ values were obtained for isomers with large π*/π ratios and no extended π system. The PM3 and PM6 α values were found to be in excellent agreement with the HF/6-31+G(d,p) ones. The PM3 values for γ were significantly larger than those calculated by HF/6-31+G(d,p), with an average PM3/HF ratio of 1.43. The PM6 results were noticeably better with a ratio of 0.85. The calculation of α and γ at MP2/6-31+G(d,p) level for representative isomers showed that the contribution of the electron correlation to their values was small and that the HF/6-31+G(d,p) method provides reliable values at much lower computational cost.     

Complete basis set limit of Ab initio binding energies and geometrical parameters for various typical types of complexes

Using basis‐set extrapolation schemes for a given data set, we evaluated the binding energies and geometries at the complete basis set (CBS) limit at the levels of the second order Møller–Plesset perturbation theory (MP2) and the coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)]. The systems include the hydrogen bonding (water dimer), aromatic interaction (benzene dimer), π–H interaction (benzene–water), cation–water, anion–water, π–cation interaction (cation–benzene), and π–anion interaction (anion–triazine). One extrapolation method is to exploit both BSSE‐corrected and BSSE‐uncorrected binding energies for the aug‐cc‐pVNZ (N = 2, 3, 4, …) basis set in consideration that both binding energies give the same CBS limit (CBS^B). Another CBS limit (CBS^C) is to use the commonly known extrapolation approach to exploit that the electron correlation energy is proportional to N^?3. Since both methods are complementary, they are useful for estimating the errors and trend of the asymptotic values. There is no significant difference between both methods. Overall, the values of CBS^C are found to be robust because of their consistency. However, for small N (in particular, for N = 2, 3), CBS is found to be slightly better for water–water interactions and cation–water and cation–benzene interactions, whereas CBS is found to be more reliable for bezene–water and anion–water interactions. We also note that the MP2 CBS limit value based on N = 2 and 3 combined with the difference between CCSD(T) and MP2 at N = 2 would be exploited to obtain a CCSD(T)/CBS value for aromatic–aromatic interactions and anion–π interactions, but not for cationic complexes. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008     

Solvent-dependent luminescent Cu(I) framework based on 5-(4-pyridyl)tetrazole

A new Cu(Ι) coordination compound, Cu₄(L)₄·2EtOH (1), has been obtained from the solvothermal reaction of CuBr, HL (L=5-(4-pyridyl) tetrazole), EtOH and NH₃·H₂O. The structure determination reveals that 1 has a 2D network, where each Cu(I) atom adopts a trigonal coordination mode. The 2D networks stacked in an ABAB sequence through the π–π interaction to form a 3D supramolecular framework, giving a 1D channel along the b-axis. The TGA and powder XRD measurements reveal that the framework is stable after removal of the guest molecules. Gas (N₂) adsorption measurement was carried out for the framework. Framework 1 shows II sorption profile with N₂, which indicates that N₂ molecules cannot diffuse into the micropore and only surface adsorption occurs. The photoluminescent research shows that compound 1 displays an interesting solvent-dependent luminescence.     

Basis sets for molecular interactions. 2. Application to H3N?HF,H3N?HOH,H2O?HF, (NH3)2, and H3CH?OH2

Modifications of the standard 6-31G** basis set as recommended in the accompanying paper are found to markedly lower the basis set superposition error (BSSE) in the title complexes, in contrast to enlargement to a triple-ζ scheme or by addition of a diffuse sp shell or a second set of d-functions without prior optimization, all of which lead to BSSE increase. After appropriate correction for correlation and superposition effects, all basis sets (with the exception of the standard 6-31G** and 6-311G** with their very large BSSE) predict the cyclic geometry of NH₃ dimer to be more stable than the linear arrangement. Correlation and BSSE can shift the equilibrium intermolecular distance in H₃CH-OH₂ by up to 0.4 Å. Failure to correct for superposition error leads to a drastic exaggeration of both the SCF and MP2 components of the interaction energy in this complex. Much better estimates are furnished by our recommended basis sets with their smaller superposition errors.     

Accuracy of geometries: influence of basis set,exchange–correlation potential,inclusion of core electrons,and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.     

平面五元水分子簇的量子化学研究

选用Gaussian03的B3LYP/6-31G(d,p)、DMol3的BLYP/DNP和deMon的BLYP/TZVP等方法计算了甲烷水合物(结构-1)中平面五元水分子簇的结合能和氢键能,作了基组重叠误差(BSSE)和色散能(dispersion)的修正,估算了次级相互作用的贡献.在DMol3程序中使用了大型数值基组DNP,将基组重叠误差降至最低.在Gaussi-an03的B3LYP/6-31G(d,p)计算中,采用平衡法(Counterpoise)校正基组重叠误差.两种计算方法给出了一致的结果,证实了在使用6-31G(d,p)基组时,一对水分子在平衡距离的基组重叠误差高达8 kJ/mol.为估算色散能的贡献,使用了新近发展的包含色散能的密度泛函的DFT程序deMon计算了五元水分子簇.用多种方法计算出了经基组重叠误差和色散能修正的五元水分子簇的分子间结合能和氢键能的较为精确的势能超曲面,为甲烷和其他气体水合物的分子动力学模拟提供了依据.     

Hydrogen-bonding interaction of 5,6-dihydrouracil with RNA bases: DFT and MP2 studies

5,6-Dihydrouracil (DHU) is a rare pyrimidine base naturally occurring in tRNAs, it differs from the base uracil due to the saturation of the C₅–C₆ bond. This work presents the interaction energies of complexes formation involving DHU bound to the natural RNA bases adenine (A), uracil (U), guanine (G), and cytosine (C). Full geometry optimization has been performed for the studied complexes by B3LYP/6-31+G(d,p) and MP2/6-31+G(d,p) calculations. The interaction energies were corrected for the basis-set superposition error (BSSE), using the full Boys–Bernardi counterpoise correction scheme. We find that the stability order is DHU:G > DHU:A > DHU:C  DHU:U.     

Aromatic Rings as Molecular Determinants for the Molecular Recognition of Protein Kinase Inhibitors

Protein kinases are key enzymes in many signal transduction pathways, and play a crucial role in cellular proliferation, differentiation, and various cell regulatory processes. However, aberrant function of kinases has been associated with cancers and many other diseases. Consequently, competitive inhibition of the ATP binding site of protein kinases has emerged as an effective means of curing these diseases. Over the past three decades, thousands of protein kinase inhibitors (PKIs) with varying molecular frames have been developed. Large-scale data mining of the Protein Data Bank resulted in a database of 2139 non-redundant high-resolution X-ray crystal structures of PKIs bound to protein kinases. This provided us with a unique opportunity to study molecular determinants for the molecular recognition of PKIs. A chemoinformatic analysis of 2139 PKIs resulted in findings that PKIs are “flat” molecules with high aromatic ring counts and low fractions of sp³ carbon. All but one PKI possessed one or more aromatic rings. More importantly, it was found that the average weighted hydrogen bond count is inversely proportional to the number of aromatic rings. Based on this linear relationship, we put forward the exchange rule of hydrogen bonding interactions and non-bonded π-interactions. Specifically, a loss of binding affinity caused by a decrease in hydrogen bonding interactions is compensated by a gain in binding affinity acquired by an increase in aromatic ring-originated non-bonded interactions (i.e., π–π stacking interactions, CH–π interactions, cation–π interactions, etc.), and vice versa. The very existence of this inverse relationship strongly suggests that both hydrogen bonding and aromatic ring-originated non-bonded interactions are responsible for the molecular recognition of PKIs. As an illustration, two representative PKI–kinase complexes were employed to examine the relative importance of different modes of non-bonded interactions for the molecular recognition of PKIs. For this purpose, two FDA-approved PKI drugs, ibrutinib and lenvatinib, were chosen. The binding pockets of both PKIs were thoroughly examined to identify all non-bonded intermolecular interactions. Subsequently, the strengths of interaction energies between ibrutinib and its interacting residues in tyrosine kinase BTK were quantified by means of the double hybrid DFT method B2PLYP. The resulting energetics for the binding of ibrutinib in tyrosine kinase BTK showed that CH–π interactions and π–π stacking interactions between aromatic rings of the drug and hydrophobic residues in its binding pocket dominate the binding interactions. Thus, this work establishes that, in addition to hydrogen bonding, aromatic rings function as important molecular determinants for the molecular recognition of PKIs. In conclusion, our findings support the following pharmacophore model for ATP-competitive kinase inhibitors: a small molecule features a scaffold of one or more aromatic rings which is linked with one or more hydrophilic functional groups. The former has the structural role of acting as a scaffold and the functional role of participating in aromatic ring-originated non-bonded interactions with multiple hydrophobic regions in the ATP binding pocket of kinases. The latter ensure water solubility and form hydrogen bonds with the hinge region and other hydrophilic residues of the ATP binding pocket.     

Hydrogen Bonding and Aromatic π–π Stacking in the Crystal Structures of Water-Soluble Daidzein Derivatives

Water-soluble daidzein derivatives, [Ni(H₂O)₆](C₁₆H₁₁O₄SO₃)₂⋅10H₂O and [Zn(H₂O)₆] (C₁₆H₁₁O₄SO₃)₂⋅10H₂O (C₁₆H₁₁O₄SO₃, 7-methoxy-4′-hydroxylisoflavone-3′-sulfonate) were synthesized and their crystal structures were determined by X-ray diffraction analysis. The crystals of them all belong to triclinic crystal system, space group P . The results show that the two derivatives consist of metal cation [Ni(H₂O)₆]²⁺ and [Zn(H₂O)₆]²⁺, anion C₁₆H₁₁O₄SO₃⁻ and H₂O. Ni²⁺ and Zn²⁺ are the centers of the two compounds, respectively. A hydrophilic region is built by a variety of hydrogen bonds among [Ni(H₂O)₆]²⁺ or [Zn(H₂O)₆]²⁺, C₁₆H₁₁O₄SO₃⁻ and the lattice water molecules. Aromatic π–π stacking interactions assemble the isoflavone skeletons into a column and the columns form a hydrophobic region of daidzein derivatives. The sulfo-groups bridge the hydrophilic and hydrophobic region as well as the inorganic and organic components.     

Molybdenum(VI) network polymers based on anion–π interaction and hydrogen bonding: Synthesis, crystal structures and oxidation catalytic application

A crystallographic investigation of anion–π interactions and hydrogen bonds on the preferred structural motifs of molybdenum(VI) complexes has been carried out. Two molybdenum(VI) network polymers MoO₂F₄·(Hinca)₂ (1) and MoO₂F₃(H₂O)·(Hinpa) (2), where inca = isonicotinamide and inpa = isonipecotamide, have been synthesized, crystallographically characterized and successfully applied to alcohol oxidation reaction. Complex 1 crystallizes in the monoclinic space C2/c: a = 16.832(3) Å, b = 8.8189(15) Å, c = 12.568(2) Å, β = 118.929(3)°, V = 1560.1(5) Å³, Z = 4. Complex 2 crystallizes in the triclinic space P-1: a = 5.459(2) Å, b = 9.189(4) Å, c = 12.204(5) Å, α = 71.341(6)°, β = 81.712(7)°, γ = 77.705(7)°, V = 564.8(4) Å³, Z = 2. Complex 1 consists of hydrogen bonding and anion–π interactions, both of which are considered as important factors for controlling the geometric features and packing characteristics of the crystal structure. The geometry of the sandwich complex of [MoO₂F₄]²⁻ with two pyridine rings indicates that the anion–π interaction is an additive and provides a base for the design and synthesis of new complexes. For complex 2, the anions and the protonated inpa ligands form a 2D supramolecular network by four different types of hydrogen contacts (N–HF, N–HO, O–HF and O–HO). The catalytic ability of complexes 1 and 2 has also been evaluated by applying them to the oxidation of benzyl alcohol with TBHP as oxidant.     

Structures and excitation energies of Zn–tetraarylporphyrin analogues: A theoretical study

The photophysical properties of β-substituted Zn–tetraarylporphyrin (ZnTAP) analogues used as dyes in dye-sensitized solar cells were studied using density functional theory (DFT). Singlet-excitation energy calculations of ZnTAP analogues were performed using time-dependent DFT with B3LYP, B3PW91, PBE0 exchange–correlation functionals at 6-31G(d) and 6-31+G(d) basis sets using B3LYP/6-31G(d) geometries. The PBE0 functional at 6-31+G(d) basis set provided a better correlation with the experimental data for both B- and Q-bands. The inclusion of solvation effect in the calculations provided a good agreement in terms of B:Q_ave ratio of the oscillator strengths for both analogues with the experimental values. Analogue 2 has a higher and a more balanced charge-carrier transport rates than analogue 1. In general, the addition of an electron-donating group in the meso-substituent (analogue 2) resulted in a narrower band gap, higher oscillator strength, a more red-shifted absorption spectra, and better charge-transfer characteristics than analogue 1.     

Theoretical study on the structure and UV–visible spectrum of pyridine–chloranil charge-transfer complex

The ground-state structure of the charge-transfer complex formed by pyridine (Py) as electron donor and chloranil (CA) as acceptor has been studied by full geometry optimization at the MP2 and DFT levels of theory. Binding energies were calculated and counterpoise corrections were used to correct the BSSE. Both MP2 and DFT indicate that the pyridine binds with chloranil to form an inclined T-shape structure, with the pyridine plane perpendicular to the chloranil. The CP and ZPE corrected binding energies were calculated to be 14.21 kJ/mol by PBEPBE/6-31G(d) and 23.21 kJ/mol by MP2/6-31G(d). The charge distribution of the ground state Py–CA complex was evaluated with the natural population analysis, showing a net charge transfer from Py to CA. Analysis of the frontier molecular orbitals reveals a σ–π interaction between CA and Py, and the binding is reinforced by the attraction of the O₇ atom of CA with the H₂₃ atom of Py. TD-DFT calculations have been performed to analyze the UV–visible spectrum of Py–CA complex, revealing both the charge transfer transitions and the weak symmetry-relieved chloranil π–π^* transition in the UV–visible region.     

The total π-electron energy as a problem of moments: application of the Backus–Gilbert method

The total π-electron energy problem can be formulated as a classical problem of moments. This observation allows us to apply general methodologies developed in the field of moment’s theory to solve the total π-electron energy problem. In the present article, we apply the Backus–Gilbert method to obtain analytical expressions for the total π-electron energy in terms of its spectral moments.AMS subject classification: 30E05, 05C50, 92E10, 78M05     

A molecular orbital study of nitrogen inversion in aniline with extensive geometry optimization

The geometry and energy of aniline have been calculated using the 6-31G and 6-31G^*(5D) basis sets for the planar structure and various pyramidal structures, assuming that the ring and the N-atom bonded to it lie in the same plane, but otherwise with full geometry optimization. With the 6-31G basis set the planar structure is predicated to be the most stable, whereas the inclusion of polarization functions in the 6-31G^*(5D) basis set finds a pyramidal structure with the out-of-plane angle =42.3° to be most stable and the energy barrier to inversion via the planar transition state to be 1.59±0.02 kcal mol^–1, in close agreement with experiment. Completing the optimization, allowing the N-atom and the C- and H-atoms of the ring to take up equilibrium out-of-plane positions increases the calculated energy carrier to inversion by less than 0.1 kcal mol^–1 to 1.66 kcal mol^–1. The ring adopts a very shallow inverted boat-type conformation with N₇-C₁C₄ = 2.0°.     

Density functional theory study on surface-enhanced Raman scattering of 4,4′-azopyridine on silver

Surface-enhanced Raman scattering (SERS) of 4,4′-azopyridine (AZPY) on silver foil substrate was measured under 1064 nm excitation lines. Density-functional theory (DFT) methods were used to calculate the structure and vibrational spectra of models such as Ag–AZPY, Ag₄–AZPY and Ag₆–AZPY complexes with B3LYP/6-31++G(d,p)(C,H,N)/Lanl2dz(Ag) basis set. The Raman bands of AZPY were identified on the ground of analog computation of potential energy distribution. The calculated spectra of Ag₄–AZPY and Ag₆–AZPY models were much approximated to the experimental results than that of Ag–AZPY model. The DFT results showed that the angles between two pyridyl rings keep 0° from AZPY to Ag–AZPY, Ag₄–AZPY and Ag₆–AZPY model. The energy gaps between the HOMO and LUMO changed from 363 to 1140 nm for AZPY-Ag complexes according to the DFT results. An conclusion was conceived that chemical enhancement mechanism may play an important role in the SERS of AZPY on silver substrate.