Covalent bond fragmentation suitable to describe solids in the fragment molecular orbital method

To improve the accuracy of the fragment molecular orbital method (FMO), we introduce a new fragmentation scheme based on using frozen orbitals to describe fractioned bonds. By applying this scheme to a set of polyalanine systems of up to 40 residues for the alpha-helix and beta-strand isomers, we established its accuracy, which is considerably improved compared to the original hybrid orbital projection method used for detaching bonds in FMO. For instance, at the two-body FMO expansion with the 6-311G* basis set, the error was typically reduced 2-4 times, and for 6-31G* the accuracy increase was even larger (10 times in terms of the maximum error). For the Trp-cage protein (PDB file 1L2Y) with many charged residues, a fairly large error was observed, which was shown to become small with a larger fragment size or at the three-body level. Consequently, we applied the new scheme to the adsorption of toluene and phenol on a faujasite zeolite, and we demonstrated that good accuracy can be achieved in reproducing ab initio results.     

The prediction of (1)H chemical shifts in amines: a semiempirical and ab initio investigation

Twenty one conformationally fixed amines and their N,N-dimethyl derivatives were obtained commercially or synthesized. These included cis and trans 4-t-butyl cyclohexylamine, 2-exo and 2-endo norbornylamine, 2-adamantylamine, 4-phenylpiperidine, 1-napthylamine and tetrahydro-1-napthylamine. The (1)H NMR spectra of these amines were measured in CDCl(3) solution, assigned and the (1)H chemical shifts given. This data was used to investigate the effect of the amino group on the (1)H chemical shifts in these molecules. These effects were analyzed using the CHARGE model. This calculates the electric field and steric effects of the amino group for protons more than three bonds removed, together with functions for the calculation of two-bond and three-bond effects. The rotational isomerism about the C--N bond of the amino group was investigated by ab initio calculations of the potential energy surface (PES) about this bond at the HF/3-21G level. The resulting conformers were then minimized at the B3LYP/6-311 + + G (d,p) level. These geometries were then used to calculate the (1)H chemical shifts in the above compounds by CHARGE and the ab initio gauge-invariant atomic orbital (GIAO) method at the B3LYP/6-311 + + G(d,p) level and the shifts were compared with those observed. The compounds investigated gave 170 (1)H chemical shifts ranging from 0.60 to 8.2 ppm. The rms errors (obs.-calc.) were ca 0.1 ppm (CHARGE) and ca 0.2 ppm (GIAO). Large deviations of ca 1.0 ppm were observed for the NH protons in the GIAO calculations. The complex spectra of alkyl and aryl amines can thus be successfully predicted by both ab initio and semiempirical methods except for the NH protons, for which the ab initio calculations are not sufficiently accurate.     

Pair interaction energy decomposition analysis

The energy decomposition analysis (EDA) by Kitaura and Morokuma was redeveloped in the framework of the fragment molecular orbital method (FMO). The proposed pair interaction energy decomposition analysis (PIEDA) can treat large molecular clusters and the systems in which fragments are connected by covalent bonds, such as proteins. The interaction energy in PIEDA is divided into the same contributions as in EDA: the electrostatic, exchange-repulsion, and charge transfer energies, to which the correlation (dispersion) term was added. The careful comparison to the ab initio EDA interaction energies for water clusters with 2-16 molecules revealed that PIEDA has the error of at most 1.2 kcal/mol (or about 1%). The analysis was applied to (H2O)1024, the alpha helix, beta turn, and beta strand of polyalanine (ALA)10, as well as to the synthetic protein (PDB code 1L2Y) with 20 residues. The comparative aspects of the polypeptide isomer stability are discussed in detail.     

Multilayer formulation of the fragment molecular orbital method (FMO)

The fragment molecular orbital method (FMO) has been generalized to allow for multilayer structure. Fragments are assigned to layers, and each layer can be described with a different basis set and/or level of electron correlation. Interlayer boundaries are treated in the general spirit of the FMO method since they also coincide with some interfragment boundaries. The question of the one- and two-layer FMO accuracy dependence upon the fragmentation scheme is also addressed. The new method has been applied to predict the reaction barrier and the reaction heat for the Diels-Alder reaction with a representative set of reactants based on dividing fragments in two layers. The 6-31G* basis set has been used for the active site and the 6-31G*, 6-31G, 3-21G, and STO-3G basis sets have been used for the substituents. Different levels of electron correlation (RHF, B3LYP, and MP2) have been applied to layers in systematic fashion. The one-layer FMO errors in the reaction barrier and the reaction heat were 2.0 kcal/mol or less for all levels applied (RHF, B3LYP, and MP2), relative to full ab initio methods. For the two-layer method the error was found to be several kcal/mol. Benchmark calculations of the activation barrier for the decarboxylation of phenylcyanoacetate by beta-cyclodextrin demonstrated that the two-layer calculations are efficient, being 36 times faster than the regular DFT, as well as accurate, with the error being 1.0 kcal/mol.     

氰基苯阴离子与CO2间的内球电子转移

用半经验AM1方法以及从头算方法在3-21G和6－31G*基组水平上研究了从氰基苯阴离子到CO2的电子转移过程．结果表明，对于先驱物(precursor),三种计算方法得出的给体、受体间的距离分别为0.2728nm(AM1)、0.2479nm（UHF/3-21G）和0.2769nm(UHF/6-31G*)．在这样短的距离内给体的HOMO与受体的LUMO轨道具有相当程度的重叠，应产生较强的相互作用，说明此反应是内球电子转移反应，从而解释了此类体系的电子转移反应不符合Marcus理论的原因．计算给出先驱物的束缚能为0.19eV(AM1)和0.26eV(6-31G*)     

A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

Time-dependent density functional theory based upon the fragment molecular orbital method

Time-dependent density functional theory (TDDFT) was combined with the two-body fragment molecular orbital method (FMO2). In this FMO2-TDDFT scheme, the system is divided into fragments, and the electron density for fragments is determined self-consistently. Consequently, only one main fragment of interest and several fragment pairs including it are calculated by TDDFT. To demonstrate the accuracy of FMO2-TDDFT, we computed several low-lying singlet and triplet excited states of solvated phenol and polyalanine using our method and the standard TDDFT for the full system. The BLYP functional with the long-range correction (LC-BLYP) was employed with the 6-31G(*) basis set (some tests were also performed with 6-311G(*), as well as with B3LYP and time-dependent Hartree-Fock). Typically, FMO2-TDDFT reproduced the full TDDFT excitation energies within 0.1 eV, and for one excited state the error was about 0.2 eV. Beside the accurate reproduction of the TDDFT excitation energies, we also automatically get an excitation energy decomposition analysis, which provides the contributions of individual fragments. Finally, the efficiency of our approach was exemplified on the LC-BLYP6-31G(*) calculation of the lowest singlet excitation of the photoactive yellow protein which consists of 1931 atoms, and the obtained value of 3.1 eV is in agreement with the experimental value of 2.8 eV.     

Extending the power of quantum chemistry to large systems with the fragment molecular orbital method

Following the brief review of the modern fragment-based methods and other approaches to perform quantum-mechanical calculations of large systems, the theoretical development of the fragment molecular orbital method (FMO) is covered in detail, with the emphasis on the physical properties, which can be computed with FMO. The FMO-based polarizable continuum model (PCM) for treating the solvent effects in large systems and the pair interaction energy decomposition analysis (PIEDA) are described in some detail, and a range of applications of FMO to biological studies is introduced. The factors determining the relative stability of polypeptide conformers (alpha-helix, beta-turn, and extended form) are elucidated using FMO/PCM and PIEDA, and the interactions in the Trp-cage miniprotein construct (PDB: 1L2Y) are analyzed using PIEDA.     

Molecular structure of proline

The molecular structures of the two lowest-energy conformers of proline, Pro-I and Pro-II, have been characterized by ab initio electronic structure computations. An extensive MP2/6-31G* quartic force field for Pro-I, containing 62,835 unique elements in the internal coordinate space, was computed to account for anharmonic vibrational effects, including total zero-point contributions to isotopomeric rotational constants. New re and improved r0 least-squares structural refinements were performed to determine the heavy-atom framework of Pro-I, based on experimentally measured (A. Lesarri, S. Mata, E. J. Cocinero, S. Blanco, J. C. Lopez, J. L. Alonso, Angew. Chem. 2002, 114, 4867; Angew. Chem. Int. Ed. 2002, 41, 4673) rotational constant sets of nine isotopomers and our ab initio data for structural constraints and zero-point vibrational (ZPV) shifts. Without the ab initio constraints, even the extensive set of empirical rotational constants cannot satisfactorily fix the molecular structure of the most stable conformer of proline, a 17-atom molecule with no symmetry. After imposing the ab initio constraints, excellent agreement between theory and experiment is found for the heavy-atom geometric framework, the root-mean-square (rms) residual of the empirical rotational constant fit being cut in half by adding ZPV corrections. The most significant disparity, about 0.07 A, between the empirical and the best ab initio structures, concerns the r(N...H) distance of the intramolecular hydrogen bond. Some of the experimental quartic centrifugal distortion constants assigned to Pro-II have been corrected based on data obtained from a theoretical force field.     

Synthesis and guest recognition ability of 2,3-dimethoxy-1,4-phenylene-containing porphyrinoids

The acid-catalyzed condensation of the bispyrrolylbenzene derivative and benzaldehyde yielded macrocycles 1 and 2 bearing three and four dipyrrin units which are connected by 2,3-dimethoxy-1,4-phenylene rings. The cationic guest recognition ability of 1 was investigated by UV-vis absorption, (1)H NMR spectroscopic techniques, and ab initio calculations (HF/3-21G(*)). The tris-dipyrrin macrocycle 1 was found to recognize alkali metals in the O6 binding cavity.     

Adsorption of NH(3) and H(2)O in acidic chabazite. Comparison of ONIOM approach with periodic calculations

The adsorption of NH(3) and H(2)O in acidic chabazite has been studied with the B3LYP method within the cluster approach (5T, 48T clusters) and the periodic approach adopting a Si/Al = 11/1 chabazite and a basis set of polarized double-zeta quality. The 5T cluster has been treated fully ab initio at the B3LYP level whereas the 48T cluster has been treated with the ONIOM2 scheme using B3LYP as the high level of theory and the MNDO, AM1, and HF/3-21G methods as low levels of theory. Periodic calculations show that the adsorption of NH(3) in acidic chabazite takes place through an ion pair (NH(4)(+)-CHA(-)) structure, the computed adsorption energy being -32 kcal/mol. The adsorption of H(2)O leads to a hydrogen bonded (H(2)O-HCHA) complex with the computed adsorption energy of -20 kcal/mol. All ONIOM combinations provide similar structures to those obtained with periodic calculations. Adsorption energies, however, are sensitive to the low level used, especially for NH(3). The ONIOM B3LYP:HF/3-21G method is the one that provides more satisfactory results. Present results show that, for larger zeolites, the ONIOM scheme can be successfully applied while drastically reducing the cost of a fully ab initio treatment.     

Ab initio quantum mechanical study of the binding energies of human estrogen receptor alpha with its ligands: an application of fragment molecular orbital method

We have theoretically examined the relative binding affinities (RBA) of typical ligands, 17beta-estradiol (EST), 17alpha-estradiol (ESTA), genistein (GEN), raloxifene (RAL), 4-hydroxytamoxifen (OHT), tamoxifen (TAM), clomifene (CLO), 4-hydroxyclomifene (OHC), diethylstilbestrol (DES), bisphenol A (BISA), and bisphenol F (BISF), to the alpha-subtype of the human estrogen receptor ligand-binding domain (hERalpha LBD), by calculating their binding energies. The ab initio fragment molecular orbital (FMO) method, which we have recently proposed for the calculations of macromolecules such as proteins, was applied at the HF/STO-3G level. The receptor protein was primarily modeled by 50 amino acid residues surrounding the ligand. The number of atoms in these model complexes is about 850, including hydrogen atoms. For the complexes with EST, RAL, OHT, and DES, the binding energies were calculated again with the entire ERalphaLBD consisting of 241 residues or about 4000 atoms. No significant difference was found in the calculated binding energies between the model and the real protein complexes. This indicates that the binding between the protein and its ligands is well characterized by the model protein with the 50 residues. The calculated binding energies relative to EST were very well correlated with the experimental RBA (the correlation coefficient r=0.837) for the ligands studied in this work. We also found that the charge transfer between ER and ligands is significant on ER-ligand binding. To our knowledge, this is the first achievement of ab initio quantum mechanical calculations of large molecules such as the entire ERalphaLBD protein.     

Theoretical study of C24N4 molecule

Both ab initio 6-31G, 3-21G and STO-3G basis sets and semiempirical PM3 and AM1 molecular orbital calculations are carried out on the C₂₄N₄ molecule of the T_d symmetry group. Results on the fully optimized structure which constrained T_d symmetry, molecular orbitals and vibrational frequency were obtained by both ab initio and semiempirical methods. The binding energy and various thermodynamic properties were also calculated via the PM3 and AM1 semiempirical methods. All the evidence of this work proves that the C₂₄N₄ molecule is stable and that its four six-membered rings with a remarkable delocalized C…C bond are similar to the related rings in the C₆₀ buckminsterfullerene structure.     

Examination of numerical accuracy on fragment-DFT calculations with integral values of total electron density functions

Fragment molecular orbital (FMO) method gives a powerful tool to investigate electronic structures for biological substances, and ABINIT-MP program has been developed to implement ab initio FMO calculations effectively. We introduced DFT code into ABINIT-MP and applied fragment-DFT (F-DFT) calculations to model polypeptides. The total accuracy of numerical integrations employed in those calculations was examined by the total numbers of electrons in the molecules. It is shown that the numerical integral of the total density function under the fragment approximation works as an indicator for the numerically total accuracy on the F-DFT implementation.     

Theoretical study of the N---H tautomerism in free base porphyrin

The N---H tautomerism of free base porphyrin is investigated at the semiempirical spin-unrestricted AM1 (UAM1) and ab initio RHF/3-21G levels. The UAM1 method provides delocalized geometries for all stationary structures without imposing any symmetry constraint. RHF/3-21G geometry optimizations have to be performed under symmetry restrictions to ensure that realistic delocalized structures are obtained. Both the semiempirical and the ab initio calculations predict that the interconversion between trans tautomers proceeds in an asynchronous two-step process via intermediate cis tautomers. The cis tautomers are characterized as minima in the potential energy surface and are 8–10 kcal mol⁻¹ higher in energy. The activation energy for the trans → cis interconversion is calculated to be approximately 23 kcal mol⁻¹ at the 3-21G level. The activation energy for the synchronous trans → trans interconversion is higher and has a value of 30.5 kcal mol⁻¹. The activation energies obtained at the semiempirical UAM1 level are twice as large as the ab initio values.     

Energy decomposition analysis in solution based on the fragment molecular orbital method

We develop the pair interaction energy decomposition analysis (PIEDA) in solution by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM). The solvent screening of the electrostatic interaction and the desolvation penalty in complex formation are described by this approach from ab initio calculations of fragments and their pairs. The applications to the complex of solvated sodium and chlorine ions, as well as to lysine and aspartic acid, show how the analysis helps reveal the physical picture. The PIEDA/PCM method is also applied to a small protein chignolin (PDB: 1UAO), and the solvent screening of the pair interactions is discussed.     

Semiempirical (AM1) and ab initio calculations of 2-X-adenine (X = H, F, Cl) and β-D-1-amino-2,3-didehydro-1,2,3-trideoxyribofuranose

We performed semiempirical (AM1) and ab initio (3-21G and 4-31G^**) calculations, with complete optimization of geometry, for 2-X-adenine (X = H, F, Cl) and selected conformers of β-D-1-amino-2,3-didehydro-1,2,3-trideoxyribo-furanose. Together (as 2-X-2',3'-didehydro-2',3'-dideoxyadenosine), or in separate conjunction with similar fragments, these structures belong to a group of 2',3'-dideoxynucleosides with potential anti-HIV activity.

The 2-X-adenine molecules are basically flat. For the halogenated species, especially the chlorine derivative, the results of the semiempirical method differ from the ab initio findings more widely than for adenine.

The results for the ribose derivative show the existence of conformers differing very little in energy. Ring puckering does not appear to depend on exocyclic torsion angles, structures with different conformations around the exocyclic C-C bond having similar ring conformations in all the cases analysed. The AMI method yielded geometries similar to those obtained ab initio with 3-21G.     

芴与苯并硒化二唑共聚物的电子结构和光谱性质的理论研究

用密度泛函B3LYP方法对低聚体(DEF-BSeD)n(n=1~4)[其中9,9二乙基芴(DEF)单元与苯并硒化二唑(BSeD)单元的摩尔比分别为1∶1和2∶1]进行全优化, 计算电离能(PI)、电子亲和势(EA)和能隙(ΔH-L), 在基态结构的基础上用TD-DFT和ZINDO方法计算激发能和电子吸收光谱, 并利用外推法得到高聚物的相应性质. 从外推结果看出, 随着聚合物中BSeD比例的增大, 聚合物的最低单激发能呈减小的趋势, 最大电子吸收光谱红移. 用CIS方法优化得到单体的S1激发态结构, 计算结果表明, 激发态的结构更趋近于平面构型.     

A combined ab initio and semi-empirical study on the theoretical vibrational spectra and physical properties of polypyrrole

This study concentrates on the important conducting polymer, polypyrrole. Detailed atomistic molecular models have been developed with the help of ab initio and semi-empirical quantum mechanical calculations.The vibrational spectra of isolated pyrrole monomers and oligomers from n=1 and 2, where n is the number of structural repeat units used, have been computed using the ab initio 3-21G basis set. The results obtained are compared with data for the case of oligomers with n=2–5 for both neutral benzenoid and quinonoid oligopyrroles, from semi-empirical predictions obtained by AM1 and PM3. The trends in the computed harmonic force fields, vibrational frequencies and intensities are monitored as a function of the chain length. The data are analysed in conjunction with the trends in computed equilibrium geometries.Also the examination of the heat of formation of these two degenerate forms (quinonoid and benzenoid) has been conducted with respect to increases in the number of rings and the change of methods from AM1 to PM3.     

Geometry optimizations of open-shell systems with the fragment molecular orbital method

The ability to perform geometry optimizations on large molecular systems is desirable for both closed- and open-shell species. In this work, the restricted open-shell Hartree-Fock (ROHF) gradients for the fragment molecular orbital (FMO) method are presented. The accuracy of the gradients is tested, and the ability of the method to reproduce adiabatic excitation energies is also investigated. Timing comparisons between the FMO method and full ab initio calculations are also performed, demonstrating the efficiency of the FMO method in modeling large open-shell systems.