Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree-Fock and density functional theory

An efficient and accurate analytic gradient method is presented for Hartree-Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of N2 molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree-Fock and density functional theory. A highly precise Hartree-Fock optimization for the H2O molecule produced six digits for the geometric parameters.     

Hartree-Fock and density functional theory study of alpha-cyclodextrin conformers

Herein, we report the geometry optimization of four conformers of alpha-cyclodextrin (alpha-CD) by means of PM3, HF/STO-3G, HF/3-21G, HF/6-31G(d), B3LYP/6-31G(d), and X3LYP/6-31G(d) calculations. The analysis of several geometrical parameters indicates that all conformers possess bond lengths, angles, and dihedrals that agree fairly well with the crystalline structure of alpha-CD. However, only three of them (1-3) resemble the polar character of CDs and show intramolecular hydrogen-bonding patterns that agree with experimental NMR data. Among them, conformer 3 appears to be the most stable species both in the gas phase and in solution; therefore, it is expected to be the most suitable representative structure for alpha-CD conformation. The purpose of selecting such a species is to identify an appropriate structure to be employed as a starting point for reliable computational studies on complexation phenomena. Our results indicate that the choice of a particular alpha-CD conformer should affect the results of ab initio computational studies on the inclusion complexation with this cyclodextrin since both the direction and the magnitude of the dipole moment depend strongly on the conformation of alpha-CD.     

Noncovalent interactions in paired DNA nucleobases investigated by terahertz spectroscopy and solid-state density functional theory

Cocrystallized adenine and thymine derivatives, along with the pure monomeric crystals, were investigated by terahertz spectroscopy and solid-state density functional theory (DFT). The methylated nucleobase derivatives crystallize in planar hydrogen-bonded adenine-thymine pairs similar to the manner found in DNA. The spectra obtained for 1-methylthymine, 9-methyladenine, and the 1:1 cocrystal in the range of 10-100 cm(-1) clearly demonstrate that absorptions in this spectral range originate from the uniquely ordered assembly and the intermolecular interactions found in each individual crystal system. The quality of spectral reproduction for the DFT simulations of each system was clearly improved by the inclusion of an empirical correction term for London-type dispersion forces to the calculations. Notably, it was found that these weak dispersion forces in the adenine-thymine cocrystal were necessary to produce a properly converged crystal structure and meaningful simulation of the terahertz vibrational spectrum.     

Self-consistent treatment of spin-orbit interactions with efficient Hartree-Fock and density functional methods

Efficient self-consistent field (SCF) schemes including both scalar relativistic effects and spin-orbit (SO) interactions at Hartree-Fock (HF) and density functional (DFT) levels are presented. SO interactions require the extension of standard procedures to two-component formalisms. Efficiency is achieved by using effective core potentials (ECPs) and by employing the resolution-of-the-identity approximation for the Coulomb part (RI-J) in pure DFT calculations as well as also for the HF-exchange part (RI-JK) in the case of HF or hybrid-DFT treatments. The procedures were implemented in the program system TURBOMOLE; efficiency is demonstrated for comparably large systems, such as Pb54. Relevance of SO effects for electronic structure and stability is illustrated by treatments of small Pb and Po clusters with and without accounting for SO effects.     

Electronic and geometrical structure of bulk rutile studied with Hartree-Fock and density functional methods

We present electronic and structural parameters for bulk rutile (TiO₂) determined by means of different theoretical methods, namely, the periodic Hartree-Fock approach, subsequent post-Hartree-Fock density functional correlation correction, and a linear-combination-of-atomic-orbitals approach based entirely on density functionals. Differences between the use of effective core potentials, a frozen-core treatment, and all-electron calculations are investigated. © 1996 John Wiley & Sons, Inc.     

Performance of the Harris functional for extended basis sets at the Hartree-Fock and density functional levels

The Harris functional is a noniterative variational procedure that uses an input charge density to produce an energy that is surprisingly accurate compared to the converged Kohn-Sham self-consistent result. We adapted and generalized this functional for the Hartree-Fock closed- and open-shell cases as well as examined its use for hybrid density functional methods such as B3LYP. Analysis of extended basis set calculations shows that at the B3LYP level an input density formed from a double zeta + polarization orbital basis is accurate enough to reproduce the energy of triple zeta + double polarization + diffuse orbital basis. For large molecules this translates into a computational speed that can be an order of magnitude faster. In the case of Hartree-Fock calculations a "bootstrapping technique" that employs successive applications of the Harris functional can further reduce computational times while retaining sufficient accuracy.     

苯并二呋喃酮类染料及其取代物的密度泛函理论研究

采用密度泛函理论(DFT)方法,在B3LYP/6-31G*的水平上对苯并二呋喃酮类染料及其芳环6,6’-,9,9’-,10,10’-,11,11’-,12,12’-,13,13’-取代衍生物进行理论计算,讨论了CH3、OCH3、Cl、NO2在不同位置取代对分子的几何结构、电子结构和能量的影响。同时采用含时的密度泛函理论(TD-DFT)方法在相同水平下计算其电子光谱。结果表明:母体被取代后能量降低,结构变稳定;苯并二呋喃酮类染料及其芳环取代物的最低单重激发态均主要源自HOMO-LOMO(π-π*)跃迁。     

Electron attachment to the DNA bases adenine and guanine and dehydrogenation of their anionic derivatives: Density functional study

Density functional theory (DFT) calculations have been used to explore electron attachment to the purines adenine and guanine and their hydrogen atom loss. Calculations show that the dehydrogenation at the N9 site in the adenine and guanine transient anions is the lowest‐cost channel of hydrogen loss, and the N9? H bond scission has Gibbs free energies of dissociation ΔG° of 8.8 kcal mol^?1 for the anionic adenine and 13.9 kcal mol^?1 for the anionic guanine. The relatively high feasibility of low‐energy electron (LEE)‐induced N9? H bond cleavage in the purine nucleobases arises from high electron affinities of their H‐deleted counterparts. Unlike adenine, other N? H bond dissociations are competitive with the N9? H bond fission in the anionic guanine. The replacement of hydrogen in the ring of purine has a significant effect on the N9? H bond fragmentation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory

The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.     

Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations

We present projected gradient algorithms designed for optimizing various functionals defined on the set of N-representable one-electron reduced density matrices. We show that projected gradient algorithms are efficient in minimizing the Hartree-Fock or the Muller-Buijse-Baerends functional. On the other hand, they converge very slowly when applied to the recently proposed BBk (k=1,2,3) functionals [O. Gritsenko et al., J. Chem. Phys. 122, 204102 (2005)]. This is due to the fact that the BBk functionals are not proper functionals of the density matrix.     

Periodic Hartree-Fock and density functional theory calculations for Li-doped polyacetylene chains

We have performed periodic restricted Hartree-Fock/6-31G** and B3LYP6-31G** density functional theory calculations on Li-doped trans-polyacetylene at various dopant concentrations, using C(2m)H(2m)Li2 unit cells (m = 7-14). Except for maintaining P1 rod symmetry the geometry was completely optimized for both uniform and nonuniform doping structures. In addition to geometry we obtain atomic charges, along with soliton formation and dopant binding energies, as well as band structures and densities of states. A thorough analysis of the band structure and density of states, as a function of dopant concentration, is presented. We also characterize the complex nature of the binding interaction between Li and the polyacetylene chain.     

Hartree-Fock与密度泛函混合处理中的电子自相关和自旋平行相关问题

电子气近似中的电子相关能与量子化学中的Hartree-Fock相关能在定义上不相互等同。作者从假想的、含N个电子的"有限电子气"出发, 通过比较这类体系与无限电子气在物理模型上的差异, 合理地把电子气相关能定量地分解为单电子自相关、电子自旋平行相关以及Hartree-Fock相关三个部分。并阐明了各组分的构成随N的变化规律。在此基础上建立的Hartree-Fock与密函混合处理方案, 无须借助任何经验参数, 仅通过简捷的计算即可实现原子和分子的相关能校正。平均误差为4.2%, 优于CI-SD和MP4等Hartree-Fock处理的结果。     

密度泛函理论与Hartree-Fock方法混合处理中的稳态相关能校正

本文分析了通常的Hartree-Fock(HF)相关能定义和密度泛函理论(DFT)中的相关能定义的等价性条件。认为在参考电子密度与真实密度相差很大时两种定义是不等价的, 严格的DFT相关能比HF相关能(绝对值)要大。而在DFT与HF混合处理中得到的相关能比HF相关能(绝对值)要小, 两者之差相当于稳态相关能。实际计算表明, 通过合理地选择组态, 采用有限CI可以求得这一差值。本文描绘了双原子分子H2(X^1∑g^+), HF(X^1∑^+), N2(X^1∑g^+)的势能曲线, 结果比完全CISD和MP4的曲线还要好。H2的离解能是0.17a.u., 逼近实验值0.1747a.u..。     

Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules

We present the implementation of a variational finite element solver in the HelFEM program for benchmark calculations on diatomic systems. A basis set of the form is used, where (μ, ν, φ) are transformed prolate spheroidal coordinates, B _n(μ) are finite element shape functions, and are spherical harmonics. The basis set allows for an arbitrary level of accuracy in calculations on diatomic molecules, which can be performed at present with either nonrelativistic Hartree-Fock (HF) or density functional (DF) theory. Hundreds of DFs at the local spin density approximation (LDA), generalized gradient approximation (GGA), and the meta-GGA level can be used through an interface with the Libxc library; meta-GGA and hybrid DFs are not available in other fully numerical diatomic program packages. Finite electric fields are also supported in HelFEM , enabling access to electric properties. We introduce a powerful tool for adaptively choosing the basis set by using the core Hamiltonian as a proxy for its completeness. HelFEM and the novel basis set procedure are demonstrated by reproducing the restricted open-shell HF limit energies of 68 diatomic molecules from the first to the fourth period with excellent agreement with literature values, despite requiring orders of magnitude fewer parameters for the wave function. Then, the electric properties of the BH and N₂ molecules under finite field are studied, again yielding excellent agreement with previous HF limit values for energies, dipole moments, and dipole polarizabilities, again with much more compact wave functions than what were needed for the literature references. Finally, HF, LDA, GGA, and meta-GGA calculations of the atomization energy of N₂ are performed, demonstrating the superb accuracy of the present approach.     

QSAR and 3D-QSAR studies of the diacyl-hydrazine derivatives containing furan rings based on the density functional theory

QSAR studies of 27 diacyl-hydrazine derivatives containing furan rings were conducted and compared with the DFT method and AM1-MOPAC method. q ² values of 0.61 and 0.40 validated the predictability and reliability of eq. (5) from the DFT method were higher than those of eq. (6) from the AM1-MOPAC method. The DFT-optimized conformations and ESP-fitting charges of the target compounds were also used for 3D-QSAR analysis, including CoMFA and CoMSIA. The leave-one-out cross-validation correlation coefficient and the good correlation between the predicted and experimental activities of excluded test compounds revealed that CoMFA and CoMSIA models were robust. The QSAR results were consistent with the 3D-QSAR results, indicating that the electrostatic and hydrophobic properties of the target compounds were significant to the biological activity. These models are useful tools for predicting the larvicidal activities of new compounds and designing new specific insect growth regulators.     

Microarray of DNA probes on carboxylate functional beads surface

The microarray of DNA probes with 5′-NH₂ and 5′-Tex/3′-NH₂ modified terminus on 10 μm carboxylate functional beads surface in the presence of 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) is characterized in the present paper. It was found that the microarray capacity of DNA probes on the beads surface depends on the pH of the aqueous solution, the concentration of DNA probe and the total surface area of the beads. On optimal conditions, the minimum distance of 20 mer single-stranded DNA probe microarrayed on beads surface is about 14 nm, while that of 20 mer double-stranded DNA probes is about 27 nm. If the probe length increases from 20 mer to 35 mer, its microarray density decreases correspondingly. Mechanism study shows that the binding mode of DNA probes on the beads surface is nearly parallel to the beads surface.     

Microarray of DNA probes on carboxylate functional beads surface

The microarray of DNA probes with 5' -NH2 and 5' -Tex/3' -NH2 modified terminus on 10 um carboxylate functional beads surface in the presence of 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC) is characterized in the preseni paper. it was found that the microarray capacity of DNA probes on the beads surface depends on the pH of the aqueous solution, the concentra-tion of DNA probe and the total surface area of the beads. On optimal conditions, the minimum distance of 20 mer single-stranded DNA probe microarrayed on beads surface is about 14 nm, while that of 20 mer double-stranded DNA probes is about 27 nm. If the probe length increases from 20 mer to 35 mer, its microarray density decreases correspondingly. Mechanism study shows that the binding mode of DNA probes on the beads surface is nearly parallel to the beads surface.     

Noncovalent interactions between modified cytosine and guanine DNA base pair mimics investigated by terahertz spectroscopy and solid-state density functional theory

Modified cytosine and guanine nucleobases cocrystallize in a hydrogen bonding configuration similar to that observed in native DNA. The noncovalent interactions binding these base pairs in the crystalline solid were investigated using terahertz (THz) spectroscopy and solid-state density functional theory (DFT). While stronger hydrogen bonding interactions are responsible for the general molecular orientations in the crystalline state, it is the weaker dipole-dipole and dispersion forces that determine the overall packing arrangement. The inclusion of dispersion interactions in the DFT calculations was found to be necessary to accurately simulate the unit cell structure and THz vibrational spectrum. Using properly modeled intermolecular potentials, the lattice vibrational motions of the cytosine and guanine derivatives were calculated. The vibrational characters of the modes exhibited by the DNA base pair mimic in the THz region were primarily rotational motions and are indicative of the energies and the nature of vibrations that would likely be observed between similar base pairs in DNA molecules.     

Bounds on the overlap of the Hartree-Fock, optimized effective potential, and density functional approximations with the exact energy eigenstates

In this paper, we examine the limits of accuracy of the single determinant approximations (Hartree-Fock, optimized effective potential, and density functional theory) to the exact energy eigenstates of many electron systems. We show that an approximate Slater determinant of S(z)=M gives maximum accuracy for states with S=M, provided that perturbation theory for the spin up minus spin down potential is applicable. The overlap with the exact energy eigenstates with S not equal M is much smaller. Therefore, for the case that the emphasis is on wave functions, one must use symmetry preserving theories, although this is at the expense of accuracy in energy.