Fock Density Research Articles

FTIR and Ab Initio Studies of Diisopropylsulfoxide and its Solutions

Fourier transform infrared (FTIR) measurements, ab initio quantum chemical calculations at the restricted Hartree–Fock (RHF) level and density functional theory (DFT) calculations have been performed to study molecular interactions in pure diisopropylsulfoxide (DiPSO) and the binary mixtures DiPSO/CCl4 and DiPSO/water. The optimized molecular geometry, vibrational wavenumbers, dipole moments and several thermodynamic parameters of free DiPSO and DiPSO/water 1:1 complex in the ground state were calculated using the RHF and B3LYP methods with the 6-31G(d) basis set. A fitting procedure has been performed for both SO and CH stretching regions and a detailed spectral interpretation has been done based on the data obtained from ab initio calculations, infrared spectra and band deconvolution analysis.

Self-consistent field for fragmented quantum mechanical model of large molecular systems.

Fragment-based linear scaling quantum chemistry methods are a promising tool for the accurate simulation of chemical and biomolecular systems. Because of the coupled inter-fragment electrostatic interactions, a dual-layer iterative scheme is often employed to compute the fragment electronic structure and the total energy. In the dual-layer scheme, the self-consistent field (SCF) of the electronic structure of a fragment must be solved first, then followed by the updating of the inter-fragment electrostatic interactions. The two steps are sequentially carried out and repeated; as such a significant total number of fragment SCF iterations is required to converge the total energy and becomes the computational bottleneck in many fragment quantum chemistry methods. To reduce the number of fragment SCF iterations and speed up the convergence of the total energy, we develop here a new SCF scheme in which the inter-fragment interactions can be updated concurrently without converging the fragment electronic structure. By constructing the global, block-wise Fock matrix and density matrix, we prove that the commutation between the two global matrices guarantees the commutation of the corresponding matrices in each fragment. Therefore, many highly efficient numerical techniques such as the direct inversion of the iterative subspace method can be employed to converge simultaneously the electronic structure of all fragments, reducing significantly the computational cost. Numerical examples for water clusters of different sizes suggest that the method shall be very useful in improving the scalability of fragment quantum chemistry methods.

Hydrocarbon chains and rings: bond length alternation in finite molecules

We present a theoretical study of Peierls distortion in carbon rings. We demonstrate using the Longuet-Higgins–Salem model that the appearance of bond alternation in conjugated carbon polymers is independent of the boundary conditions and does in fact appear in carbon rings just as in carbon chains. We use the Hartree–Fock approximation and density functional theory to show that this behaviour is retained at the first principles level.

Second-order Møller–Plesset perturbation (MP2) theory at finite temperature: relation with Surján’s density matrix MP2 and its application to linear-scaling divide-and-conquer method

In 2005, Surjan showed two explicit formulas for evaluating the second-order Moller–Plesset perturbation (MP2) energy as a functional of the Hartree–Fock density matrix D (Chem Phys Lett 406:318, 2005 ), which are referred to as the Δ E MP2[D] functionals. In this paper, we present the finite-temperature (FT) MP2 energy functionals of the FT Hartree–Fock density matrix. There are also two formulas for the FT-MP2, namely the conventional and renormalized ones; the latter of which has recently been formulated by Hirata and He (J Chem Phys 138:204112, 2013 ). We proved that there exists one-to-one correspondence between the formulas of two FT-MP2 and the Δ E MP2[D] functionals. This fact can explain the different behavior of two Δ E MP2[D] functionals when an approximate Hartree–Fock density matrix is applied, which was previously investigated by Kobayashi and Nakai (Chem Phys Lett 420:250, 2006 ). We also applied the FT-MP2 formalisms to the linear-scaling divide-and-conquer method for improving the accuracy with tiny addition of the computational efforts.

Nonadiabatic Dynamics for Electrons at Second-Order: Real-Time TDDFT and OSCF2.

We develop a new model to simulate nonradiative relaxation and dephasing by combining real-time Hartree-Fock and density functional theory (DFT) with our recent open-systems theory of electronic dynamics. The approach has some key advantages: it has been systematically derived and properly relaxes noninteracting electrons to a Fermi-Dirac distribution. This paper combines the new dissipation theory with an atomistic, all-electron quantum chemistry code and an atom-centered model of the thermal environment. The environment is represented nonempirically and is dependent on molecular structure in a nonlocal way. A production quality, O(N(3)) closed-shell implementation of our theory applicable to realistic molecular systems is presented, including timing information. This scaling implies that the added cost of our nonadiabatic relaxation model, time-dependent open self-consistent field at second order (OSCF2), is computationally inexpensive, relative to adiabatic propagation of real-time time-dependent Hartree-Fock (TDHF) or time-dependent density functional theory (TDDFT). Details of the implementation and numerical algorithm, including factorization and efficiency, are discussed. We demonstrate that OSCF2 approaches the stationary self-consistent field (SCF) ground state when the gap is large relative to k(b)T. The code is used to calculate linear-response spectra including the effects of bath dynamics. Finally, we show how our theory of finite-temperature relaxation can be used to correct ground-state DFT calculations.

Analysis of Different Fragmentation Strategies on a Variety of Large Peptides: Implementation of a Low Level of Theory in Fragment-Based Methods Can Be a Crucial Factor.

We have investigated the performance of two classes of fragmentation methods developed in our group (Molecules-in-Molecules (MIM) and Many-Overlapping-Body (MOB) expansion), to reproduce the unfragmented MP2 energies on a test set composed of 10 small to large biomolecules. They have also been assessed to recover the relative energies of different motifs of the acetyl(ala)18NH2 system. Performance of different bond-cutting environments and the use of Hartree-Fock and different density functionals (as a low level of theory) in conjunction with the fragmentation strategies have been analyzed. Our investigation shows that while a low level of theory (for recovering long-range interactions) may not be necessary for small peptides, it provides a very effective strategy to accurately reproduce the total and relative energies of larger peptides such as the different motifs of the acetyl(ala)18NH2 system. Employing M06-2X as the low level of theory, the calculated mean total energy deviation (maximum deviation) in the total MP2 energies for the 10 molecules in the test set at MIM(d=3.5Å), MIM(η=9), and MOB(d=5Å) are 1.16 (2.31), 0.72 (1.87), and 0.43 (2.02) kcal/mol, respectively. The excellent performance suggests that such fragment-based methods should be of general use for the computation of accurate energies of large biomolecular systems.

Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations

In this paper, various implementations of the analytic Hartree–Fock and hybrid density functional energy second derivatives are studied. An approximation-free four-centre implementation is presented, and its accuracy is rigorously analysed in terms of self-consistent field (SCF), coupled-perturbed SCF (CP-SCF) convergence and prescreening criteria. The CP-SCF residual norm convergence threshold turns out to be the most important of these. Final choices of convergence thresholds are made such that an accuracy of the vibrational frequencies of better than 5 cm−1 compared to the numerical noise-free results is obtained, even for the highly sensitive low frequencies (<100–200 cm−1). The effects of the choice of numerical grid for density functional exchange–correlation integrations are studied and various weight derivative schemes are analysed in detail. In the second step of the work, approximations are introduced in order to speed up the computation without compromising its accuracy. To this end, the accuracy and efficiency of the resolution of identity approximation for the Coulomb terms and the semi-numerical chain of spheres approximation to the exchange terms are carefully analysed. It is shown that the largest performance improvements are realised if either Hartree–Fock exchange is absent (pure density functionals) and otherwise, if the exchange terms in the CP-SCF step of the calculation are approximated by the COSX method in conjunction with a small integration grid. Default values for all the involved truncation parameters are suggested. For vancomycine (176 atoms and 3593 basis functions), the RIJCOSX Hessian calculation with the B3LYP functional and the def2-TZVP basis set takes ∼3 days using 16 Intel® Xeon® 2.60GHz processors with the COSX algorithm having a net parallelisation scaling of 11.9 which is at least ∼20 times faster than the calculation without the RIJCOSX approximation.

A comparative study between post-Hartree–Fock methods and density functional theory in closed-shell aurophilic attraction

The inter- and intramolecular aurophilic [ClAuPH3]2, [S(AuPH3)2] and [AuPH3]42+ interactions were studied using ab initio post-Hartree–Fock and DFT methodologies. The post-Hartree–Fock methods provide results closer to the experimental data than DFT-based methods. It is possible to highlight the results obtained by the SCS-MP2 and CCSD(T) methods. In the classic [ClAuPH3]2 dimer, the aurophilic interaction is driven by the induction and dispersion terms. When DFT is used, the best results of geometry and interaction energy are obtained with the PW91 level. We find -D3 Grimme correction, M06HF, M06L, M06 M062X, M052X, CAM-B3LYP and LC-ωPBE provided results of similar accuracy as MP2.

Periodic Hartree-Fock and hybrid density functional calculations on the metallic and the insulating phase of (EDO-TTF)2PF6.

The insulating and conducting phases of (EDO-TTF)2PF6 were studied by all electron, periodic Hartree-Fock and hybrid density functional calculations. Electronic properties, such as the electronic band structure, the density of states and the Fermi surface are discussed in relation to the metal-insulator transition in this material. The nature of conduction is confirmed in both phases from their band structures and density of states. The hybrid DFT band gaps are in good agreement with experiment. Interactions are discussed on the basis of band dispersion in the inter-stack, intra-stack and inter-sheet directions. We discuss the phase transition in terms of the Peierls mechanism and our results fully support this view.

Molecular Structure, Vibrational Assignments and Non-Linear Optical Properties of 4,4’ Dimethylaminocyanobiphenyl (DMACB) by DFT and &amp;lt;i&amp;gt;ab Initio&amp;lt;/i&amp;gt; HF Calculations

In the present study, structural properties of 4,4’ dimethylaminocyanobiphenyl (DMACB) have been studied extensively by using ab initio Hartree Fock (HF) and density functional theory (DFT) employing B3LYP/B3PW91 exchange correlation levels of theory. The vibrational frequencies of DMACB in the ground state have been calculated by using Hartree Fock level and density functional method (B3LYP/B3PW91) with 6-31G(d, p), basis set. Nonlinear optical (NLO) behavior of the examined molecule is investigated by the determination of the electric dipole moment μ, the polarizability α, and the hyperpolarizability β by using the B3LYP/B3PW91 methods.

Mixed pentele-chalcogen cationic chains from aluminum and gallium halide melts.

The reactions of tellurium or selenium with bismuth or antimony in chloridogallate and iodidoaluminate melts in the presence of group 15 trihalides as weak oxidants yielded the compounds (Sb2Te2)[GaCl4] (1), (Sb2Te2)I[AlI4] (2), (Bi2Te2)Cl[GaCl4] (3a), (Bi2Se2)Cl[GaCl4] (3b), (Sb3Te4)[GaCl4] (4), and (SbTe4)[Ga2Cl7] (5). In the crystal structures one-dimensional polymeric cations (Sb2Te2(+))n (1), (Sb2Te2(2+))n (2), (Bi2Te2(2+))n (3a), (Bi2Se2(2+))n (3b), (Sb3Te4(+))n (4), and (SbTe4(+))n (5) are present. The polymeric cationic strands in 2, 3a, 3b, and 4 consist of pentele/chalcogen dumbbells, which are connected to ladder-shaped bands. The strands in 1 and 5 consist of condensed rings that involve four-membered Sb2Te2 rings for 1, and five-membered SbTe4 rings for 5. The counteranions are the weakly coordinating [GaCl4](-), [AlI4](-), and [Ga2Cl7](-) in addition to Cl(-) and I(-) anions, which are coordinated to the atoms of the cations. The crystal structures of 1-4 are characterized by a statistical disorder in the anions with alternatively occupied positions for the Al and Ga atoms. For 4 superstructure reflections appear in the diffractions patterns, indicating a partial order. A correct assignment of the Sb and Te positions in the cation of 5 was achieved by periodic quantum-chemical calculations, which were performed via a Hartree-Fock density functional theory hybrid method. A clear preference of the 4-fold coordinated site was obtained for Sb.

Spectroscopic studies and quantum chemical investigations of (3,4-dimethoxybenzylidene) propanedinitrile

The Fourier Transform Infrared (FTIR), Ultra-Violet Visible (UV–Vis) spectroscopy and Thermogravimetric (TG) analysis of (3,4-dimethoxybenzylidene) propanedinitrile have been carried out and investigated using quantum chemical calculations. The molecular geometry, harmonic vibrational frequencies, Mulliken charges, natural atomic charges and thermodynamic properties in the ground state have been investigated by using Hartree Fock Theory (HF) and Density Functional Theory (DFT) using B3LYP functional with 6-311G(d,p) basis set. Both HF and DFT methods yield good agreement with the experimental data. Vibrational modes are assigned with the help of Vibrational Energy Distribution Analysis (VEDA) program. UV–Visible spectrum was recorded in the spectral range of 190–800nm and the results are compared with the calculated values using TD-DFT approach. Stability of the molecule arising from hyperconjugative interactions, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. The results obtained from the studies of Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO) are used to calculate molecular parameters like ionization potential, electron affinity, global hardness, electron chemical potential and global electrophilicity.

MPW1PW91‐Calculated Structures, IR Spectra, and Frontier Orbitals of Benzoylmethoxythiacalix[4]arene Complexed with Alkali Metal Ions

The molecular structures of four conformers [cone (CONE), partial cone (PACO), 1,2‐alternate (12A), and 1,3‐alternate (13A)] of benzoylmethoxythiacalix[4]arene 1 and the corresponding alkali metal ion complexes were optimized by using a mPW1PW91/6‐31G(d,p) (hybrid Hartree–Fock density functional) calculation method. The 13A conformer was the most stable among the various conformers of 1 because of less steric hindrance. The total electronic and Gibbs free energies, complexation energies, and the gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) frontier orbitals of the complexes of 1 with the sodium and potassium ions were analyzed. Among the ditopic complexes, the 13A‐type 1•2Na+ complex exhibited the strongest binding efficiency. The binding efficiency of the CONE‐type 1•Na+ complex was much stronger than that of the 12A‐type 1•Na+ complex. However, the 1•K+ complexes were relatively insensitive to the conformation of host 1. The calculated binding preference of the various conformers is consistent with the empirical solution data. The infrared spectra of the conformers of 1 and their exo complexes with the alkali metal ions were calculated by mPW1PW91 and analyzed.

First-principles study of nitrogen doping and oxygen vacancy in cubic PbTiO3

The structural and electrical properties of the intrinsic PbTiO3, N-doped PbTiO3 and N-VO co-doping PbTiO3 have been studied by using the first-principles calculations based on the hybrid Hartree–Fock density functionals. In addition, Hall effect measurement experiment is performed, both the experimental and theoretical results are compared. In N-doped PbTiO3 system, the N impurity states occur at the top of valance band, and Fermi energy level intersects with valance bands. The band gap becomes narrowed, the N-doped PbTiO3 shows a typical p-type semiconductor characteristic. When oxygen vacancy and N impurity coexist in PbTiO3, the conduction bands move downward and the acceptors are found to be fully compensated.

Hirshfeld atom refinement.

Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly-l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree-Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints - even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Åfor temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å(2) as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements - an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.

Second harmonic generation and electro-optical Pockels effect of 1- and 3-nitro-6-azabenzo[a]pyrene N-oxide isomers: A Hartree–Fock and Coulomb-attenuating density functional theory investigation

Structural, energetic, spectroscopic, linear and nonlinear optical (NLO) properties of the environmental mutagens 1- and 3-nitro-6-azabenzo[a]pyrene N-oxides were characterized by means of Hartree–Fock as well as B3LYP and CAM-B3LYP density functional theory computations. The NLO investigations were performed for the second harmonic generation (SHG) and electro-optical Pockels effect (EOPE) at the incident wavelength of 1064 nm. The results show that, the predicted structures, vibrational spectra, nucleus independent chemical shifts, ionization energy, electron affinity as well as electronic polarizabilities are little influenced by the position of the nitro substituent. Differently, the dipole moment (μ) and the first-order hyperpolarizabilities (β μ ) are significantly dependent on the isomerization. The rather different mutagenic activity of the investigated isomers could be related to their diverse polarity. At the CAM-B3LYP level, when passing from the 1- to the 3-nitro-6-azabenzo[a]pyrene N-oxide isomer, the μ datum increases by about 5 D (a factor of three), whereas the static and dynamic β μ values decrease by ca. 50%. Dipole moment measurement and SHG and EOPE NLO techniques are potentially useful to distinguish these important environmental mutagens. Dipole moment (μ) and first-order hyperpolarizability (βvec) vectors of 1- and 3-nitro-6-azabenzo[a]pyrene N-oxide isomers were investigated.

MPW1PW91 study for conformational isomers of methylene bridge-monosubstituted tetramethoxycalix[4]arenes

Structures of ten conformational isomers of methylene bridge-monosubstituted tetramethoxycalix[4]arenes, 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetramethoxy-2-ethylcalix[4]arene (1), and methyl 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetramethoxycalix[4]arene-2-carboxylate (2) were optimized by quantum mechanical mPW1PW91/6-31G(d,p) (hybrid Hartree–Fock density functional) calculations. The total electronic and Gibbs free energies of the various conformations (cone, partial cone, 1,2-alternate, and 1,3-alternate) of 1 and 2 were analyzed. The cone (equatorial) and partial cone (equatorial) conformers were disclosed to be the most stable among all the isomers of 1 and 2. The calculated structures agreed well with the experimental results. The IR spectra were calculated at the mPW1PW91/6-31G(d,p) level for the most stable conformer of each methylene bridge-monosubstituted tetramethoxycalix[4]arene.

A perspective on the localizability of Hartree–Fock orbitals

A common perception about molecular systems with a nonlocal electronic structure (as manifested by a nonlocal Hartree–Fock (HF) density matrix), such as conjugated p-systems, is that they can only be described in terms of nonlocal molecular orbitals. This view is mostly founded on chemical intuition, and further, this view is strengthened by traditional approaches for obtaining local occupied and virtual orbital spaces, such as the occupied Pipek–Mezey orbitals, and projected atomic orbitals. In this article, we discuss the limitations for localizability of HF orbitals in terms of restrictions posed by the delocalized character of the underlying density matrix for the molecular system and by the orthogonality constraint on the molecular orbitals. We show that the locality of the orbitals, in terms of nonvanishing charge distributions of orbitals centered far apart, is much more strongly affected by the orthogonality constraint than by the physical requirement that the occupied orbitals must represent the electron density. Thus, the freedom of carrying out unitary transformations among the orbitals provides the flexibility to obtain highly local occupied and virtual molecular orbitals, even for molecular systems with a nonlocal density matrix, provided that a proper localization function is used. As an additional consideration, we clear up the common misconception that projected atomic orbitals in general are more local than localized orthogonal virtual orbitals.

FOLDING MODEL ANALYSIS OF 6He+120Sn ELASTIC SCATTERING

In this study, the elastic scattering of 6 He projectile from 120 Sn nucleus has been analyzed in terms of optical model (OM). Microscopic double folding (DF) model has been used to generate the real central part of the OM potential. The imaginary part has been restricted to Woods–Saxon phenomenological form. Skyrme–Hartree–Fock, Symmetrized Fermi and Gaussian-Exponential densities for 6 He nucleus while Hartree–Fock–Bogolyubov (HFB) density of 120 Sn nucleus have been used to construct the real DF potential. For the effective interaction, the widely used M3Y has been adopted in the DF procedure. The results of DF have been compared with both literature experimental data and phenomenological analysis.

Antimicrobial Investigation and Structural Study of 4′‐Methylazobenzene‐2‐sulfenyl Thiocyanate by X‐Ray Diffraction, DFT, and Ab Initio HF Calculations

ABSTRACT4′‐Methylazobenzene‐2‐sulfenyl thio‐cyanate (MABS‐SCN) was synthesized in an aqueous medium and characterized by 1H nuclear magnetic resonance, Fourier transform infrared spectroscopy, ultraviolet–visible spectroscopy, and elemental analysis. The crystal structure was confirmed by single crystal X‐ray diffraction and its geometry was optimized in ground state by Hartree–Fock model and (B3LYP) density functional theory, and in solution (ethanol) using polarized continuum model at restricted HF using the basis set 6–31+G*. The compound crystallizes in orthorhombic space group Pbca, with unit cell parameters a = 7.165 (7) Å, b = 18.846 (2) Å, c = 20.379 (2) Å, V = 2752.1 (5) Å3, and Z = 8. It attains a planar thiadiazolium salt structure due to strong ortho azo–sulfur interaction imparting exceptional thermal stability, nonreactive solubility in aqueous medium, and high melting crystalline solid nature. A weak intramolecular CH…S type interaction, one CH…S type, four CH…N type intermolecular hydrogen bonds, and van der Waal's interactions are believed to be the stabilizing force for the crystal structure. MABS‐SCN was also tested for antimicrobial activity.