Extrapolation of real-space quantum chemical calculations from finite-size super cells to the ideal infinite system. I. Theory

A method is proposed how to calculate the correct density matrix of an infinite polymeric chain from that of a standard finite supercell calculation. The density matrix of the finite supercell is transformed into k-space for all k-values allowed by the periodic boundary conditions. The k-dependent matrices are then unitarily transformed, with each unitary matrix being represented by a set of complex rotation matrices. It is shown that the corresponding angles can be interpolated and extrapolated toward the zone boundaries in a straghtforward manner and that this extrapolation can be done from any finite supercell with reasonable accuracy. This gives rise to an infinite system density matrix for which all fundamental properties are guaranteed by construction. This infinite system density matrix may be used to construct a corrected density matrix for the finite supercell calculation. © 1994 John Wiley & Sons, Inc.     

Ab initio calculation of maximum bond order hybrid orbitals

Summary The maximum bond order hybrid orbital (MBOHO) procedure is tested onab initio level by use of the density matrix in Löwdin orthogonalized atomic orbital basis. The direct MBOHO calculation based on the whole density matrix includes also the hybridization of the inner atomic orbitals, and the MBOHO calculation based on the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The concrete MBOHO calculations based on theab initio calculation with STO-3G basis show that the components of the s atomic orbitals in MBOHOs and the maximum bond orders obtained from the two kinds of MBOHO calculations are very close to each other, and that the two kinds of MBOHOs all have the excellent correlativity with the nuclear spin-spin coupling constants.The project supported by National Natural Science Foundation of China and the Excellent Young University Teacher's Foundation of State Education Commission of China.     

Experimental and Theoretical Charge Density Study on Di‐2‐pyrazylamine (Hdpza) Molecule in Crystal

Electron density distribution of Di‐2‐pyrazylamine ( Hdpza ) is studied both by single‐crystal X‐ray diffraction method at 100K and theoretical calculation. Structural determination reveals that Hdpza molecules crystalize in a syn‐anti conformation with an intramolecular C? H?N hydrogen bond between two pyrazine rings and then gather together via two intermolecular N? H?N and C? H?N hydrogen interaction and π? π stacking interaction between pyrazine rings. Charge density analysis is made in terms of deformation density (Δπ), Laplacian distribution and topological analysis of total electron density based on multipole model and theoretical calculation. The agreement between experiment and theory is good. The topological properties at bond critical points of C? C and C? N bonds reveal a covalent bond character, and those of intermolecular interactions, such as hydrogen bonds and π? π stacking interactions, reveal a closed‐shell interaction. The potential energy curve of Hdpza molecule shows that the syn‐anti conformation is the most stable one (global minima) than the other two of syn‐syn and anti‐anti conformations.     

Two-body Reduced Density Matrix Reconstruction for Van der Waals Systems

A method for the calculation of the electronic energy of a correlated system is presented. This approach is based on the reconstruction of the total two-body reduced density matrix by doing separate configurations interaction calculations on fragments. The method has been tested on Van der Waals systems and has been implemented by considering restrictive N-representability conditions. It is shown that the computational strategy presented in this work can describe with good accuracy weak dispersion interactions, and considerably lowers the size-consistency error of a classical configuration interaction calculation.     

Energy band structure of (SN)x chain: Unrestricted Hartree–Fock and charge density wave solutions

The ab initio Hartree–Fock crystal orbital method is used for the calculation of the energy band structure of a one-dimensional model of (SN)_x. Two energy band structures are described corresponding to the self-consistent spin density wave (SDW ) and the self-consistent charge density wave (CDW ) solution, respectively.     

Effect of substituents on electron energy redistribution in uracil derivatives and their ionization in polar solvents

It is assumed that the chemical reactivity may be described in terms of the appropriate energy density calculated for each atom. Indices of energy density for deprotonization of uracil, 5-nitro- and 5-aminouracil are presented. The results of a quantum chemical calculation of the deprotonization energy are in qualitative agreement with experimental pK and ΔH values.     

Overlapping shells model applied to diamondlike crystals

The model based on the assumption of the existence of an interatomic distance-dependent, local, effective crystal field applied to the alkaline metals (Int. J. Quantum Chem. 52, 321–328 (1994)) is modified and applied to the diamondlike structure crystals (C, Si, Ge, Sn). In the referred to model, a part of the electron density was missed—not included in the calculation (the density in the spaces between the shells). Such an approach could be used for the alkaline metals, but for the covalent crystals, this is a bad approximation. To avoid that problem, we assumed that the atom shells can overlap in such a way that the entire electron density is taken into the calculation. In this case, the electron density is “moved” from the outside of the shells mostly into the interatomic bond region. We applied the modified model to the calculation of the binding energy and the bulk modulus for the diamondlike crystals. The results show that well-chosen parameters allows one to reproduce the proper values of the binding energy at the equilibrium position. The bulk moduli calculated for these crystals are in quite good agreement with ones calculated as (regular crystal structure) B = 1/3(C₁₁ + 2 C₁₂), where C₁₁ and C₁₂ are elastic constants. © 1997 John Wiley & Sons, Inc.     

Bond orders and valences in the SCF theory: a comment

The calculation of bond order and valence indices for ab initio and semi-empirical wave functions is discussed by emphasizing their relations to the exchange part of the second order density matrix. Comments are also given on a recent work of Gopinathan and Jug, as well as propositions made to avoid ambiguity in the nomenclature.     

Toward a semiempirical density functional theory of chemical binding

The new ideas ofbond electronegativity andbond hardness are introduced, and a semiempirical density functional approach to the theory of molecular electronic structure and chemical binding is outlined. There result effective electronegativity equalization procedures that permit calculation of binding energies as well as partial charges. By a modelling of the bond electronegativity and bond hardness, a density functional interpretation of earlier bond charge models is established. Some numerical results are given for diatomic molecules.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

A sequential product of geminals and its applications

In this paper, an SPG function, which is associated with an extreme point of the set of N-representable second-order reduced density matrices, is used to perform the calculation of the ground state energy of LiH with the variation of internuclear separation. The result of our calculation essentially is in accordance with that of AGP function.     

Analysis and Investigation of Electronic Transport Coulomb Blockade in Al68 Based on DFT

Electronic transport properties in an Al cluster are investigated theoretically in this paper. We propose a possible illustration of Coulomb blockade based on variable electrostatic potential (ESP ). Density functional theory (DFT ) was used to achieve the global minimum structure and wave function for analyzing the ESP and density of states (DOS ) of Al₆₈ in different charged states. Al₆₈ is able to contain multiple electrons. According to the calculation of systematic energy and surface ESP, respectively, the surface of Al₆₈ presents a 0–6.33 eV ESP barrier after electron injection, which is 0 eV at first. The probability density of flow of electrons was calculated under one‐dimensional model with double barriers. Expected results were obtained, containing a nonlinear relationship between J and V and flow density steps. Moreover, an assumption is proposed associated with nonlinear conductance phenomenon of zero‐dimensional nanomaterials. Significantly, Al films with different thicknesses were prepared by the low vacuum physical vapor deposition (LVPVD ) method, exhibiting novel fluorescent behaviors. In addition, the I–V curve of a 25‐nm Al film exhibited two steps at 7 and 27 V, respectively, which meant that the step effect was caused by Coulomb blockade, in accordance with the theoretical calculation.     

The calculation of NMR shielding tensors based on density functional theory and the frozen-core approximation

The application of the frozen-core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed and an implementation is presented. A complete formulation of the shielding calculation within the frozen-core approximation is given, both in general terms and for the special case of density functional theory (DFT) and “gauge including atomic orbitals” (GIAOs). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen-core approximation is a useful tool for shielding calculations—if the valence space is increased to contain at least the ns, np, (n − 1)p, (n − 1)d (fourth period and higher) shells, where n is the number of the given period in the periodic table of elements. The new method is applied to ⁷⁷Se shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts, whereas calculated absolute shieldings are generally too small by about 300–400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitly incorporated into the experimental absolute shielding scale. © 1996 John Wiley & Sons, Inc.     

Density matrix expansions and their application in the theory of the many-electron systems

A method of calculation of the correlation energy is proposed, which includes the superposition of configurations and the two particle approach. This method is based on the density matrix formalism. The approximate, but N-representable expressions for the reduced density matrices are used. The correlation energy of the beryllium atom is calculated as an example.     

Structural and Electron Density Studies on a Chromium(IV)-Oxo Complex [CrIV(O)(TMP)]

The electron density distribution of a chromium(IV)-oxo complex, [Cr^IV(O)(TMP)] (TMP = 5,10,15,20-tetrakis-p-methoxyphenyl porphyrin), is investigated by molecular orbital calculation. The molecular and crystal structure of the compound is studied by x-ray diffraction. It belongs to the space group 1 2, Z = 2, a = 14.979(4) Å, b = 9.752(3), c = 15.605(3) Å, β = 100.97(2)°, V = 2238(1) ų, Mo Kα radiation λ = 0.7107 Å, R = 4.9%, Rw = 3.5% for 3575 observed reflections. Cr is five-coordinated in a square pyramidal fashion with the Cr atom located 0.42 Å toward the oxo-ligand. Deformation density maps are derived from the single point molecular orbital calculation on the basis of HF and DFT(density functional theory) calculations. The accumulation of deformation density along the C-H, C-C, C-N and C-O bonds in the porphyrin ligand is well represented. The asphericity in electron density around the Cr ion is clearly demonstrated. Natural bond orbital analysis (NBO) reveals that the Cr-O_oxo is actually a triple-bond character (σ²π⁴) and the four N of pyrrole serves as a σ-donor to Cr. The Cr-N_pyrrole bond is essentially a dative bond d-Orbital populations of Cr derived from both calculations are in good agreement with each other. Planar d_π-orbital is the most populated, which is in accord with the prediction from crystal field theory. Detail bond characterization of the Cr-L, multiple bond is discussed.     

Adsorption studies of dodecylamine at the quartz interface using an electrode-separated piezoelectric sensor

The adsorption process of dodecylammonium chloride (DAC) from aqueous solutions onto a quartz crystal interface was investigated in situ using an electrode-separated piezoelectric sensor (ESPS). Increasing amounts of DAC adsorbed onto a quartz crystal surface resulted in linearly decreasing oscillating frequencies of the ESPS. The adsorption density can be monitored by the frequency decrease. The adsorption density obtained by calculation using the Sauerbrey equation in the ESPS method is greater than that in solution depletion method. A calibration coefficient is added into the Sauerbrey equation to correct the influence of surface roughness of the quartz crystal on the adsorption density. The influence of solution properties on the adsorption density measurement was discussed. A dependence of the adsorption density on pH was reported. Received: 17 April 1997 / Revised: 1 December 1997 / Accepted: 7 December 1997     

Adsorption studies of dodecylamine at the quartz interface using an electrode-separated piezoelectric sensor

The adsorption process of dodecylammonium chloride (DAC) from aqueous solutions onto a quartz crystal interface was investigated in situ using an electrode-separated piezoelectric sensor (ESPS). Increasing amounts of DAC adsorbed onto a quartz crystal surface resulted in linearly decreasing oscillating frequencies of the ESPS. The adsorption density can be monitored by the frequency decrease. The adsorption density obtained by calculation using the Sauerbrey equation in the ESPS method is greater than that in solution depletion method. A calibration coefficient is added into the Sauerbrey equation to correct the influence of surface roughness of the quartz crystal on the adsorption density. The influence of solution properties on the adsorption density measurement was discussed. A dependence of the adsorption density on pH was reported. Received: 17 April 1997 / Revised: 1 December 1997 / Accepted: 7 December 1997     

Computation of the Electronic and Spectroscopic Properties of Carbohydrates Using Novel Density Functional and Vibrational Self-Consistent Field Methods

ABSTRACT

A novel density functional method is presented for the calculation of electronic and thermodynamical properties of oligosaccharides. This method, termed K2-BVWN, offers two advantages; it scales as N ³, where N is the number of basis functions, and there are only two adjustable parameters. The current density functional method is tested in terms of reproducing high level gas phase ab initio calculations in eleven low energy conformers of D-glucopyranose including exo-anomeric and different hydroxymethyl orientations (G ^?, G ⁺, and T). The K2-BVWN method is also tested in terms of reproducing the spectroscopic features of D-glucopyranose and D-mannopyranose (α/β) as compared with both a vibrational self-consistent field calculation (VSCF) as well as experimental infrared spectroscopy. The VSCF calculations offer the advantage that it is possible to include higher order mode coupling and anharmonic effects directly into the calculation of the vibrational frequencies. In general, the K2-BVWN method reproduces the ab initio energetic trends of the different conformers of D-glucose. While the absolute energies are not the same between the ab initio and the K2-BVWN method, both methods do predict a preference for the α-anomer in the gas phase (0.4 kcal/mol ab initio, 0.0 – 0.5 kcal/mol K2-BVWN). The K2-BVWN method was able to reproduce the experimental and VSCF calculated spectrum of both D-glucopyranose and D-mannopyranose in the frequency range between 1500 – 800 cm^?1. Because the current density functional method is both relatively quick and accurate, it represents a significant advancement in the development of oligosaccharide force fields.     

Unit-cell dimensions of bulk- and solution-crystallized linear polyethylene

The unit-cell dimensions and density, at room temperature, of bulk- and solution-crystallized linear polyethylene have been determined. The macroscopic measured densities for the bulk-crystallized samples ranged from 0.917 to 0.993 g/cc, and the lattice parameters were found to be independent of the sample density. In contrast, for solution-formed crystals, despite the limited range in macroscopic densities that can be attained, there is a systematic variation in the a and b dimensions with the measured density and the crystallite thickness. The implication of these results for the calculation of the degree of crystallinity and the interpretation of certain infrared bands are discussed.     

Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo

We propose a theoretical/computational protocol based on the use of the Ground State Path Integral Quantum Monte Carlo for the calculation of the kinetic and Coulomb energy density for a system of N interacting electrons in an external potential. The idea is based on the derivation of the energy densities via the (N ? 1)‐conditional probability density within the framework of the Levy–Lieb constrained search principle. The consequences for the development of energy functionals within the context of density functional theory are discussed. We propose also the possibility of going beyond the energy densities and extend this idea to a computational procedure where the (N ? 1)‐conditional probability is an implicit functional of the electron density, independently from the external potential. In principle, such a procedure paves the way for an on‐the‐fly determination of the energy functional for any system. © 2012 Wiley Periodicals, Inc.     

A NEW REFRACTION METHOD FOR DETERMINING THE DEGREE OF ETHOXYLATION OF NON-IONIC SURFACTANTS

We have proposed two refractometic methods for determination of the degree of ethoxylation, n, of non-ionic surfactants. The first method allows calculation of n from, the measured values of the refractive index and the density of the sample. In the second method n is found from a calibration curve and the measured refractive index.