Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω⁻¹ HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH⁺ and N₂ molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI. Received: 2 July 1998 / Accepted: 28 August 1998 / Published online: 11 November 1998     

Analytical Representation of Solutions to Lattice‐Hole Theory

The Simha and Somcynsky (S‐S) lattice‐hole theory has been shown to represent accurately the pressure‐volume‐temperature (PVT) surface of chain molecular melts and their mixtures. Proceeding beyond its original intent, it has led to correlations with other properties and extension into the steady state and relaxing glass. The equilibrium results appear as the solutions of two coupled equations, involving the variables of state and the hole fraction, h = h (V, T) – a kind of free volume quantity. These are to be solved numerically. Notwithstanding the theory's quantitative success, its implicit form has on some occasions been a practical limitation. We remedy this situation by fitting the scaled and thus general solutions of the coupled equations to accurate algebraic equations, V = V (T, P) and h = hV, T). In this manner, explicit analytical expressions for configurational thermodynamic functions and their derivatives are now available. The new expressions for V and h are simple to employ; the convergence of the non‐linear least‐squares fit is obtained in seconds. The numerical values of the scaling parameters so derived are nearly identical to those computed from the original coupled equations. Having h and V from the original theory, the cohesive energy density [CED = δ²V, T)] was also considered. The results are again well represented by a simple algebraic expression. An expression for the reduced solubility parameter δ = δ (T, P) is also given. The usefulness of these solutions is further illustrated by an application to the PVT surfaces of polystyrene and polyphenylene ether blends.     

Autosomal deletion/insertion polymorphisms for global stratification analyses and ancestry origin inferences of different continental populations by machine learning methods

A lot of population data of 30 deletion/insertion polymorphisms (DIPs) of the Investigator DIPplex kit in different continental populations have been reported. Here, we assessed genetic distributions of these 30 DIPs in different continental populations to pinpoint candidate ancestry informative DIPs. Besides, the effectiveness of machine learning methods for ancestry analysis was explored. Pairwise informativeness (In) values of 30 DIPs revealed that six loci displayed relatively high In values (>0.1) among different continental populations. Besides, more loci showed high population-specific divergence (PSD) values in African population. Based on the pairwise In and PSD values of 30 DIPs, 17 DIPs in the Investigator DIPplex kit were selected to ancestry analyses of African, European, and East Asian populations. Even though 30 DIPs provided better ancestry resolution of these continental populations based on the results of PCA and population genetic structure, we found that 17 DIPs could also distinguish these continental populations. More importantly, these 17 DIPs possessed more balanced cumulative PSD distributions in these populations. Six machine learning methods were used to perform ancestry analyses of these continental populations based on 17 DIPs. Obtained results revealed that naïve Bayes manifested the greatest performance; whereas, k nearest neighbor showed relatively low performance. To sum up, these machine learning methods, especially for naïve Bayes, could be used as the valuable tool for ancestry analysis.     

Substituent effect on ionisation potential in a series of related molecules: A theoretical study in a molecular orbital framework

The effect of replacing the hydrogen atoms in thioformaldehyde by halogen atoms (F, Cl) on the ionisation potential of the non-bonding electron is analysed by using the Hellman-Feynman theorem, regarding the nuclear charge of the substituent as a parameter in the many-electron Hamiltonian. The trends predicted by our theory nicely agree with the relevant ionisation potentials computed either by applying Koopmans’ theorem or by the ΔE _SCF method. For the carbonyls, avaible experimental data indicate the reliability of our prediction.     

Hydrodynamic properties of regular star-branched polymer in dilute solution

We calculate quantities such as g = [η]_b/[η]_l and h = (f_t)_b/(f_t)_t for regular star-branched polymer with and without excluded volume. We have applied a numerical method introduced by Barrett for the linear chain and have solved the integral equations which are conducive to calculate the translational coefficient friction and the intrinsic viscosity in the Kirkwood-Riseman theory. We utilize preaveraging but avoid other approximations. In general, we obtain values which have a better accord with experimental data than traditional Kirkwood-Riseman and Zimm-Kilb formulas. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 563–567, 1997     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

Theoretical and experimental studies of the electrochemistry of <Emphasis Type="Italic">p</Emphasis>-aminophenol on a golden electrode

The geometric parameters, vibrational frequencies, and thermochemical values of p-quinonimine (p-AQ) and p-aminophenol (p-AP) were computed ab initio (IIF) and by the density functional theory (DFT) method with the 6-31G(d, p) basis set. Cyclic voltammetry with a golden electrode of p-AP solutions in phosphate buffers at pH 7.30 showed that the standard electrode potential of half reaction for p-QI and p-AP was 0.728 V. The standard electrode potentials of half reactions for p-QI and p-AP were calculated using the free energies and solvation energies of p-QI, p-AP, p-benzoquinone (p-BQ), and hydroquinone (p-HQ). The results showed that the standard electrode potential of half reaction for p-QI and p-AP was 0.743 V at the B3LYP/6-31G(d, p) level and 0.755 V at the HF/6-31G(d, p) level. The standard electrode potentials computed at the B3LYP/6-31G(d, p) and HF/6-31G(d, p) levels were close to their experimental values. The article is published in the original.     

Tetra-tert-butyl-s-indacene is a Bond-Localized C2h Structure and a Challenge for Computational Chemistry

Whether tetra-tert-butyl-s-indacene is a symmetric D_2h structure or a bond-alternating C_2h structure remains a standing puzzle. Close agreement between experimental and computed proton chemical shifts based on minima structures optimized at the M06-2X, ωB97X-D, and M11 levels confirm a bond-localized C_2h symmetry, which is consistent with the expected strong antiaromaticity of TtB-s-indacene.     

Unitary group tensor operator algebras for many-electron systems: I. Clebsch-Gordan and Racah coefficients

A basis for the Racah-Wigner algebra of irreducible representations of the unitary group U(n) that are pertinent to quantum chemical models of many-electron systems is developed. Standard Clebsch-Gordan coefficients and isoscalar factors (also called coupling factors or reduced Wigner coefficients) for both symmetric (S _N ) and unitary [U(n)] groups are extended to transformation coefficients and corresponding isoscalar factors relating canonical Young-Yamanouchi or Gel'fand-Tsetlin bases to simple partitioned bases. All these different types of isoscalar factors are interrelated using the well-known reciprocity between the S _N and U(n) tensor representations, and general expressions relating these different factors are given. For the two-column representations characterizing the many-electron theory, detailed explicit expressions are presented for both the above-mentioned relationships and for all relevant U(n) isoscalar factors. Finally, U(n) Racah coefficients are introduced and explicit expressions derived for certain special classes of these coefficients.Killam Research Fellow 1987–89.     

Relationship between the Auger parameter and the ground state valence charge of the core-ionized atom: The case of Cu(I) and Cu (II) compounds

We develop a simple semiempirical model that correlates the Auger parameter to the ground state valence charge of the core-ionized atom with closed shell electron configuration. Until now, the Auger parameter was employed to separate initial and final state effects that influence the core electron binding energy. The model is applied to Cu(I) and Cu (II) compounds with the Auger parameter defined as α' = E_b^FL (2p_3/2) + E_k^FL (L₃M₄₅M₄₅;¹G). The Auger parameter shift for Cu(I) ion in CuI, CuBr, CuFeS₂, Cu₂S, and Cu₂O compounds—with respect to the copper free atom—increases with the electronic polarizability of the nearest-neighbour ligands suggesting a nonlocal screening mechanism. This relaxation process is interpreted as due to an electron transfer from the nearest-neighbour ligands toward the spatially extended 4sp valence orbitals of the core-ionized Cu(I) ion. In agreement with our model, a linear relationship is found between the Auger parameter shift and the ground state Bader valence charge obtained by density functional theory calculations. The Auger parameter shift for the Cu (II) ion in CuF₂, CuCl₂, CuBr₂, CuSO₄, Cu (NO₃)₂•3H₂O, Cu₃(PO₄)₂, Cu (OH)₂, and CuO compounds is very close to the Auger parameter of metallic copper, and therefore, it is not related to the calculated ground state Bader valence charge. The relaxation process in the final state is dominated by the local screening mechanism, which involves an electron transfer from the nearest-neighbour ligands toward the spatially contracted 3d orbitals of the core-ionized Cu (II) ion.     

Graph theoretical procedure for obtaining analytical expressions of eigenspectra of linear chains and cycles with alternant vertex weights and same edge weight: Application to some complicated graphs

A graph theoretical procedure for obtaining eigenvalues of linear chains and cycles having alternant vertex weights (h₁, h₂, h₁, h₂, h₁, h₂, …) and the same edge weight (k) have been developed. The eigenvalues of some complicated graphs, such as graphs of linear polyacenes, methylene‐substituted linear polyacenes and cylindrical polyacene strips, stack graphs, and reciprocal graphs have been shown to be generated in closed analytical forms by this procedure. Many such graphs represent chemically important molecules or radicals. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the relation between positron annihilation lifetime spectroscopy and lattice‐hole‐theory free volume

A coincidence between the temperature‐dependent hole (free volume) fraction h above the glass transition temperature, derived from lattice‐hole theory, and the corresponding function h_Ps obtained from positronium lifetime spectroscopy has been previously observed for four polystyrene fractions ranging from 4000 to 400,000 in molar mass. This result was based on the assumed proportionality of h_Ps and the product of the orthopositronium intensity I₃ and the mean cavity volume, the proportionality constant C being molar mass dependent. However, a recent analysis of the data based on volume arguments by Olson and Jamieson revealed systematic departures between the two sets of free volume functions. We reexamine the situation by departing from the customary assumption of spherical cavities, and allowing for nonspherical geometries represented by prismatic or cylindrical disks. Agreement between spectroscopic and thermodynamic functions ensues with fixed, temperature‐independent asymmetry factors decreasing with increasing molar mass. These tentative findings suggest that systematic studies of melts with varying chain flexibility and molar mass should be attempted. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2225–2229, 2005     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Electronic,optical, and charge transfer properties of porphyrin and metallated porphyrins in different media

Porphyrin and M-Porphyrin (M = Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, and Zn²⁺) complexes were designed to examine their organic light-emitting diode (OLED) properties. All calculations were performed in different media, which are gas, benzene, DMSO, and water phases. The calculations of both porphyrin and its metal complexes as a monomer form were performed at B3LYP/6-31G(d) level by using the Gaussian 16 and GaussView 6 package programs. On the other hand, emission calculations for the monomer form and dimer form computations of the studied compounds were carried out at PBE0/TZP and B3LYP/TZP levels, respectively, by using Amsterdam density functional (ADF) 2019 package program. The OLED tensors of the mentioned molecules, which are emission energies, reorganization energies (λ_e and λ_h), the ionization potentials and the electron affinities (adiabatic and vertical), the effective transfer integrals (V_e and V_h), and the charge transfer rates (W_e and W_h), were calculated to evaluate the OLED behaviors and determine the best OLED structure.     

Decay modes of muonic lithium-hydrogen molecules

Radiative, Auger and predissociation decay modes of muonic lithium-hydrogen molecule, Liμh, (h = p, d or t is a hydrogen isotope) are considered. Results obtained for the corresponding reaction rates indicate that predissociation is a dominating decay mode for h = p, d while Auger decay dominates for h = t. The calculated conversion coefficient is significantly larger than that for helium muonic molecule and ranges between 37 and 42 (on the basis of one electron) depending on isotope composition of the molecule. Reaction rates for rotational 1 → 0 transitions in Liμh and Heμh due to inner Auger process are also calculated.     

Addition of S‐Heterocyclic Carbenes to Fullerenes: Formation and Characterization of Dithiomethano‐Bridged Derivatives

The reactions of novel S‐heterocyclic carbenes (SHCs), which were prepared by the cycloaddition of disilenes and digermenes to CS₂, with C₆₀ and Sc₃N@I_h‐C₈₀ afforded the corresponding methano‐bridged fullerenes. The [6,6]‐closed and [6,6]‐open structures were characterized for the SHC adducts of C₆₀ and Sc₃N@I_h‐C₈₀, respectively. These derivatives exhibited relatively low oxidation potentials, indicative of the electron‐donating effects of the SHC addends. The electronic properties of the SHC derivatives were clarified by the density functional theory calculations.     

Classical limit of quantum mechanics in the large

Hilbert space may be regarded as a convenient standard approximation by interpolation and extrapolation to a unitary space, in general decomposable into a sum of semisimple spaces. In the limit we expect a particle theory expanded in powers of h according to the number of interacting particles. In the classical limit h tending to zero, phase space, with equations of motion reducible to Hamiltonian form, replaces Hilbert space. The modification of states by observing them is taken care of by considering probability distributions of petty ensembles. If the equations for any single observer can be made autonomous by replacing empirical time by universal time with an arrow we have a causal system. We then obtain the relation between probability and negentropy required for the second law of thermodynamics. An approximate Newtonian theory provides proximate particles with internal and external variables and admits the Poincaré group. For the internal variables we have approximately the Breit interaction. For the external variables we have equivalence for observers of the homogeneous Lorentz group of relativity. We introduce grand ensembles of ultimate particles, and nebulae as proximate particles in the large. We assume the Einstein principle of equivalence for the ten parameter set of observers suggested by relativity and suppose the second law of thermodynamics holds for each observer. The Einstein law of gravitation follows in classical theory to the order of the reciprocal of the large constant, in general with positive natural curvature as well as that corresponding to mass. Replacing particle interactions by fields we include them in classical theory.