Expectation values and density matrices in the Coupled-Cluster theory

A scheme for calculating expectation values in coupled-cluster wave functions is given. The unlinked terms originating from the norm of the wave function are eliminated. Hermiticity and trace conditions for the density matrices are exhibited in such a way as to guarantee their conservation in any reasonable truncation scheme.     

Relative information in excited-state orbital-free density functional theory

Euler equations of the orbital-free excited-state density functional theory of Coulomb systems are derived for specific relative information. Derivation via variational extremization of the relative Fisher information is also presented. Relationships between the Fisher and Shannon information, the local wave vector, and the relative information are displayed.     

Approximately N-representable density functional density matrices

For the first time, we obtain practical density matrices approximately N-representable by correlated-determinant wave functions, which are functionals of the electron density and entirely defined by information obtainable from the X-ray coherent diffraction experiment. © 1994 John Wiley & Sons, Inc.     

Calculation of transition density matrices by nonunitary orbital transformations

An efficient scheme for calculating one- and two-electron transition density matrices for two wave functions is described. The method applies to CAS (complete active space) wave functions and certain multireference CI expansions. The orbital sets of the two wave functions are not assumed to be equal. They are transformed to a biorthonormal basis, and the corresponding transformation of the CI coefficients is carried out directly, using the one-electron coupling coefficients.     

Inequalities for fermion density matrices

A partial trace over the occupation numbers of all but k states in the density matrix of an ensemble with an arbitrary number of single-particle states is defined as the (reduced) k-state density matrix. This matrix is used to obtain a complete, practical solution to the problem of determining the representability of the diagonal elements of the one- and two-particle (reduced) density matrices. This solution is expressed as a series of linear inequalities involving the density-matrix elements; the inequalities are identical with those derived previously by Davidson and McCrae by a different method. In addition, our method is used to obtain nonlinear, matrix inequalities on the off-diagonal elements of the density matrices.     

Nonspherical model density matrices for Rung 3.5 density functionals

"Rung 3.5" exchange-correlation functionals for Kohn-Sham density functional theory depend linearly on the nonlocal one-particle density matrix of the noninteracting Kohn-Sham reference system. Rung 3.5 functionals also require a semilocal model for the one-particle density matrix. This work presents new model density matrices for Rung 3.5 functionals. The resulting functionals give reasonable predictions for total energies, molecular thermochemistry and kinetics, odd-electron bonds, and conjugated polymer bandgaps. Global-hybrid-like combinations of semilocal and Rung 3.5 exchange, and empirical density matrix models, also show promise.     

A density functional theory investigation on the formation mechanisms of DNA interstrand crosslinks induced by chloroethylnitrosoureas

Chloroethylnitrosoureas (CENUs) are an important family of alkylating agents used in the clinical treatment of cancer. Their anticancer mechanism primarily involves the formation of DNA interstrand crosslinks (ICLs) induced by the chloroethyldiazonium ion derived from the decomposition of CENUs. In this work, the mechanism for the formation of ICLs was investigated by density functional theory (DFT) with B3LYP, wB97XD, and M062X functinoals using conductor‐like polarizable continuum model solvent model. Three pathways leading to the formation of three types of G–C crosslinks were compared. G(N1)–C(N3) crosslink is predicted to be the dominant crosslinking product other than G(O⁶)–C(N⁴) and G(N²)–C(O²) crosslinks, which is consistent with the previous results obtained from QM/MM computations. The results indicate that the formation of the G(N1)–C(N3) crosslink via pathway A is the most favorable mechanism from both kinetic and thermodynamic standpoints. In this pathway, the chloroethyldiazonium ion alkylates guanine on the O⁶ site followed by intramolecular cyclization to form O⁶,N1‐ethanoguanine ( 4 ). The cytosine then reacts with intermediate 4 on the C^α atom to yield the G(N1)–C(N3) crosslink. This work provides reasonable explanations for the supposed mechanism of CENUs‐induced ICLs formation obtained from experimental investigations. © 2012 Wiley Periodicals, Inc.     

Novel silylphenol antioxidants by density functional theory

We have scrutinized five novel silylphenol antioxidants, including 2-silylphenol ( 1 ), 4-silylphenol ( 2 ), 2,6-disilylphenol ( 3 ), 2,4-disilylphenol ( 4 ), and 2,4,6-trisilylphenol ( 5 ), at M06/6–311++G** level of theory. To evaluate the antioxidant efficiency, the electronic effects on O─H bond dissociation energy (BDE) and vertical ionization potential (IP_v) of 1 – 5 are investigated, which are mainly governed by electronic effects. The conductor-like polarized continuum model (CPCM) is applied to measure the antioxidant capacity in the solution phase. The results show that antioxidants with the lowest BDE and IP_v values can efficiently act via hydrogen atom transfer (HAT) and single electron transfer (SET) mechanisms, respectively. The stability of resulting radicals is measured by nucleus independent chemical shift (NICS) index, natural bond orbital (NBO) analysis, and nucleophilicity (N) index. The BDE shows lower values in the gas phase with respect to water, while water exhibits lower IP_v values than gas. Structure 5 turns out as the most efficient antioxidant. The overall order of antioxidant efficiency in both gas and water phases is 5 > 2 > 3 > 4 > 1 .     

Traces of spin-adapted reduced density matrices

The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ² and Ŝ_z operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.     

Permutational symmetry of reduced density matrices

The problems of permutational symmetry of the density matrices in reduction are studied. Some necessary and sufficient conditions for N, [λ₁], [λ₂]-derivability problem are given.     

Suggested calculations using transition density matrices

It is suggested that certain transition density matrices, N-representable in a limit, be used in a variational calculation. It is noted that such trial matrices should yield reasonable values for the ground state energies of small atoms or molecules provided a set of overlap integrals is maximised.

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Zusammenfassung Es wird vorgeschlagen, bestimmte Übergangsdichtematrizen, die im Limit N-darstellbar sind, in einer Variationsrechnung zu benutzen. Es wird festgestellt, daß solche Näherungsmatrizen gute Werte für die Energie des Grundzustandes kleiner Atome oder Moleküle geben sollten, falls im Satz von Überlappungsintegralen maximiert wird.

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Résumé On propose d'utiliser dans un calcul variationnel certaines matrices densité de transition, N représentables à la limite. Ces matrices d'essai devraient fournir des valeurs raissonnables pour l'énergie de l'état fondamental dans les petits atomes et les petites molécules à condition de maximiser un ensemble d'intégrales de recouvrement.

     

Application of reference materials for quality assessment in neutron activation analysis-use of information theory

It is generally accepted that an analytical procedure can be regarded as an information production system yielding information on the composition of the analyzed sample. Thus, information theory can be useful and the quantities characterizing the information properties of an analytical method may be applied not only as evaluation criteria but also as objective functions in the optimization. The usability of information theory is demonstrated on the example of neutron activation analysis. Both precision and bias of NAA results are taken into account together with the possible use of reference materials for quality assessment. The influence of the above-mentioned parameters on information properties such as information gain and profitability of NAA results is discussed in detail. It has been proved that information theory is especially useful in choosing suitable reference materials for the quality assessment of routine analytical procedures not only with respect to matrix and analyte concentration in the sample but also to concentrations and uncertainties of certified values in the CRM used. In the extreme trace analysis, CRMs with relatively large uncertainties and very low certified concentrations can still yield rather high information gain of results.     

Description of functional groups by means of domain-restricted reduced density matrices

This report constitutes an application of our previous theoretical works on partitionings of the first-order reduced density matrix according to the atomic domains defined in the theory of atoms in molecules. The numerical determinations obtained reveal that the domain-restricted reduced density matrices, which are the tools resulting from the former treatments, are suitable devices to describe chemical features of molecular fragments. We have focused attention on a study of functional groups in several series of organic compounds confirming the usefulness of these tools.     

Ensemble-representable reduced density matrices suggested by the Xα transition state

The transition state for the calculation of excitation energies in the Xα method is considered in terms of the exact reduced density matrices. It is shown that the occupation numbers which define the transition state correspond, in the exact case, not to a configuration interaction but to an ensemble of two single determinants.     

Protonated primary amines induced thymine quintets studied by electrospray ionization mass spectrometry and density functional theory calculations

As the novel magic number clusters of nucleobases, the thymine quintets induced by ammonium ion (NH₄⁺), and particularly by its derivatives such as protonated alkyl amines and protonated aryl amines, have been studied by electrospray ionization mass spectrometry (ESI‐MS) and density functional theory (DFT) calculations. The DFT‐optimized geometry of NH₄⁺ induced thymine quintet ([T₅ + NH₄]⁺) reveals some new features including three additional hydrogen bonds between NH₄⁺ and its surrounding thymine molecules when compared with that of the alkali metal ions induced thymine quintets. In addition, the fourth hydrogen atom of NH₄⁺ is sticking out the assembly, and, thus, it might be replaced by an organic group R to form the protonated primary amine induced thymine quintet ([T₅ + R ? NH₃]⁺), a hypothesis that has been confirmed by both DFT calculations and ESI‐MS experiments. Furthermore, the relative abilities of the different protonated primary amines for inducing the thymine quintets are investigated by ESI‐MS competition experiments, and the results have shown a clear trend of stronger ability as the alkyl chain gets longer or as the aryl ring gets larger for the alkyl amines or the aryl amines. Two basic influence factors are consequently identified: one is the ability of the alkyl amine to accept proton, another is the π–π stacking interaction between the aryl ring and the π‐surface of the thymine molecule(s), whose explanations are strongly supported by multiple types of thermochemical data, various control experiments and DFT calculations. Copyright © 2014 John Wiley & Sons, Ltd.     

Supramolecular binding thermodynamics by dispersion-corrected density functional theory

The equilibrium association free enthalpies ΔG(a) for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG(a) values in the range 0 to -21?kcal?mol(-1) (on average -6?kcal?mol(-1) ) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60?kcal?mol(-1) (up to 200?% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG(a) values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG(a) values with errors of only 2?kcal?mol(-1) on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.     

Auxiliary density perturbation theory

A new approach, named auxiliary density perturbation theory, for the calculation of second energy derivatives is presented. It is based on auxiliary density functional theory in which the Coulomb and exchange-correlation potentials are expressed by auxiliary function densities. Different to conventional coupled perturbed Kohn-Sham equations the perturbed density matrix is obtained noniteratively by solving an inhomogeneous equation system with the dimension of the auxiliary function set used to expand the auxiliary function density. A prototype implementation for the analytic calculation of molecular polarizabilities is presented. It is shown that the polarizabilities obtained with the newly developed auxiliary density perturbation approach match quantitative with the ones from standard density functional theory if augmented auxiliary function sets are used. The computational advantages of auxiliary density perturbation theory are discussed, too.