Exact expressions for ensemble functionals from particle number dependence

Some properties of exact ensemble density functionals can be determined by examining the particle number dependence of ground state ensemble density matrices for systems where the integer ground state energies satisfy a convexity condition. The results include the observation that the integral of the product of the functional derivative and Fukui function of functionals that can be expressed as the trace of an operator is particle number independent for particle numbers between successive integers and the integral itself is equal to the difference between functionals evaluated at successive integer particle numbers. Expressions that must be satisfied by 2nd and higher order functional derivatives are formulated and equations that must be satisfied point by point in space are derived. Using the analytic Hooke's atom model, it is shown that commonly used correlation functional approximations do not bear any resemblance to a spatially dependent expression derived from the exact second order functional derivative of the correlation functional. It is also shown that two expressions for the mutual Coulomb energy are not equal when approximate exchange and correlation functionals are used.     

Wavelet Derivative: Application in Multicomponent Analysis of Electrochemical Signals

The wavelet derivative was developed for resolving overlapped signals in electrochemical analysis. It has been shown that the wavelet derivative could be used as an effective tool in resolution enhancement of the electrochemical signals. Since signal‐to‐noise ratio (SNR) does not degrade significantly at high order derivatives, the wavelet derivative is much better than the conventional numerical derivative in resolving practical signals with low SNR, particularly in the case when the overlapped degree of complex is high and high order derivatives are required for the further resolution enhancement. In this article, applications of the wavelet derivative in the voltammetric determination of small mounts of substances in the presence of large mounts of potentially interfering species are presented, and the advantages of this technique are discussed as well.     

Influence of alkali and alkaline earth ions on the O -alkylation of the lower rim phenolic-OH groups of p-tert -butyl-calix[4]arene to result in amide-pendants: Template action of K+ and the structure of K+ bound tetra-amide derivative crystallized with a p-tert -butyl-calix[4]arene anion

Role of alkali and alkaline earth ions on the formation of calix[4]arene-amide derivatives through O-alkylation of the lower rim phenolic-OH groups in general and template action of K⁺ in particular have been explored. Na⁺ and K⁺ ions among alkali, and Ca²⁺ and Sr²⁺ ions among alkaline earth have shown tetra-amide derivatives bound to metal ion species. Among all these, potassium salts act as template and yields a K⁺ bound tetra-amide derivative where the charge is counter balanced by a calix[4] arene-monoanion and the product is crystallographically characterized. Change in the amide precursor used in these O-alkylation reactions has no effect on the type of the amide derivative formed. Also demonstrated is a direct one-step reaction for the preparation of 1,3-di-amide derivative in high yield and low reaction period using CsHCO₃.     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

NMR spectra and structures of oridonin derivatives complexes with β‐cyclodextrin

Complexations between three oridonin derivatives and β‐cyclodextrin (βCD) were studied by nuclear magnetic resonance (NMR) method. Job's plots for complexes were depicted by ¹H NMR spectra chemical shifts, which proved the 1:1 stoichiometry inclusion complex formation between each derivative and βCD. Two‐dimensional rotating frame overhauser effect spectroscopy (2D ROESY) support the above conclusion and also proved that ring A of each oridonin derivative deeply enters into hydrophobic cavity from the wider rim and the other parts are outside the cavity. Apparent formation constants (K_a) of complexes between three oridonin derivatives and two CDs are calculated according to Scott's equation. Copyright © 2011 John Wiley & Sons, Ltd.     

Proper Choice of XC Functionals and Calculations of Fluorescence-Emitting Energies for Coumarin Derivatives

A scheme of time-dependent density functional theory (TDDFT) combined with single-excitation configuration interaction (CIS) approach was employed to make a detailed investigation of the emitting energy for fifteen well-known coumarin derivatives. The results showed that the predicted emitting energies as well as the absorption ones were dominated mainly by the exchange-correlation (XC) functional to be used. So long as a functional is properly chosen, the experimental emitting energy of most derivatives can be accurately reproduced within 0.16 eV by a calculation at the TDDFT/6-31G(d)//CIS/3-21G(d) theoretical level. It was found that, nevertheless, the hybrid functional, B3LYP, well predicted the absorption energies for all the fifteen coumarin derivatives but none of the functionals could work equally well for the emitting energy calculations. Two pure functionals, OLYP and BLYP, yield good emitting energies for the 7-aminocoumarins or derivatives with a N atom connected to 7-position, which exhibit inconspicuous charge transfer (CT) in their excited states, whereas the B3LYP hybrid functional, with 20% Hartree-Fock (HF) exchange energy, performs significantly better than OLYP and BLYP for those 3-substituted coumarins with larger CT in excited states. Thus, in comparison with the absorption energies, the selection of proper functionals for the emitting energy calculations becomes more complex. In all probability, it is effective and doable to choose an XC-functional with alterable fraction of HF exchange energy according to the composition and structure characteristics of molecule.     

三唑嘧啶衍生物的催化制备方法

本文报道了三唑嘧啶酮类化合物的催化合成方法。烷基胺与氰基亚胺硫代二甲酯在季氨盐催化作用下得到质量好、收率高的3-烷氨基-5-氨基-1,2,4-三氮唑,进一步经过亚胺中间体并与α,β-不饱和酸酯作用后,中间产物在Lewis酸催化作用下水解得到三唑嘧啶酮。该催化方法成本低,反应条件温和,工艺安全并对环境友好。同时报道了所有中间产物的核磁共振氢谱分析结果。     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Electronic Structure Characteristics of ESIPT and TICT Fluorescence Emissions and Calculations of Emitting Energies

A scheme of time-dependent density functional theory (TDDFT) combined with the single-excitation configuration interaction (CIS) approach was employed to investigate the first excited singlet state (S₁) for eight salicylanilide derivatives and analogues, which have similar structural formulas. The results showed that fluorescence-emitting mechanisms of these molecules were in two distinct manners (excited-state intramolecular proton transfer (ESIPT) and twisted intramolecular charge transfer (TICT)), which agreed with the well-known experiments. For ESIPT compounds with inconspicuous charge transfer (CT) during electron transition, pure functionals without Hartree-Fock (HF) exchange energy, such as OLYP and BLYP, were suitable to calculate emitting energies. For TICT compounds with large CT during electron transition, hybrid functionals with about 37% HF exchange energy, such as mPW1B95 and MPW1K, performed well. On condition that the exchange-correlation (XC) functionals were chosen properly according to the rules above, reliable emitting energies for salicylanilide derivatives and analogues could be obtained at the TDDFT/6-31G(d)//CIS/3-21G(d) level. The average accuracy reached about 0.2 eV. For the salicylanilides with both proton transfer (PT) and CT reaction channels, only one channel occurred actually according to the principle of energy minimum. This actual reaction decided proper XC functionals, whereas the reaction that did not occur actually was trivial. Eight appendent compounds were calculated to prove that this successful scheme is expected to be suitable for other ESIPT and TICT compounds.     

Synthesis of water-soluble cationic cellulose derivatives with tertiary amino groups

Water-soluble cellulose derivatives with tertiary amino groups up to substitution degree 0.8 (4.2% of coupled nitrogen) were prepared in a controlled manner by the interaction of cellulose acetate with N,N-diethylepoxypropylamine. It was shown that two reactions take place simultaneously, i.e., hydrolysis of acetyl groups and aminoalkylation of free hydroxyl groups of cellulose. The amino groups coupled to the cellulose are of middle basicity with pK _α ~9.5. Solubility of the products was found to be determined by the chemical composition of the cellulose derivative.     

Third-order energy derivative corrections to the Kohn-Sham orbital hardness tensor

The third term in the Taylor expansion of the total energy functional around the number of electronsN is evaluated as the second-order derivative of orbital Kohn-Sham energies with respect to orbital occupancy. Present approach is an extension of an efficient algorithm to compute densityfunctional based orbital reactivity indices. Various energy derivatives used to approximate orbital reactivity indices are defined within the space spanned by the orbital occupation numbers and the Kohn-Sham one-electron energies. The third-order energy functional derivative has to be considered for singular hardness tensor ([η]). On the contrary, this term has negligible influence on the reactivity index values for atomic or molecular systems with positively defined hardness tensors. In this context, stability of a system in equilibrium state estimated through the eigenvalues of [η] is discussed. Numerical illustration of the Kohn-Sham energy functional derivatives in orbital resolution up to the third order is shown for benchmark molecules such as H₂O, H₂S, and OH⁻.     

A self-contained and portable density functional theory library for use in Ab Initio quantum chemistry programs

A major unresolved problem of density functional theory is the yet unknown exchange-correlation functional, which leads to a proliferation of its less or more successful approximations. A practical implementation of these numerous functionals can present a substantial challenge particularly if the higher order functional derivatives are required. We present a systematic method of functional implementation. The method allows a clean handling of a large number of functionals in a mutually independent way. We developed an extensive set of automatic test routines to facilitate functional and derivative testing with respect to the implementation correctness and numerical stability. An integral part of the presented solution is a program for automatic code generation from analytical formulas that uses only freely available tools. Code for evaluation of functionals and their first, second, third, and fourth derivatives can be generated, which accelerates the development, implementation, and testing of new functionals.     

Further investigation of the spatial generalization of Kato's theorem by a variational density-functional approach

In a recent work, Csvinszky formulated a variational density-functional approach for the investigation of the spatial generalization of Kato's theorem by March. In the previous work, a 10-electron model system (filled K and L shells) was considered. In the present work, the investigation is extended to two other cases: a 28-electron model system (filled K, L, and M shells) and a 60-electron model system (filled K, L, M, and N shells). As in the previous work, several expressions are adapted for the kinetic-energy functional of the electrons and the intriguing question of identifying the “best” kinetic-energy functional is raised and discussed.     

Non-local relation between kinetic and exchange energy densities in Hartree–Fock theory

A non-local generalization K( r, r' ) of the kinetic energy t( r ) such that t( r ) = ∫K( r, r' ) dr' is defined using the idempotency property of the Hartree–Fock first-order density matrix. This is, in turn, related by means of an explicit differential equation to the non-local exchange energy density X( r, r' ). The relationship is illustrated for a couple of examples: with the Fermi-hole in a uniform electron gas, of importance in the local density version of density functional theory, and with inhomogeneous electron systems.     

Study of ionization of tyrosine residues in proteins by second-derivative UV spectroscopy

Four spectrally different forms of tyrosine residues were shown to be present in proteins, namely, nonionized residues, either buried or exposed to solvent, and ionized residues buried or exposed to solvent. A method for determining the pK _a values of the tyrosine residues in proteins was proposed. It is based on the decrease in the absorption intensity in the second derivative of the UV spectrum at 284.2 nm, which is the wavelength of the isobestic point corresponding to the transition of the nonionized tyrosine residues from the buried to the exposed state. Several proteins were studied by this method; the results obtained were found to be close to the corresponding published data. This method is simpler than the conventional UV titration. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1394–1398, July, 1997.     

Electrochemical Studies for the Interaction of DNA with an Irreversible Redox Compound – Hoechst 33258

An electrochemical equation suitable for examining the interaction of irreversible redox compounds with DNA is established. According to the equation, diffusion coefficients of both free and binding compounds (D_f , D_b), binding constant (K) and binding site size (s) of compounds with DNA could be obtained simultaneously by nonlinear fit analysis of electrochemical data. Bis‐benzimidazole derivative (Hoechst 33258), as an irreversible redox compound, was investigated for its electrochemical behavior and the interaction with natural fish sperm DNA (fsDNA) using cyclic voltammetry, chronocoulometry, bulk electrolysis and scanning electrochemical microscope technique. A nonlinear fit analysis of the experimental data yielded: D_f=8.3×10^?5 cm² s^?1, D_b=6.0×10^?6 cm² s^?1, K=2.1×10⁸ cm³ mol^?1, s=3.9. The overall results suggest that Hoechst 33258 binds tightly to the minor groove of fsDNA and covers four base pairs.