Analytical derivative techniques for TDDFT excited-state properties: Theory and application

We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory(TDDFT).The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown.It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency.The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation.With the low computational complexity of the developed analytical approaches,it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies,vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission,and resonance Raman spectroscopies for medium-to large-sized systems.     

Second-order Nonlinear Optical Properties of a Series of Benzothiazole Derivatives

The second-order nonlinear optical (NLO) properties of a series of benzothiazole derivatives were studied by use of the ZINDO-SOS method.These chromophores are formed by a donor- π- bridge-acceptor system,based on a nitro group connected with benzothiazole as the acceptor and a hydroxyl-functional amino group as the donor.For the purpose of comparison,we also designed molecules in which nitrobenzene is an acceptor,The calculation results indicate that benzothiazole derivatives exhibit larger second-odrder polarizabilities than nitrobenzene derivatives.In order to clarify the origin of the NLO response of these chromophores,their electron properties were investigated as well.The benzothiazole derivatives are good candidates for application in electro-optical device due to their high optical nonlinearities,good thermal and photonic stability.     

FAST ATOM BOMBARDMENT MASS SPECTROMETRY OF BILE ACIDS AND THEIR SUCCINYL DERIVATIVES

The new technique of fast atom bombardment mass spectrometry has.been applied to the investigation of some free bile acids and their succinyl derivatives using glycerol or thioglycbl as "matrix compatible solvent".The pseudomoiecular species are observed giving molecular weight information.In negative ion mass spectra the(M-1)-ion is the most intense ion which is the base peak for each of the samples.Additionally,dimer ions and adduct ions with species which are from the matrix are obtained with low intensity.The technique allows the determination of the mixture of bile acids and the pseudomoiecular species observed to give molecular weight information for the component.     

The relative energies of polypeptide conformers predicted by linear scaling second-order Møller-Plesset perturbation theory

We describe an implementation of the cluster-in-molecule(CIM) resolution of the identity(RI) approximation second-order M?ller–Plesset perturbation theory(CIM-RI-MP2), with the purpose of extending RI-MP2 calculations to very large systems. For typical conformers of several large polypeptides, we calculated their conformational energy differences with the CIM-RI-MP2 and the generalized energy-based fragmentation MP2(GEBF-MP2) methods, and compared these results with the density functional theory(DFT) results obtained with several popular functionals. Our calculations show that the conformational energy differences obtained with CIM-RI-MP2 and GEBF-MP2 are very close to each other. In comparison with the GEBF-MP2 and CIM-RI-MP2 relative energies, we found that the DFT functionals(CAM-B3LYP-D3, LC-?PBE-D3, M05-2X, M06-2X and ?B97XD) can give quite accurate conformational energy differences for structurally similar conformers, but provide less-accurate results for structurally very different conformers.     

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface(PES)for the dissociative chemisorption of HCl on Au(111)using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory(DFT)calculations.The resulting PES is accurate and smooth,based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations.Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points,as well as to the fitting process.The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite diferent from the four-dimensional fixed-site calculations,indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.     

Benchmark Calculations on the Atomization Enthalpy, Geometry and Vibrational Frequencies of UF6 with Relativistic DFT Methods

Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.     

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.     

Some formal properties of ensemble density functionals

Formal properties of ensemble density functionals are examined. Expressions for the difference between energy functionals where the particle number differs by one are constructed in terms of their first functional derivatives for the universal energy functional, the electron–electron repulsion energy functional, and the interacting kinetic energy functional. Equations that must be satisfied by second and higher order functional derivatives are derived. It is also shown that the shape of ${\delta V_{ee}[\rho]\over\delta\rho({\bf r})}$ and ${\delta K[\rho]\over\delta\rho({\bf r})}$ , the functional derivatives of the mutual electron–electron repulsion, and kinetic energy, respectively, are separately particle number independent for particle numbers between successive integers. © 2013 Wiley Periodicals, Inc.     

Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory

A unified Mulliken valence with Parr ground‐state electronegativity picture is presented. It provides a useful analytical tool on which the absolute hardness as well ionization potential and electron affinity functionals are based. For all these chemical reactivity indices, systematic approximate density functionals are formulated within density functional softness theory and are applied to atomic systems. For the absolute hardness, a special relationship with the new electronegativity ansatz and a particular atomic trend paralleling the absolute electron affinity are established that should complement and augment the earlier finite‐difference energetic approach. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Accelerating the convergence of the total energy evaluation in density functional theory calculations

A special feature of the Strutinsky shell correction method (SCM) [D. Ullmo et al., Phys. Rev. B 63, 125339 (2001)] and the recently proposed orbital-corrected orbital-free density functional theory (OO-DFT) [B. Zhou and Y. A. Wang, J. Chem. Phys. 124, 081107 (2006)] is that the second-order corrections are incorporated in the total energy evaluation. In the SCM, the series expansion of the total electronic energy is essentially the Harris functional with its second-order correction. Unfortunately, a serious technical problem for the SCM is the lack of the exact Kohn-Sham (KS) density rho KS(r) required for the evaluation of the second-order correction. To overcome this obstacle, we design a scheme that utilizes the optimal density from a high-quality density mixing scheme to approximate rho KS(r). Recently, we proposed two total energy density functionals, i.e., the Zhou-Wang-lambda (ZW lambda) and the Wang-Zhou-alpha (WZ alpha) functionals, for use in the OO-DFT method. If the two interpolation parameters, lambda and alpha, are chosen to allow the second-order errors of the ZW lambda and the WZ alpha functionals to vanish, these two functionals reduce to the Hohenberg-Kohn-Sham functional with its second-order correction. Again, the optimal density from a high-quality density mixing scheme is used to approximate rho KS(r) in the evaluation of lambda and alpha. This approach is tested in iterative KS-DFT calculations on systems with different chemical environments and can also be generalized for use in other iterative first-principles quantum chemistry methods.     

Translational and rotational invariance requisites for density functional derivatives

Translational and rotational invariance of functionals lead to hierarchies of equations between successive derivatives. These hierarchies allow alternating series expansions of some density functionals in terms of functional derivatives and charge density. Translational and rotational invariance also give rise to integrodifferential equations that link derivatives of all orders. From the minimal properties of the kinetic energy functional T_s[ρ] and the functional F[ρ] = min_Ψ→ρ <Ψ|T + V_ee|Ψ>, it follows that $int dˆ3 r dˆ3 rˆprimef({bold r}) {delˆ2 T―s[rho]}over{delrho({bold r})delrho({bold rˆprime})}f({bold rˆprime}) geq 0hspace{1cm}hbox{and}hspace{1cm}int dˆ3 r dˆ3 rˆprimef({bold r}) {delˆ2 F[rho]}over{delrho({bold r})delrho({bold rˆprime})}f({bold rˆprime}) geq 0$ for all ∫ d³ r d³ f′ f(r) = 0. This property combined with constraints on functionals due to translational invariance lead to inequalities satisfied by first derivatives of selected density functionals. © 1997 John Wiley & Sons, Inc.     

The SCC-DFTB method and its application to biological systems

The Self-consistent charge density functional tight-binding (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy expression. Here, we review in detail the application of SCC-DFTB to biological systems and several extensions of the original formalism. The biological systems discussed turn out to be a challenge for DFT due to the occurrence of weak binding forces and charge transfer problems, both of which are not properly described by recent DFT-GGA functionals. Possible solutions and alternative strategies are presented and the role of SCC-DFTB in a general quantum chemical approach to biological systems is discussed     

Simple modification of the Lee?Yang?Parr correlation functional to satisfy exact nonuniform scaling requirements

In density functional theory (DFT) the exchange-correlation energy has to be approximated. One of the most widely used approximations to the correlation component, the Lee(SINGLEBOND)Yang(SINGLEBOND)Parr (LYP) functional does not obey nonuniform scaling requirements. We propose a modifying function that makes this functional satisfy nonuniform scaling constraints. As a result, two modified LYP functionals are suggested. One of them, optimized in a preliminary way, exhibits some properties better than the original LYP functional. This implies that nonuniform scaling requirements convey very important information and all approximate functionals in DFT should be made to satisfy these requirements. Our modifying factor could be used to improve the nonuniform scaling properties not only of E_c ^LYP [n] but also of most functionals which do not obey these conditions. © 1996 John Wiley & Sons, Inc.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazoles

The chemistry of thiadiazoles and their derivatives is of considerable interest in chemistry owing to their pharmacological and potential industrial applications. In this context, a detailed study of isomeric thiadiazole molecules has been done using local (SVWN; Slater, and Vosko, Wilk and Nusair) and nonlocal (BLYP; Becke, and Lee, Yang and Parr) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecule has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. The condensed Fukui functions are shown to be one of the best criteria for predicting chemical reactivity.     

ABEEM方法预测响应函数

在密度泛函理论和原子-键电负性均衡模型基础上,定义了与化学键有关的响应函数以及化学键区域的Fukui函数,建立了一套快速确定分子中各区域(包括原子区域和化学键区域)响应函数的新方法.对大量分子的响应函数的计算结果表明,该方法得到的响应函数可以较好地预测分子中各点的反应活性,并更加快捷省时,展示了原子-键电负性均衡模型的广阔应用前景.     

Molecular fragments in density functional theory

The second-order density functional approach to the partitioning of the molecular density of Cedillo, Chattaraj, and Parr (Int. J. Quantum Chem. 2000, 77, 403-407) is used, together with a local assumption for the function that projects the total density into its components, to show that the distribution function adopts a stockholders form, in terms of the local softness of the isolated fragments, and that the molecular Fukui function is distributed in the molecular fragments in the same proportion as the electronic density.