On the calculations of the variational correlation energy using Møller—Plesset first-order wavefunctions

A method is developed, based on first-order symmetry-adapted pair functions obtained within the framework of the Rayleigh—Schrödinger Hartree—Fock perturbation theory, for obtaining a variational upper bound to the correlation energy in the form of pair increments. The correlation-energy functional obtained is written in terms of second- and third-order energy increments of Møller—Plesset perturbation theory. Application of the procedure to the ground states of the Ne-like systems yields energies of greater accuracy than those obtained from CI calculations using very extensive sets of singly and doubly excited configurations. Our pair energies and the total correlation energy obtained for Zn²⁺ represent the most accurate variational results reported so far for atomic systems containing 3d-electrons.     

Partial third-order quasiparticle theory: An application to the photoelectron spectrum of S-tetrazine

An alternative choice of reference state averages in electron propagator theory and retention of all self-energy terms through third-order gives rise to the partial third-order self-energy approximation, P3. Quasiparticle P3 calculations avoid the chief computational bottlenecks of third-order theory and the outer valence Green's function (OVGF). P3 requires no multiplicative factors for scaling self-energy terms and produces better accuracy than OVGF. An application to the photoelectron spectrum of s-tetrazine illustrates the ability of the P3 method to predict correct final state orderings. © 1997 John Wiley & Sons, Inc.     

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.     

Third-order optical susceptibility of single-walled carbon nanotubes

The third-order susceptibility of tetrachloroethane dispersions of capped single-wall carbon nanotubes (SWCNT) has been analyzed by the z-scan technique using a femtosecond laser, and the SWCNT image obtained by atomic force microscopy has been also presented.     

Theoretical studies of third-order nonlinear optical response for B12N12, B24N24 and B36N36 clusters

In this paper, we have calculated the third-order nonlinear optical polarizabilities corresponding to three optical processes: third-harmonic generation (THG), electric-field-induced second-harmonic generation (EFISHG) and degenerate four-wave mixing (DFWM) for B₁₂N₁₂, B₂₄N₂₄ and B₃₆N₃₆ clusters. The calculations have been performed by employing ab initio time-dependent density functional theory combined with sum-over-states method (SOS//TDDFT). We obtained the similar dynamic behavior of third-order NLO polarizabilities for three BN clusters. At input photon energy below 1.25 eV, the resonance enhancements of response haven't occurred. This is due to the fact that the calculated BN clusters have the large transition energy. B₂₄N₂₄ cluster has the larger transition dipole moments and the third-order polarizabilities of B₂₄N₂₄ are much larger than those of B₁₂N₁₂ and B₃₆N₃₆. We also estimate the static third-order optical susceptibility χ⁽³⁾ for BN fullerene materials from the average static third-order polarizability <γ>. The static χ⁽³⁾ of B₂₄N₂₄ fullerene materials are 1.36×10⁻¹⁴ esu for three NLO processes.     

An efficient approach to calculation of zero-flux atomic surfaces and generation of atomic integration data

A new robust method for variational determination of atomic zero-flux surfaces is presented. The zero-flux surface sheets are expressed in terms of variational trial functions in prolate spheroidal coordinates. The trial functions are optimized with a Newton procedure to satisfy the zero-flux condition on a grid. The data required for radial integrations are generated by an adaptive quadrature procedure that employs model electron densities and utilizes an original third-order algorithm for linear search. Results of test calculations involving variational determination of atomic surfaces are presented for a representative set of 20 molecules. The new approach is both less time consuming and substantially more accurate than the previously published algorithms. © 1995 John Wiley & Sons, Inc.     

Author index to volume 75

Møller-Plesset perturbation theory is used to find the second- and third-order correlation corrections to some oneelectron properties of HC1 and CO. An estimate of the fourth-order correction is made. It is shown that the perturbed wavefunctions can be constructed efficiently using the techniques of the direct CI methods. The results are comparable in accuracy with those obtained from large-scale CI calculations, but require considerably less computation.     

Semidirect algorithms for third-order electron propagator calculations

An efficient procedure for third-order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self-energy expressions that are suitable for large molecules are empolyed. The outer-valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self-energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C with a 231 atomic orbital basis and for Zn(C₅H₅)₂ with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.     

Preparation and nonlinear optical properties of Au nanoparticles doped TiO2 thin films

Nano-sized noble metal nanoparticles doped dielectric composite films with large third-order nonlinear susceptibility due to the confinement and the enhancement of local field were considered to be applied for optical information processing devices, such as optical switch or all optical logical gates. In this paper, sol–gel titania thin films doped with gold nanoparticles (AuNPs, ~10 nm in average size) were prepared. AuNPs were firstly synthesized from HAuCl₄ in aqueous solution at ~60 °C, using trisodium citrate as the reducing agent, polyvinylpyrrolidone as the stable agent; then the particle size and optical absorption spectra of the AuNPs in aqueous solutions were characterized by transmitting electron microscopy and UV–Vis–NIR spectrometry. Sol–gel 2AuNPs–100TiO₂ (in %mol) thin films (5 layers, ~1 μm in thickness) were deposited on silica glass slides by multilayer dip-coating. After heat-treated at 300–1,000 °C in air, the AuNPs–TiO₂ thin films were investigated by X-ray diffraction, scanning electron microscopy and atomic force microscopy. The nonlinear optical properties of the AuNPs–TiO₂ thin films were measured with the Z-scan technique, using a femtosecond laser (200 fs) at the wavelength of 800 nm. The third-order nonlinear refractive index and nonlinear absorption coefficient of 2AuNPs–100TiO₂ films were at the order of 10^?12 cm²/W, and the order of 10^?6 cm/W, respectively, and the third-order optical nonlinear susceptibility χ⁽³⁾ was ~6.88 × 10^?10 esu.     

Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis

The static and dynamic second hyperpolarizability gamma has been investigated by time-dependent density functional cubic response theory. The third-order coupled perturbed Kohn-Sham equations were solved to obtain the third-order perturbed charge density. Calculations on a number of small molecules (N(2), CO(2), C(2)H(4), CO, HF, H(2)O, and CH(4)), paradisubstituted oligoacetylene chains, benzene, and eight paradisubstituted benzenes were performed to verify the implementation and to assess the accuracy of the nonhybrid and hybrid time-dependent density functional theory computations. Nitroaniline and a derivative were taken as examples to investigate the distribution of the "gamma density" and to demonstrate the feasibility of analyzing cubic response functions in terms of contributions from natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The results highlight the contributions from atoms and bonds on different functional groups to the total value of gamma based on the NBO/NLMO analysis, which might be helpful for new nonlinear optical materials design.     

Assessment of transition operator reference states in electron propagator calculations

The transition operator method combined with second-order, self-energy corrections to the electron propagator (TOEP2) may be used to calculate valence and core-electron binding energies. This method is tested on a set of molecules to assess its predictive quality. For valence ionization energies, well known methods that include third-order terms achieve somewhat higher accuracy, but only with much higher demands for memory and arithmetic operations. Therefore, we propose the use of the TOEP2 method for the calculation of valence electron binding energies in large molecules where third-order methods are infeasible. For core-electron binding energies, TOEP2 results exhibit superior accuracy and efficiency and are relatively insensitive to the fractional occupation numbers that are assigned to the transition orbital.     

General variation method for the relativistic calculations of atoms and molecules

Use of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as 1p_½ or 2d_3/2 appearing in atomic systems. Problems in extending the method to many-electron atoms and molecules are discussed.     

Calculation of macroscopic first- and third-order optical susceptibilities for the benzene crystal

Starting from a set of high-level ab initio frequency-dependent molecular first- and third-order polarizabilities, the macroscopic first-order (linear) and third-order (cubic) susceptibilities of the benzene crystal are calculated. Environmental effects are taken into account using a rigorous local-field theory and are compared with the anisotropic Lorentz field factor approach. The experimentally determined first-order susceptibility of crystalline benzene is accurately reproduced. Dispersion curves for the first-order susceptibility and results for electric-field-induced second-harmonic generation and third-harmonic generation experiments are predicted. Comparison with similar calculations conducted in the course of molecular simulations of liquid benzene shows that the theoretical results for the two phases are of comparable accuracy. Overall, the results show that for the fairly compact nonpolar benzene molecules, environmental effects on the effective molecular response are small. Received: 11 February 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

Relativistic correlating basis sets for the sixth-period d-block atoms from Lu to Hg

Contracted Gaussian-type function sets to describe valence correlation are developed for the sixth-period d-block atoms Lu through Hg. A segmented contraction scheme is employed for their compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals generated from configuration interaction calculations, in which relativistic effects are incorporated through the third-order Douglas-Kroll approximation. The present basis sets yield more than 99% of atomic correlation energies predicted by accurate natural orbital sets of the same size. Relativistic model core potential calculations with the present correlating sets give the spectroscopic constants of the AuH molecule in excellent agreement with experimental results.     

Cu7.2S4量子点玻璃的制备及三阶非线性光学性质

利用溶胶-凝胶法结合气氛控制合成了含Cu7.2S4量子点的玻璃. 通过热重-差热分析仪对干凝胶样品的热分解机制进行了分析, 并利用X射线粉末衍射仪、 X射线光电子能谱、 透射电子显微镜、 X射线能量色散谱)、 高分辨透射电子显微镜及选区电子衍射对 Cu7.2S4量子点在玻璃中的微结构进行了表征, 利用飞秒Z扫描技术研究了材料在800 nm的三阶非线性光学性质. 结果表明, 尺寸在9~21 nm之间的Cu7.2S4纳米晶已经在玻璃中形成, 该玻璃展示出了优异的三阶非线性光学性能, 其三阶非线性光学折射率(γ)、 三阶非线性吸收系数(β)和三阶非线性极化率[X(3)]分别为1.11×10-15 m2/W, 8.91×10-9 m/W和9.56×10-18 m2/V2.     

One-Parameter double-zeta atomic functions for the hartree–fock energies of helium isoelectronic sequence

The double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree–Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rⁿ of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.     

Comparison of perturbative and multiconfigurational electron propagator methods

Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC (3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques. © 1996 John Wiley & Sons, Inc.     

ICP-MS法测定土壤中有效态砷的研究

分别以等离子体质谱法和原子荧光法,测定了国标土壤样品中有效态砷的含量,研究了两种方法的准确度;对等离子体质谱测定方法做消除基体干扰的对比研究。两种方法的测定值均在土壤样中有效砷的允许误差范围内,ICP-MS法的检出限为2.8 ng/g,精密度(RSD)在10％以下,符合分析测定要求。