First‐principles calculations of Mössbauer hyperfine parameters for solids and large molecules

Electronic structure calculations based on density functional theory were performed for solids and large molecules. The solids were represented by clusters of 60–100 atoms embedded in the potential of the external crystal. Magnetic moments and Mössbauer hyperfine parameters were derived.     

Mindo/3 semi-empirical quantum chemical calculations of the force constants and electrooptical parameters of complex esters

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 4, pp. 558–562, October, 1991.     

Results and techniques of multi-loop calculations

In this review some recent multi-loop results obtained in the framework of perturbative quantum chromodynamics (QCD) and quantum electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore, the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low-energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α_s⁴ and α_s³, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e⁺e⁻ annihilation. The knowledge of the complete mass dependence at order α_s² has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α² QED corrections to the μ decay. Its relevance for the determination of the Fermi constant G_F is discussed. Finally, the calculation of the three-loop relation between the $\text{MS}$ and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the appendix, where also explicit analytical results are listed.     

An effective Hamiltonian for diatomic molecules: Ab initio calculations of parameters of HCl+

The form of the effective Hamiltonian for a diatomic molecule in an electronic state intermediate between Hund's cases (a) and (b) is reexamined. The derivation is performed in three stages: (i) an electronic contact transformation removes the effects of matrix elements which couple different electronic states; (ii) a vibrational contact transformation removes matrix elements coupling different vibrational states; and (iii) a spin-rotational contact transformation removes indeterminacies in the final Hamiltonian. Expressions for the effective parameters resulting from these transformations are presented. The Hamiltonian is in a convenient form for fitting to experimental data, and the formulas for the parameters assist in the comparison with ab initio calculations. The relations between the present parameters and those employed in the computer program of Zare, Schmeltekopf, Harrop, and Albritton [J. Mol. Spectrosc.46, 37–66 (1973)] are given, and make it possible to correct a previous misunderstanding regarding the value of the spin-rotation parameter γ_e in the X²Π state of HCl⁺. The parameters obtained for this state are compared with ab initio calculations which take account of first-order perturbations within the state and second-order perturbations from the A²Σ⁺ state and from the four states of the configuration … $\text{σ}{}^2\text{π}{}^2\text{σ}{}^1$. The A²Σ⁺ state is the dominant perturber, but the contributions from the other states are not negligible. For example, their contribution to γ_e is larger than the first-order contribution.     

Monte Carlo calculations of atoms and molecules

The variational and Green's function Monte Carlo (GFMC) methods can treat many interesting atomic and molecular problems. These methods can give chemical accuracy for up to 10 or so electrons. The various implementations of the GFMC method, including the domain Green's function method and the short-time approximation, are discussed. Results are presented for several representative atoms and molecules.     

AlC,SiC基态分子结构与分析势能函数的量子力学计算

用密度泛函理论的B3LYP方法和二次组态相互作用(QCISD(T))方法,选择6-31G(d,p)、6-311 G(2df,2pd)、6-311 G(3df,3pd)、cc-PVTZ、AUG-cc-PVTZ基组,优化计算了AlC和SiC分子基态的能量,平衡结构,谐振频率.根据原子分子反应静力学原理,导出了AlC和SiC分子基态的合理离解极限和离解能.通过优化计算结果和实验数据的对比,选择QCISD(T)/6-311 G(3df,3pd)方法对AlC和SiC分子基态的势能面进行了单点能扫描.采用最小二乘法拟合得到了AlC和SiC分子基态的Murell-Sor-bie势能函数.同时计算了光谱参数(Be,eα,ωe,ωeχe)和力常数(f2,f3,f4),并与实验结果进行比较.结果表明,计算结果与实验数据吻合的较好.     

极性分子量子气体

超冷极性分子的研究是当前原子分子和光物理研究的前沿之一.由于分子是组成物质材料的基本单元,所以这一前沿研究会很自然地和化学、量子信息、凝聚态物理和天体物理密切地交叉,并且有可能带来新的技术突破.操控分子间的相互作用也因此成为几代物理学家长期探索的重要科学问题.在过去的30年间,研究人员已经成功地将原子冷却     

Comparison of ab initio quantum chemistry calculations on matrix isolated molecules with Mössbauer effect studies

All-electron ab initio calculations are performed for free FeX-molecules, X=H, C, N, O, CO, (CO)₂. Geometry optimization is obtained at SCF level and correlation effects on electronic configurations are studied at MP4 level. Calculated electron densities and electric field gradients of FeX are compared with measured isomer shifts and quadrupole splittings of matrix-isolated molecules. The influence of a solid noble-gas matrix on Fe^o, Fe⁺ and FeC is estimated from molecular clusters including neon or argon atoms.     

Dependence of lifetime on design parameters of an nipi doping superlattice: Results of self-consistent calculations

This paper presents a scheme for calculating recombination lifetimes in a doping superlattice at arbitrary temperatures and forward biases. The scheme involves the self-consistent calculation of sub-band energies, populations and envelope functions, followed by the calculation of lifetime using overlap integrals. Results of these calculations are then presented for a variety of combinations of layer thicknesses and dopings, all at a temperature of 300 K and a forward bias of 1 V. Our results give room temperature lifetimes as high as ∼30 ms for n and p layer thicknesses of 750 Å each, i-layer thickness of 50 Å, and dopings in the n and p layers of 2×10¹⁸ cm⁻³.     

Ab initio calculations of the photoionization of diatomic molecules

A review is presented of the calculation of photoionization spectra, particularly in the spectral range where electron autoionization of diatomic molecules takes place. In addition to some interesting results obtained over years that compare favourably with experiment, the emphasis here is put on the relation between the methods developed for the calculation of observables associated with the continuum energy spectrum of the electrons and the Alchemy system of programs. This system of programs serves as a basis for initial and intermediate calculations. The examples presented show that diatomic molecules not only in gas phase but also oriented in space or physisorbed at surfaces may be studied readily.     

Coherent dynamics in InGaAs quantum dots and quantum dot molecules

We measure the dephasing time of the exciton ground state transition in InGaAs quantum dots (QD) and quantum dot molecules (QDM) using a sensitive four-wave mixing technique. In the QDs we find experimental evidence that the dephasing time is given only by the radiative lifetime at low temperatures. We demonstrate the tunability of the radiatively limited dephasing time from 400 ps up to 2 ns in a series of annealed QDs with increasing energy separation of 69–330 meV from the wetting layer continuum. Furthermore, the distribution of the fine-structure splitting δ₁ and of the biexciton binding energy δ_B is measured. δ₁ decreases from 96 to with increasing annealing temperature, indicating an improving circular symmetry of the in-plane confinement potential. The biexciton binding energy shows only a weak dependence on the confinement energy, which we attribute to a compensation between decreasing confinement and decreasing separation of electron and hole. In the QDM we measured the exciton dephasing as function of interdot barrier thickness in the temperature range from 5 to 60 K. At 5 K dephasing times of several hundred picoseconds are found. Moreover, a systematic dependence of the dephasing dynamics on the barrier thickness is observed, showing how the quantum mechanical coupling in the molecules affects the exciton lifetime and acoustic-phonon interaction.     

Hochschild and cyclic homology of quantum groups

For an arbitrary complex linear semisimple Lie groupG, we consider Hopf algebras of the deformations of the formal and algebraic functions onG. The Hochschild and cyclic homology of these Hopf algebras are computed when the value of the deformation parameter is generic.The main result of this paper was announced at the AMS meeting at University Park in April 1990Supported by Department of Energy under Grant DE-FG02-88ER25062Supported by Harvard Prize Fellowship. Address after July, 1990: Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA     

The value of rough quantum mechanical calculations

During a few years beginning in 1927 rough quantum mechanical calculations of the energy of the ground states with simple wave functions based upon certain models were made for H ₂ ⁺ , H₂, and He ₂ ⁺ . These calculations provided much insight into the nature of the chemical bond, a concept formulated empirically in the 19th century, and of the chemists' classical valence-bond theory, also formulated in the 19th century. Moreover, ideas suggested by the rough calculations permitted the valence-bond theory to be greatly refined and made more powerful. Extensive knowledge about the properties of atomic nuclei was obtained only after quantum mechanics had been discovered. Nuclear physicists have for the most part striven to carry out very accurate quantum mechanical calculations of nuclear properties, with results that are often in excellent agreement with experiment. I suggest that rough calculations based on simple models might give additional insight and suggest new experiments.     

Revisiting the quantum group symmetry of diatomic molecules

We propose a q-deformed model of anharmonic vibrations in diatomic molecules. We study the applicability of the model to the phenomenological Dunham expansion by comparison with experimental data. In contrast with other applications where it is difficult to find a physical interpretation for the deformation parameter, q, in our analysis it is directly related to the third-order coefficient in the Dunham expansion. We study the consistency of the parameters that determine the q-deformed system by comparing them with the vibrational terms fitted to 161 electronic states of diatomic molecules. We show how to include both positive and negative anharmonicities in a simple and systematic way.Received: 16 July 2004, Published online: 24 August 2004PACS: 33.15.Mt Rotation, vibration, and vibration-rotation constants - 02.20.Uw Quantum groups - 31.15.Hz Group theory - 03.65.Fd Algebraic methods - 02.20.-a Group theoryV.K. Dobrev: Permanent address, and after 30 April 2004: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria