Ab initio calculation of the spin-orbit coupling constant from gaussian lobe SCF molecular wavefunctions

The spin-orbit coupling constants of BH⁺ and CH have been calculated using ab initio molecular SCF wavefunctions with the gaussian lobe function basis set. It is demonstrated that fair agreement with experimental values can be achieved even with a relatively small basis set, provided that no terms are neglected in calculating the matrix elements.     

Ab initio calculation of 14N nuclear quadrupole coupling constants

The use of ab initio Hartree-Fock electric field gradient calculations to predict nitrogen nuclear quadrupole coupling constants is examined using basis sets of split valence to triple zeta plus polarization size. From results on 20 to 35 molecules for each basis, such calculations are shown to be of predictive value if systematic errors are eliminated by using regression-derived scaling factors, and the reliability of each basis is assessed. For field gradient calculations on larger molecules, a significantly better alternative to a minimal basis which adds little extra computational cost, is proposed.     

Ab initio calculation of force constants and equilibrium geometries

Force constants of the molecules HF, NH₃, CH₄ and BH₄ ^- have been calculated ab initio by the force method with a 73/3 + 1 gaussian lobe basis set. The results, including a former calculation on H₂O, agree well with experiment: the average relative error is 12 per cent for the diagonal force constants and the average absolute error is 0·06 mdyn/Å for the off-diagonal ones. The trends are also correctly reproduced. It is concluded that ab initio calculations of this accuracy can help to solve a number of spectroscopic problems. Force constants of BH₄ ^- have been determined from a combination of spectroscopic and ab initio information. Geometries have been obtained with little computing work and show good agreement with experiment.     

Non-empirical calculation of spin-orbit coupling constants for some linear triatomic molecules

Higher-order sum rules of the form , are derived for the rotatory strengths of randomly oriented and oriented molecules. In randomly oriented molecules R ⁽ⁿ⁾ = 0 for one-electron systems when n<5, whereas R ⁽⁰⁾=R ⁽²⁾=R ⁽⁴⁾=0 for many-electron systems. In oriented molecules R ⁽ⁿ⁾=0 for one-electron systems when n<3, whereas R ⁽⁰⁾=R ⁽²⁾=0 for many-electron systems. The remaining non-vanishing R ⁽ⁿ⁾ can all be evaluated as diagonal matrix elements of the ground-state wave-function. The resulting expressions are applied to the one-electron model of Condon, Altar and Eyring, and to the coupled oscillator model of Born, Oseen and Kuhn. It is found that the rotatory strengths of the latter model do not fulfil some of the general sum rules. The reason for this discrepancy is discussed. Finally the implications of the present results for the controversy of one-electron versus coupled oscillator models are discussed, and it is proposed that the non-vanishing moments be used as ‘chirality indices’ for specific ground-state wave-functions.     

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

The force constants and equilibrium geometry of water were calculated ab initio from Hartree-Fock self-consistent field wavefunctions using the force method, and a 53/31, a 73/3 + 1 and a 95/41 + 2 gaussian lobe basis set. The force method proved to be very economic and numerically accurate.

The calculated values agree well with the experimental ones. Especially good is the agreement for the interaction constant F_rα . Calculated force constants for the 95/41 + 2 basis are: F_r = 9·158 mdyn/å, F_α = 0·8513 mdyn/å, F_rα = +0·3007, F_rr = -0·1724; the experimental values from isotope frequencies are: F_r = 8·456, F_α = 0·762, F_rα = +0·246, F_rr = -0·100 mdyn/å. The agreement in the geometry is also good for the 95/41 + 2 basis r _e = 0·9518 å, α = 107·49°, and the experimental r _e = 0·9572 å, α = 104·52°.

Force constants were found to be quite insensitive to variation in the basis functions, all three sets giving almost the same result. On the other hand, the dipole moment derivative is very sensitive.     

Ab initio方法研究~(40)Ca~(35)Cl分子的自旋轨道耦合效应和跃迁性质

本文研究了~(40)Ca~(35)Cl分子低态的自旋轨道耦合分裂以及获得更精确的光谱常数和更高的激发态.以从头算理论为基础,使用多参考组态相互作用方法获得了该分子的势能曲线和自旋轨道分裂,之后求解径向一维薛定谔方程获得光谱常数.得到了~(40)Ca~(35)Cl分子7个Λ-S低电子态的势能曲线和永久偶极矩,以及A~2Π→~2Σ~+,1~2Δ和C~2Π→~2Σ~+,1~2Δ跃迁的跃迁偶极矩,得到的光谱常数(不管是考虑了自旋轨道耦合(SOC)还是没有考虑SOC)与实验值非常符合,且要好于之前的理论计算结果 .值得注意的是,目前的计算还首次得到了C~2Π→~2Σ+,1~2Δ跃迁的跃迁性质,为之后实验观察~(40)Ca~(35)Cl分子的高激发态光谱和跃迁性质提供有益的理论参考.     

Ab initio fermi surface calculation for charge-density wave instability in transition metal oxide bronzes

The electronic structure of the charge density wave (CDW) bronze (PO2)(4)(WO3)(2m), m = 4, is determined using ab initio density functional theory. The calculation shows that the Fermi surface (FS) consists in the superposition of three one-dimensional FS's associated with three types of chains. The q dependence of the electronic response function calculated from the electronic structure quantitatively accounts for the anisotropy of the fluctuations probed by x-ray diffuse scattering. The results validate the hidden nesting mechanism proposed for the CDW transitions in this series of bronzes.     

Ab initio lattice dynamics and elastic constants of ZrC

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 222 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. Received 2 July 1999 and Received in final form 26 November 1999     

Ab initio calculation of the Hoyle state

The Hoyle state plays a crucial role in the helium burning of stars heavier than our Sun and in the production of carbon and other elements necessary for life. This excited state of the carbon-12 nucleus was postulated by Hoyle as a necessary ingredient for the fusion of three alpha particles to produce carbon at stellar temperatures. Although the Hoyle state was seen experimentally more than a half century ago nuclear theorists have not yet uncovered the nature of this state from first principles. In this Letter we report the first ab initio calculation of the low-lying states of carbon-12 using supercomputer lattice simulations and a theoretical framework known as effective field theory. In addition to the ground state and excited spin-2 state, we find a resonance at -85(3) MeV with all of the properties of the Hoyle state and in agreement with the experimentally observed energy.     

Ab initio calculation of double ionization of atoms

The Solov’ev-Vinitsky method was used to perform an ab initio calculation of the triple-differential cross section for the double single-photon photoionization of helium for the case of equal emitted-electron energies. A Gaussian width γ describing angular electron-electron correlations at the total electron energy E taking values in range between 0.1 and 100 eV was obtained for this cross section. The results agree with available experimental data, but they raise a doubt as to whether the well-known Wannier law γ ∝ E ^1/4 is applicable at experimentally accessible energies. The Gaussian width γ was investigated as a function of the total emitted-electron energy for targets that have a strongly asymmetric configuration of the initial state—specifically, a negative atomic-hydrogen ion H^? and heliumin the 1s2s ¹ S and 1s3s ¹ S excited states. It was found that this function, γ(E), had a maximum at low energies. It was also shown that, at low energies, the dependence of the double-differential cross section on the angle between the emitted-electron momenta for the targets indicated above differed substantially from the Gaussian dependence, featuring maxima whose number was equal to the number of radial nodes in the initial state. This opens new possibilities for a qualitative analysis of the electron structure of targets.     

Ab initio calculation of double mass differences for near-magic nuclei

Double mass differences between nuclei with a magic number of protons (neutrons) and their neighbors differing from them by one or two protons (neutrons) are calculated within the semimicroscopic model proposed recently for the nuclear pairing problem. The main term in the effective nucleon interaction is calculated on the basis of the realistic Argonne nucleon-nucleon potential v₁₈. This term is supplemented with a small phenomenological term involving one universal parameter common to protons and neutrons. The double mass differences are calculated for the proton neighbors of the Z = 82, 50, 28, and 20 lead, tin, nickel, and calcium isotopic chains and for the neutron neighbors of the N = 126, 82, 50, and 20 isotonic chains. The corrections to the model that are induced by the contribution of low-lying surface vibrations (phonons) are discussed.     

Ab initio calculation of the superconducting transition temperature

The superconducting transition temperature is calculated for a series of representative metals from a selfconsistent LMTO-bandstructure calculation. We carefully avoid any uncontrolled approximations apart from the use of a local exchange-correlation potential and the rigid-ion approximation for the electron-phonon interaction, Our results for V, Nb, Ta, Mo, W, Pd, Pt, Pb clearly indicate that these popular approximations are incapable of reproducing the observed transition temperatures.     

Ab initio calculation of phonons in semiconductor surfaces

The plane-wave pseudopotential approach to the density-functional theory together with the slab supercell method has been applied to determine the structural and dynamical properties of semiconductor surfaces. We compare the atomic equilibrium geometry and the phonon dispersion curves for the (110) surfaces of several III-V-compounds and investigate their hydrogen covered surfaces. Moreover, we discuss the systems Si(111):H-(1×1) and Si(111):Ga-(√3×√3)R30°. Our results are in good agreement with all available experimental data.     

ZnSe弹性常数和相变的从头计算

利用平面波密度泛函理论研究了ZnSe从闪锌矿结构到盐石结构的相变.结果发现通过H相等得到的相变压力为16.8 GPa,与通过高压弹性常数值判断所得到的结果相符.     

HeNO分子光谱常数和非谐振力场的从头算研究

在本论文中,我们在Gaussian 03软件下,采用密度泛函理论（B3LYP）以及二阶微扰理论（MP2）的方法结合Dunning相关一致基组cc-pVNZ (N=T,D,Q)以及6-311G、6-311G**、6-311G（2df,2pd）、6-311G（3df,3pd）基组优化了HeNO分子的几何结构,然后在此基础上计算了它们的光谱常数和非谐振力场。通过计算得到了分子的平衡几何结构、基频、转动常数、四次和六次离心畸变常数等,并与相关的实验值和理论值进行了比较;预测了部分光谱常数,其中包括谐振频率、非谐性常数、振转相互作用常数、三次力常数、四次力常数和科里奥利耦合常数。结果表明,在MP2方法下计算的结果要优于B3LYP计算的结果;基组6-311G、6-311G**、6-311G（2df,2pd）、6-311G（3df,3pd）下的结果普遍优于cc-PVNZ (N=T,D,Q)得到的结果。结果还表明,MP2理论方法结合基组6-311G、6-311G**、6-311G（2df,2pd）、6-311G（3df,3pd）基组计算的结果非常接近实验值,对实验测量某些光谱数据有较好的预测作用     

Ab initio analysis of electron-phonon coupling in molecular devices

We report a first principles analysis of electron-phonon coupling in molecular devices under external bias voltage and during current flow. Our theory and computational framework are based on carrying out density functional theory within the Keldysh nonequilibrium Green's function formalism. Using a molecular tunnel junction of a 1,4-benzenedithiolate molecule contacted by two aluminum leads as an example, we analyze which molecular vibrational modes are most relevant to charge transport under nonequilibrium conditions. We find that the low-lying modes are most important. As a function of bias voltage, the electron-phonon coupling strength can change drastically while the vibrational spectrum changes at a few percent level.     

Ab initio calculation of the dipole moment of cyanamide

The He(I) photoelectron spectra of the isoelectronic series Fe(CO)₂(NO)₂, Co(CO)₃NO and Ni(CO)₄ are reported and interpreted by means of ab initio SCF-MO calculations. For the nitrosyl complexes it is found that ionization potentials calculated assuming Koopmans' theorem are seriously in error due to the considerably greater orbital relaxation accompanying ionization from metal than from NO valence orbitals. When such allowance is made for orbital relaxation by performing restricted Hartree-Fock (RHF) calculations on the ionic states, the experimental spectra are accurately reproduced and the observed similarity of the spectra of all three molecules is explained.