The use of SCF-MO calculations and experimental data in evaluating general quadratic force fields of light atom molecules

The semiempirical MOCIC method, in which SCF-MO calculations are combined with limited frequency data in evaluating general quadratic force fields, has been tested on several light atom molecules (F₂CO, H₂CO, FNO, HCCH, NCCN, and H₂CCCH₂). Both MNDO and available ab initio treatments have been employed to establish the MOCIC constraints. The MOCIC potential functions are found to be remarkably close to potential functions determined uniquely from a plethora of experimental data. In comparison with potential constants evaluated using SCF-MO methods, the MOCIC functions are in much better agreement with experimentally determined counterparts. In addition to improving the estimates of primary potentials, the MOCIC approach gives statistically significant improvement in the estimate of interaction constants for these multiply bonded molecules where stretch-stretch interactions are large. The MOCIC constraint procedure is shown to work extremely well for fluorinated molecules.     

The combined use of SCF-MO calculations and experimental data in the evaluation of quadratic force fields: MOCIC potential functions for fluoroform,methyl acetylene,and methyl cyanide

A semiempirical method combining SCF-MO calculations and limited vibrational data has been employed to evaluate the completely general quadratic potential fields of fluoroform, methyl acetylene, and acetonitrile. MOCIC (molecular orbital constraint using interaction coordinates) potential fields are presented for gas phase molecules of intermediate size. Here general harmonic force fields or excellent approximations utilizing extensive experimental data are available as standards. A statistical evaluation of the interaction potentials shows that there is some improvement in going from MNDO or ab initio SCF-MO force fields to the MOCIC functions which reliably reproduce the off-diagonal vibrational potential constants in most instances. The MOCIC primary compliants are excellent approximations of their vibrational counterparts, as expected. Comparison of the calculated isotopic frequencies, Coriolis coupling constants, and centrifugal distortion constants for the SCF-MO, MOCIC, and vibrational spectroscopic potential fields with the corresponding experimental values also shows MOCICs reliability for molecules with many interaction potentials. There is substantial improvement in the calculated isotopic frequency shifts and centrifugal distortion constants in going from SCF-MO to MOCIC functions.     

The harmonic force fields of methylene chloride and dichlorosilane from combined microwave and infrared data

The harmonic force fields of methylene chloride and dichlorosilane have been obtained by combining the vibrational wavenumbers and centrifugal distortion constants of several isotopic species. Although enough data were available from earlier work for dichlorosilane, it was first necessary for methylene chloride to determine its distortion constants from microwave spectra. Transitions were measured up to J = 80 and J = 90 for CH₂Cl₂ and CD₂Cl₂, respectively, and the analysis gave accurate rotational constants, and quartic and sextic distortion constants. Ground-state effective, substitution, ground-state average and approximate equilibrium structures have been obtained for both molecules.     

A combined empirical-ab initio determination of the general harmonic force field of ketene

The general harmonic force field (GHFF) of ketene has been determined through a joint empirical-ab initio investigation. Perturbations in the infrared spectra of all isotopic species render experimental frequency data of limited discriminatory value in the empirical determination. Microwave/infrared determined quartic distortion constants are found to be mutually incompatible, both within and between isotopic species. The sensitivity of the distortion constants to truncation and constraints made in their determination is established in order to make a realistic estimate of their reliability in the force constant calculations. Ab initio calculations performed at various different levels of sophistication predict consistent values for interaction constants, some of which are markedly different from previously reported empirical values. The joint empirical-ab initio GHFF reproduces all observed and perturbation-corrected data well over five isotopic species. Coriolis interaction constants are calculated for ketene-H₂, -HD, and -D₂, which will be of assistance to future analyses, particularly of the strongly interacting four-level systems below 1000 cm⁻¹. Scaled ab initio force constants, calculated around the experimental ground state geometry as reference, are in excellent agreement with the empirical values, with one exception, which arises due to neglect of configuration interaction.     

受到与速度平方成正比的力的谐振子的普遍解

将Ermakov系统加以推广，得出受到与速度平方成正比的力的变频率谐振子的不变量，求出其普遍解．     

谐振子径向幂坐标矩阵元的一般递推关系

利用谐振子径向波函数的渐近行为和积分特性,导出了谐振子径向幂坐标矩阵元〈n′_rl′|r~k|n_rl〉的递推关系,从而把有关文献中关于对角元〈n_rl|r~k|n_rl〉的递推关系推广到更为一般的形式。     

Orientational selection of molecules in combined laser and electrostatic fields

It is shown that the combined effects of electrostatic and resonant laser fields on a molecular ensemble can be used to control the orientation of molecules by changing their internal state. In contrast to most other schemes for controlling molecular orientation, the proposed method does not require rotational cooling and can be highly efficient at room temperature.     

The infra-red spectrum of 13CH3F and the general harmonic force field of methyl fluoride

Analyses of the v ₃, 2v ₃, and (predominantly) v ₁ parallel bands, and of the v ₄ and v ₆ perpendicular fundamentals have been made for ¹³CH₃F in terms of the rotational structure observed with a resolution of ～0·2 cm^-1. In addition, the band centres of the strongly Coriolis-interacting v ₂ and v ₅ fundamentals are accurately located. Some elucidation of the complex Fermi resonance interactions in the 3000 cm^-1 region is achieved through study of spectra of crystalline samples. This enables all three components of the v ₁, 2v ₂, 2v ₅ ⁰ triad to be observed for both ¹²CH₃F and ¹³CH₃F, and estimates to be made for the unperturbed vibration frequencies.

The ¹³C frequency shifts determined for all six fundamentals are used in conjunction with existing frequency, Coriolis ζ, and centrifugal distortion data for CH₃F, CD₃F, CHD₂F and CH₂DF, to determine the general harmonic force field for methyl fluoride. The extra shift data enable all 12 parameters of the force field to be fixed within narrow limits for the first time. The disagreement with predictions of the hybrid orbital model in the A₁ species can be attributed to the effect of trans repulsions arising from the fluorine lone-pair electrons, an effect which contributes to the longer CH bond in methyl fluoride compared with the other methyl halides.     

静电系统受力和力矩计算

具有终端的静设备系统,是一种把电能转移为机械能的换能器。根据能量守恒和转换定律,导出该静电系统受力和力矩的两种计算方法及应用实例。     

Efficient nonlinear-optical frequency conversion in periodic media in the presence of diffraction of the pump and harmonic fields

It has been predicted by Shelton and Shen [Phys. Rev. A 5, 1867 (1972)] and observed by Kajikawa et al. [Jpn. J. Appl. Phys. Lett. 31, L679 (1992)] and Yamada et al. [Appl. Phys. B 60, 485 (1995)] that the efficiency of nonlinear-optical frequency conversion increases significantly in a nonlinear periodic medium and, accordingly, the intensity of the generated harmonic increases as the fourth power of the sample thickness, as opposed to the square law observed in homogeneous media. In this paper it is shown that the same enhancement of the efficiency of nonlinear-optical frequency conversion in a nonlinear periodic medium can be achieved using an ordinary pump wave in the form of a plane wave when both the pump wave and the harmonics are diffracted by the periodic structure of the nonlinear medium. The phenomenon is analyzed quantitatively in the example of second-harmonic generation. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 12, 793–799 (25 December 1999)     

Analytical and numerical calculations of optimum design frequency for focused ultrasound therapy and acoustic radiation force

Focused ultrasound therapy relies on acoustic power absorption by tissue. The stronger the absorption the higher the temperature increase is. However, strong acoustic absorption also means faster attenuation and limited penetration depth. Hence, there is a trade-off between heat generation efficacy and penetration depth. In this paper, we formulated the acoustic power absorption as a function of frequency and attenuation coefficient, and defined two figures of merit to measure the power absorption: spatial peak of the acoustic power absorption density, and the acoustic power absorbed within the focal area. Then, we derived “rule of thumb” expressions for the optimum frequencies that maximized these figures of merit given the target depth and homogeneous tissue type. We also formulated a method to calculate the optimum frequency for inhomogeneous tissue given the tissue composition for situations where the tissue structure can be assumed to be made of parallel layers of homogeneous tissue. We checked the validity of the rules using linear acoustic field simulations. For a one-dimensional array of 4 cm acoustic aperture, and for a two-dimensional array of 4 × 4 cm² acoustic aperture, we found that the power absorbed within the focal area is maximized at 0.86 MHz, and 0.79 MHz, respectively, when the target depth is 4 cm in muscle tissue. The rules on the other hand predicted the optimum frequencies for acoustic power absorption as 0.9 MHz and 0.86 MHz, respectively for the 1D and 2D array case, which are within 6% and 9% of the field simulation results. Because radiation force generated by an acoustic wave in a lossy propagation medium is approximately proportional to the acoustic power absorption, these rules can be used to maximize acoustic radiation force generated in tissue as well.     

原子在双色组合场中产生高次谐波的转换效率与激光波长的关系

利用分裂算符法求解速度规范下的含时薛定谔方程,研究了一维氦原子处于单色红外场、红外场与紫外场形成的双色组合场中产生的高次谐波谱,分析了在截止位置附近高次谐波的转换效率与激光波长(800—2000 nm)的关系,发现在双色组合场驱动下截止位置附近高次谐波的转换效率随波长的变化为η(λ)∝λ^－x,其中〈x〉的数值取决于激光场的强度,但是只要选取合适场强的组合场就能提高截止位置附近高次谐波的转换效率. 关键词： 双色组合场 分裂算符 高次谐波 转换效率     

A determination of the electronegativity parameter in molecular orbital calculations on heteronuclear molecules containing nitrogen

Using the semi-empirical LCAO molecular orbital method, the electronegativity parameter δ for nitrogen has been chosen to give reasonable fit between computed and ‘correct’ bond orders for a series of heterocyclic molecules. A δ-value of about 0·9–1·0 has been found for nitrogen in six-membered rings, and about 1·8–2·0 for pyrrole.     

The use of photoinduced light scattering for the evaluation of photoelectric fields in Lithium Niobate Crystals

The photovoltaic and diffusion fields in nominally pure single crystals of stoichiometric composition (R = Li/Nb = 1) grown from the melt with 58.6 mol % of Li₂O (LiNbO₃ stoich), in the nominally pure single crystals of congruent composition (LiNbO₃), and in congruent single crystals doped with Cu²⁺, Zn²⁺, and Gd³⁺ are found from the parameters of the photoinduced light scattering indicatrix obtained with the use of a 60-mW He-Ne laser.     

Impact of spatial modulation on the third harmonic wave propagation and far-field focal spot in frequency conversion system

Third harmonic generation (THG) of high power laser is discussed in KDP crystals utilized in frequency conversion systems of large laser facilities. The far-field focal spot of the third harmonic wave is presented based on numerical simulation of the nonlinear coupled-wave equations, in which the walk-off and paraxial diffraction are taken into account and the electric field of the fundamental wave (1053 nm, 1ω) pulse is phase and amplitude modulated in spatial domain. Impact of the modulation depth and frequency on the focal spot energy, the side lobes location and conversion efficiency are analyzed in detail. The results show that the side lobes location is equivalently determined by the modulation frequency of both phase modulation and amplitude modulation, while the energy-concentration is decreased mostly because of the 1ω modulation depth. Relatively, the phase modulation plays a more important role than the amplitude modulation in decreasing main lobe energy for different reasons. The phase modulation makes the energy flowing from the main lobe to side lobes, while amplitude modulation not only makes the energy flowing but also decreases tripling efficiency significantly.     

价键优选法：二、三周期小团簇的理论研究

使用价键优选法，在较小的计算量下，系统地得到了二、三周期元素团簇体系(直到四原子为止)关键结构的性质.还能得到团簇从双原子到四原子的演化过程.对所有团簇的电子结构进行分析，可以理解特定元素的四原子团簇出现T_d立体结构的原因.更加有趣的是，通过较小团簇结合能和对应元素单质宏观性质( 熔点、沸点等)的相应变化关系，能够理解在熔解、沸腾过程中关键结构的作用. 关键词： 价键优选法 团簇关键结构 团簇 第一原理分子动力学 物质性质