共线散射体系A+BC的平-振能量传递──无限维李代数处理方法

利用无限维李代数方法处理了在BC分子能谱中含有二级与三级非简谐项的散射体系A＋BC的平-振能量传递问题，获得了散射过程的含有主要动力学参量的跃迁矩阵元和跃迁几率的解析表达式     

四原子分子中Majorana算子矩阵元的新计算公式

李代数方法在研究双原子分子、三原子分子振－转光谱及相关问题等方面已被证明是一种有效方法[‘－0,并被成功推广到多原子分子[’－门．构造代数哈密顿量是此方法的关键,这就要求选择合适的     

准线型四原子分子高激发振动能级的动力学李代数方法

近几年来 ,人们用李代数方法处理了许多问题 [1～ 5] ,在此基础上 ,我们利用动力学李代数方法研究了准线型四原子分子高激发振动态 ,把分子的 Hamiltonian展开成 Casimir算子与 Majorana算子之和[6,7] ,然后进行代数处理 ,从而得到了代数 Hamiltonian的本征值 .1　基本理论四原子分子有 3个键 ,所满足的对称群为 G=U1(4) U2 (4) U3 (4) ,处理分子问题时 ,一般要考Fig.1　 The bond coordinates of fulminic acid(HCNO)虑键与键之间的耦合 ,为了方便 ,首先让键 1与键 2耦合 ,然后再与键 3耦合 (图 1 ) .这种耦合方式可记为 (1 2 ) 3 …     

光缔合过程中多光子振转态选择性跃迁

研究了光缔合过程中OH分子基电子态的振转态选择性跃迁. 计算结果表明通过选择适当的初始碰撞能与光场参数,两碰撞原子可以利用三光子、四光子与九光子跃迁,从连续态跃迁至目标态. 通过选取较低的光场频率,增加跃迁至目标态的光子数来控制分子布居跃迁至较低的振转态. 在光缔合过程中, 部分缔合的分子通过中间态与背景态重新发生解离,解离过程降低了目标态的布居分布.     

三原子分子振转激发态的理论研究

三原子分子振转激发态的理论研究谢代前,鄢国森,田安民（四川大学化学系,成都,６１００６４）关键词振转激发态,三原子分子,变分法能级较高的振转激发态通常包含大振幅运动,其波函数分布于很广的势能面区域内,传统的正则模理论已不适合于解决这类问题．近年来,Ｈ...     

Lie代数方法在线形三原子分子转动谱计算中的应用

利用动力学群U₁(4)ÄU₂(4)的对称性质以及相应的Lie代数给出了描写线形三原子分子振转谱的Hamilton量. 在考虑了振转相互作用后, 所得上述Hamilton量本征值的表达式具有在光谱分析计算中常用的项值方程的形式. 利用此表达式拟合观察线位可以得到分子的振转常数. 作为算例, 对N₂O及HCN分子(02⁰0-01¹0)ν₂红外跃迁谱带的转动能级进行了拟合分析, 所得均方根误差分别为0.00001和0.0014 cm^-1.     

He-N20偶极矩面及振转跃迁强度的理论研究

用超分子MP4方法和大基组(aug-cc-pVTZ)及键函数得到He-N2O体系的分子间从头算势能面及偶极矩面．用离散变量表象方法计算了^4He-N2O及^3He-N2O体系的振转能级，并进一步计算得到其振转跃迁强度，计算结果很好地解释了实验现象。     

求解弱相互作用分子A-BC的振转能级和波函数的SCF-CI方法

给出了一种计A－BC型弱相互作用分子体系的分子间振转激发态的自洽场-组态相互作用(SCF－CI)方法. 首先使用SCF方法代化径向伸缩振动和弯曲振动的基函数,再用CI方法确定精确的振转激发态能级. 在求解-维的伸缩振动SCF方程时,采用Numerov－Johnson算法在给定区间上求解获得振动波函数的数值解. 具体计算了Ar－HCI和Ar－N₂体系的振转激发态的能级以验证该方法. 结果表明,本方法可用较少的组态就能获得可与其它大计算量的方法具有相比拟的精度的结果.     

计算液态混合物内能和内压的统计热力学理论

假定二元液态混合物分子间的相互作用势能可以表示成多体相互作用势能的和,分子间的力为短程力,相互作用势能只与分子间的相对距离有关.利用分布函数理论导出了二元液态混合物的过剩内能和内压的公式.二元液态混合物的过剩内能和内压可以表示成体积的幂级数形式,其中的系数可以用多体相互作用势和多体径向分布函数表出.讨论了单元液体的内压和过剩内能的表达式,在两种特殊情形下,过剩内能和内压的表达式分别与Egelstaff的微扰论结果及Frank的实验结果具有相同的形式.讨论了二元混合物内压和内能的两个特例,其一,在特殊情形下,给出了混合液体过剩内能的混合规则的一个证明.其二,给出的二元混合物的过剩内能和内压的表达式与Frank的实验结果具有相同的形式.     

光异构化反应速率的量子理论

光异构化反应是在光场存在下，分子吸收光子引起的单分子化学反应，包括通常的异构化与环合、开环反应．一些作者用量子化学方法及分子轨道相关图和态相关图等方法对这类反应进行过研究［1］．本文用多声子光跃迁理论［2］研究光异构化反应，导出反应速率及其在低温条件下的解析表达式，对所得结果进行了讨论．1理论方法与结果在光异构化反应中，分子的电子状态与构型都发生变化，而且电子态的变化是与构型的改变紧密耦合的．分子的构型用分子的振动波函数来描写．由于电子与原子质量相差悬殊，可以采用绝热近似处理这一电子－振动相互作用…     

Discrete variable approaches to tetratomic molecules: part I: DVR(6) and DVR(3) + DGB methods

We present two discrete variable representation (DVR) based methods for the determination of the vibrational energy levels of tetratomic molecules. Both methods are designed for orthogonal internal coordinates in a body-fixed reference frame and make use of the DVR of three angular variables. The angular DVRs allow the construction of a fixed-angle three-mode Hamiltonian for the stretching vibrations. For each of the angular triples, the stretching eigenvalue problems are solved by employing 3D radial DVRs in the DVR(6) approach and real three-dimensional distributed Gaussian functions in the DVR(3) + DGB method. The angular degrees of freedom are taken sequentially into account in conjunction with a contraction scheme resulting from several diagonalization/truncation steps. Vibrationally averaged geometries, expectation values of rotational constants, and several adiabatic projection schemes developed in this work for tetratomic molecules are used to characterize the vibrational levels calculated by the DVR(6) and DVR(3) + DGB.     

Recent Advances in Recursive Solution of Large Molecular Eigenproblems

In studying highly excited ro-vibrational spectra of polyatomic molecules, the traditional direct diagonalization approach becomes impractical because of the formidable computational resources needed I will in this talk discuss some recent advances in solving large dimensional molecular eigenproblems using sparse matrix techniques. In particular, I will talk about the Lanczos algorithm and the Chebyshev-based filter-diagonalization method. These techniques are based on matrix-vector multiplication and thus amenable to larger problems. Applications to highly excited (ro-)vibrational spectra of tri- and tetratomic systems such as SO₂ and HOOH will be presented.     

Recoupling coefficients of group SO(4) and their application to linear tetratomic molecules

The general expressions for the recoupling coefficients of group SO(4) are obtained by employing the subgroup chains (2) and (11). When considering a special case, we give results that can be used for tetratomic molecules. Using these recoupling coefficients, the matrix elements of C and M operators that are not diagonal can be given. Within the dynamic algebra framework, an effective algebraic Hamiltonian of linear tetratomic molecules is obtained. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 293–301, 2003     

Spectroscopy of complex molecules in the gas phase

A brief review is presented of theoretical and experimental research into the role of statistical factors in the formation of the characteristics of absorption and emission processes of light, observed for low-density and rarefied vapours of complex molecules. It is shown, in particular, that the average energy of molecules excited per unit time differs from the mean energy of molecules in the ground state, not by the energy of the exciting photon hv, but by the sum of hv and the selective energy which is the result of different absorption probabilities for molecules of different energy. This correction is the most important in rotational—vibrational absorption bands. This was established when the selective energy was calculated using the experimental data with the help of the formulae obtained. Average energies of the initial and final combining states reduced by the average energy of molecules in the ground state are calculated. Correlation curves similar to those of Condon are plotted according to the calculated data. The electron transition frequencies and the identities of absorption and emission transitions are determined through these curves; whereas for rotational—vibrational bands the value of the rotational constant and the variation of the latter upon excitation are estimated.     

Temperature dependence of the optical rotation of fenchone calculated by vibrational averaging

On the basis of vibrational averaging, the temperature dependence of the optical rotation for fenchone has been calculated using TDDFT with the B3LYP hybrid functional at three wavelengths. The results show that very good agreement is obtained between theory and experiment. It is concluded that temperature-dependent vibrational effects are likely to account for much of the observed temperature dependence in optical rotation exhibited by rigid organic molecules in case there is only a weak temperature-dependent interaction with the solvent.     

Theoretical study of sum-frequency vibrational spectroscopy off electronic resonance on limonene chiral liquids

The sum-frequency vibrational spectroscopy (SFVS) off electronic resonance on chiral liquids is analyzed using the approach of antisymmetric nonresonant vibrational Raman scattering tensor calculation, which is based on the direct Taylor expansion of electronic transition moments in vibrational normal coordinates. A single-excitation configuration interaction treatment is applied to compute the SFVS off electronic resonance for (R)-limonene molecules, and the model spectra compare favorably with experimental data. This direct evaluation approach may provide a method of computing antisymmetric nonresonant vibrational Raman polarizabilities and predicting and assigning the SFVS off electronic resonance on chiral liquids.     

New developments in millimeter wave spectroscopy

In the past few years millimeter and submillimeter wave spectroscopy has been the backbone for modern molecular line astronomy. The detection of unstable and high-temperature molecular species in the interstellar environment has stimulated the development of methods of detecting molecular ions, radicals and unstable molecules in the laboratory by means of millimeter wave technology. Some of the recent experimental advances as well as the developments which have occurred in the analysis of high resolution rotational and vibrational spectra with regard to understanding molecular dynamics will be discussed.     

HO^3^5Cl,HO^3^7Cl,DO^3^5Cl和DO^3^7Cl的振动激发态光谱研究

本文用自洽场组态相互作用方法(SCF-CI)精确计算了次氯酸分子HOCl的振动激发态的能级以及次氯酸分子中的H和Cl分别被D和^3^7Cl取代后的HO^3^7Cl,DO^3^5Cl和DO^3^7Cl的同位素效应, 这些理论计算值与已有的实验结果吻合较好, 还预测了一些尚未观测到的谱线频率及同位素效应。     

Discrete and continuum quantum states for the Kratzer oscillator

Kratzer oscillator is a realistic zero‐order model for describing the anharmonic ro‐vibrational motion in diatomic molecules. Kratzer oscillator has an energy spectrum containing both discrete and continuum parts. Wavefunctions belonging to the continuum would be useful in the study of transitions to the continuum in molecular dissociation processes. In this article, bound and scattering wavefunctions of the Kratzer oscillator are reviewed and the bound–bound and the bound–free matrix elements are obtained. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.