Electro-optics of molecules

The natural vibrations and electro-optics of diatomic molecules are considered in the framework of the perturbation theory. The energy of anharmonic vibrations and the matrix of a dipole moment function are determined with allowance made only for nonzero perturbation contributions. In particular, the case of strong electro-optical anharmonicity of diatomic molecules (i.e., the situation where the dipole moment function significantly deviates from linear behavior) is analyzed in the second order of the perturbation theory. Within the introduced formalism of polynomials of the quantum numbers, the perturbation theory is extended to polyatomic molecules and expressions for the matrix elements of the dipole moment are derived in explicit form with due regard for the vibrational quantum numbers.     

Representation matricielle du moment dipolaire dans la base des fonctions propres de l'Hamiltonien; intensites infrarouges et moments dipolaires des etats vibrationnellement excites

The molecular dipole moment matrix is obtained in the Hamiltonian representation by a contact transformation. Infrared intensities and dipole moments of polyatomic molecules have been obtained for vibrationally-excited states. The results have been applied to the SO₂ molecule.     

Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids

We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schrödinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.     

Exciton self-trapping in molecular media with an elastic dipole moment

Exciton self-trapping in a molecular medium is considered within a self-consistent model taking into account the change in the dipole moment as a result of a displacement of molecules and the resonance interaction with an electromagnetic field. New mechanisms and specific features of the formation of localized structures in quasi-one-dimensional molecular structures are investigated. It is shown that the dependence of the dipole moment on molecular vibrations leads to new conditions for exciton self-trapping and intrinsic optical bistability, as well as for the formation of electromagnetically induced transparency. The theory proposed is used to explain the specific features of exciton self-trapping in a conjugated polymer and J aggregates of dyes under the action of an external laser field.     

Influence of molecular structure of squaraine dyes on their aggregation in aqueous solutions

The influence of the molecular structure of several squaraine dyes on their aggregation in aqueous solutions and its spectral manifestation were studied. The results are analyzed using quantum-chemical modeling. It is shown that a transverse dipole moment in squaraine molecules contributes to aggregation with an antiparallel orientation of the molecules whereas a longitudinal dipole moment leads to formation of J-type aggregation with a longitudinal orientation of the molecules. In some instances both aggregate types are present in the solution over a wide concentration range.     

Systematics of vibrational intensities for “diatomic” molecules: Approximate formulas

Several approximations are discussed which enable one to estimate electric dipole moment transition matrix elements for diatomic molecules based on a very limited amount of experimental data. For strongly polar molecules, a simplistic point-charge dipole model in which there is no vibrational charge flux predicts a simple relation between the permanent moment, M₀, and its derivative with respect to internuclear separation, M₁. This is found to be approximately valid for a surprisingly large number of polar molecules. Next, approximate matrix elements for the fundamental and overtone bands are presented for a linear dipole moment function. Finally, systematic trends for molecules having similar electronic structures are investigated and combined with the approximations discussed above in order to estimate the transition moments for several molecules of astrophysical interest. An extension to the ν₃ fundamental and overtone bands of CH₄ is suggestive that some of these ideas may be applicable to certain polyatomic molecules as well.     

Calculation of vibrational matrix elements of the CO2 molecule in the formalism of polynomials of the quantum numbers

The vibrational energies and the matrix elements of the electric dipole moment function and the rotation function are calculated for an arbitrary linear polyatomic molecule in the first order of perturbation theory using the formalism of polynomials of quantum numbers. The formulas obtained are tested for the example of the CO₂ molecule. The experimental data available at present are briefly analyzed. It is shown that the calculated matrix elements are in good agreement with the corresponding experimental data even in the first order of the theory.     

Determination of vibrational energy levels and parallel band intensities of 12C16O2 by Direct Numerical Diagonalization

The Direct Numerical Diagonalization (DND) technique has been applied to the principal symmetric species of carbon dioxide. A three-dimensional formulation of the DND method has been implemented as a first step in using the method to calculate properties of simple polyatomic molecules. Recent high-resolution observations of both line positions and intensities have been incorporated into the method to yield new values for the potential function and the dipolar coefficients. The results are compared with the potential functions calculated by earlier DND efforts as well as the contact transformation approach. The results are also discussed in terms of the effects of truncation errors caused by the use of finite matrices to represent the Hamiltonian operator. The resulting eigenvectors have been used to determine a dipole moment function from 21 observed band intensity values. This dipole moment function in turn has generated a large list of band intensity estimates for ¹²C¹⁶O₂ parallel bands which are being used to update the AFGL line parameter compilation. This list represents the first published set of band intensity values derived from a consistent quantum mechanical model for a linear polyatomic molecule.     

顺式与反式偶氮苯衍生物分子非线性光学性质理论研究

利用密度泛函理论(DFT)B3LYP/6-31G(d,p)方法优化了一系列顺式与反式偶氮苯衍生物分子,在此基础上结合有限场(FF)方法和密度泛函理论对分子非线性光学(NLO)性质及电子光谱进行了计算分析,结果表明:顺式与反式结构的变化对其偶极矩、分子内电荷分布与转移以及前线轨道跃迁都造成影响,从而影响分子的第一超极化率.同时相对于顺式偶氮苯衍生物分子,反式分子具有较大的二阶非线性光学系数.     

Ru(0001)表面氮分子和钡原子的相互作用

本文采用密度泛函理论方法研究了Ru(0001)表面氮分子和钡原子的相互作用。计算结果表明,钡原子的作用弱化了氮分子键。氮分子键长从Ru(001)-N2表面的0.113 nm伸长至Ru(001)-N2/Ba表面的0.120 nm;分子的拉伸振动频率从2221 cm-1减小到1746 cm-1;氮分子得到的电荷数从清洁表面的0.3 e增加到1.1 e。电荷从钡原子6s轨道向钌原子4d轨道转移,转移电荷增强了氮分子 空轨道和钌原子4d轨道间的杂化作用,导致 分子轨道和 杂化轨道发生极化。轨道极化使分子电偶极矩增加了约-0.136 eÅ。金属钡在Ru(0001)表面氮分子活化过程中具备电子型助催剂的特征。     

The Orientation of the Phosphorescence Dipole Moment of Erythrosine B Within Its Molecular Frame

For an unequivocal interpretation of time-resolved phosphorescence depolarization measurements on dye molecules in biophysical systems, the orientation of the transition dipole moments within the frame of the dye has to be known. The goal of this work is to find the orientation of the phosphorescence dipole moment of erythrosine B within its molecular frame. To this end, we first determine four difference angles, exciting a molecule in two of its absorption bands and measuring the fluorescence and phosphorescence anisotropy for each excitation wavelength. The next step is to position the transition dipole moments within the molecular frame, combining the results of angle-resolved fluorescence depolarization measurements with the measured difference angles. It is shown that the phosphorescence dipole moment is tilted out of the plane of the molecule. Additionally, we find that the phosphorescence dipole moment is located above the fluorescence dipole moment and not above the absorption dipole moment. This induces an extra difference angle between the absorption and the phosphorescence dipole moments which in the past has been interpreted erroneously as a larger tilt out of the plane of the molecule.     

用杂化CIS-DFT方法研究外电场对乙烯激发态的影响

采用杂化CIS-DFT方法研究了外电场对乙烯分子基态和激发态性质的影响，结果表明外电场对分子几何结构，总能量，偶极矩，极化率，振子强度和激发能有显著影响。CIS-DFT的优点在于它能确定外场下分子的对称性并且给出正确的激发顺序以及分子轨道的电子组态，由此导出乙烯分子的激发态，计算结果与实验一致。首次研究了乙烯分子的外电场效应。与其他从头算方法相比，杂化CIS-DFT方法计算精度和效率相对较高，可用于研究大分子体系。     

几种硝基苯类炸药在外电场作用下的分子特性

采用密度泛函理论中的B3LYP方法,在6-31G*水平上研究了外电场对一些硝基苯类炸药分子的总能量、偶极矩、分子轨道能级和前线轨道能量差等分子特性的影响;考察了在外电场作用下分子前线轨道能量差与炸药的电火花感度之间的关系.结果表明,在外电场作用下分子总能量降低,偶极矩增大、前线轨道能量差减小;分子前线轨道能量差与炸药的电火花感度之间几乎线性相关,且外电场对这种线性相关性无明显影响.     

Polarization of the Fluorescence Excited in the P- and R Branches of the Vibronic Lines of Jet-Cooled Complex Molecules

A model is suggested to calculate the degree of polarization of the fluorescence of jet-cooled polyatomic molecules excited within the P- and R branches of the rotational contour of the vibronic line by light not providing resolution of the rotational structure. These dependences are calculated and compared with experimental data for molecules belonging to different types of asymmetric tops with different intramolecular orientation of the fluorescence transition dipole moment: anthracene; anthracene + Ar; 1,4-diaminoanthraquinone; indole; tetracene, and triphendioxazine.     

Effective dipole moment of rotational transitions of X 2 Y molecules

Contributions determining the rotational dependence of the effective dipole moment of molecules are calculated for the ground state of H₂S and H₂O molecules. The calculation is carried out in various ordering algorithms of perturbation theory. It is shown that the convergence of the effective dipole moment for the ground state of an H₂O molecule in the polynomial representation is rather slow in the rotational operator J _z (the convergence radius is K*≤17). Nonpolynomial forms of the dipole moment as a function of rotational operators are discussed.     

Ordering of molecular dipole moments in a nanosized water cluster

A water cluster of 1000 molecules is simulated using the method of classical molecular dynamics. The calculation is performed for the “flexible” version of the TIP4P interaction potential for a constant cluster temperature of 180 K. It is found that clusters with a solid crystalline or amorphous core and a liquid-like shell are stable structures. The ferroelectric ordering of the molecular dipole moments in the central part of the cluster is found for both cluster types; this ordering is responsible for a large total dipole moment of these molecular groups. However, this effect is compensated by dipoles in the peripheral cluster layers, so that in general, the mean dipole moment of a cluster appears to be much smaller than that in the case of the random orientation of the cluster molecules.     

用杂化CIS-DFT方法研究外电场对乙烯激发态的影响

采用杂化CIS-DFT方法研究了外电场对乙烯分子基态和激发态性质的影响,结果表明外电场对分子几何结构,总能量,偶极矩,极化率,振子强度和激发能有显著影响.CIS-DFT的优点在于能确定外场下分子的对称性,给出正确的激发顺序以及分子轨道的电子组态,由此导出乙烯分子的激发态,结果与实验一致.首次研究了乙烯分子的外电场效应.与其他从头算方法相比,杂化CIS-DFT方法计算精确和效率相对较高,可用于研究大分子体系.     

A theory of magneto-optical rotation in diamagnetic molecules of low symmetry

A quantum-mechanical theory for the Faraday effect in polyatomic molecules is developed along the lines of the general theory on natural optical rotation presented by Rosenfeld, Condon, et al.

The stationary perturbation of a magnetic field and the time-dependent perturbation of a light wave are treated simultaneously by means of a second-order time-dependent perturbation theory. The treatment is restricted to molecules having non-degenerate wavefunctions and zero spin. The moment of a single molecule, in the presence of a magnetic field and a light wave, is calculated in Part I. In Part II the average electric and magnetic moments per molecule are used in macroscopic optical equations to determine the Verdet constant, which is shown to be non-vanishing for the molecules under consideration. A discussion of the results will be given subsequently, in Part III of this work.     

The deuteron and its magnetic moment the effects of non-local nuclear forces and of unitary transformations

The deuteron theory is renewed and completed for non-local Hamiltonians. A method to calculate deuteron wave functions is given. The formula for the current density and the magnetic dipole moment of a non-local potential is derived, and applied to the GCT, GT, and HJ-potential. The effects of a unitary transformation on the deuteron data — electric quadrupole moment, magnetic dipole moment, and radius — are shown. For the numerical calculations the Ristig-Kistler transformation and the HJ-potential were used. It is shown that an overall fit cannot be reached.     

Rotational energies of plar symmetric-top molecules in high electric fields

A method based on hypervirial theorems and perturbation theory is developed for calculating rotational energies of polar symmetric-top molecules in uniform electric fields. This procedure also provides expectation values of other physical observables such as the effective dipole moment.