Stability of the periodic deformations in planar nematic layers

The periodic deformations induced by external fields have been analysed by means of the Taylor expansion method based on the theorems of catastrophe theory. The analysis is restricted to the planar nematic slab influenced by a magnetic field. Two different configurations of the field which lead to periodic deformations with prevailing splay or twist we considered. The ranges of material constants at which the periodic state is stable and the threshold magnetic field strength have been found. The problem of transitions between the undeformed, uniformly deformed and periodic states is discussed.     

Axially symmetric potentials in the oscillator representation

The Wick-ordering method called the Oscillator Representation in the nonrelativistic Schrödinger equation is proposed to calculate the energy spectrum for axially symmetric potentials allowing the existence of a bound state. In particular, the method is applied to calculate the energy spectrum of (2s) states of a hydrogen atom in a uniform magnetic field of an arbitrary strength. In the perturbation (external field) approximation, the energy spectrum of the so-called quadratic and spherical quadratic Zeeman problem and the problem of a hydrogen atom in a generalized van der Waals potential is calculated analytically. The results of the zeroth approximation of oscillator representation are in good agreement with the exact values     

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.     

Perturbational and variational treatments of the Morse oscillator

The Morse oscillator hamiltonian is expressed as an infinite expansion in powers of a natural perturbation parameter, the square root of the anharmonicity constant, relative to the simple harmonic oscillator as zeroth-order hamiltonian. A transformation of variables leads to a hamiltonian which involves terms no higher than second order in this natural perturbation parameter. In both cases, the exact bound state eigenvalues of the Morse oscillator are given by second-order perturbation theory. The Schrödinger equation corresponding to the transformed Morse hamiltonian is solved variationally, via a complete set expansion in simple harmonic oscillator eigenstates. Accurate approximations to the exact eigenvalues and eigenfunctions of bound states of the Morse oscillator can be obtained for all but the very highest levels.     

Connections between perturbation theory and the Van Vleck transformation: Illustrative calculations on the perturbed harmonic oscillator

We continue to examine the connection between perturbation theory and the Van Vleck unitary transformation. Here we illustrate the formalism derived earlier by applying it to compute the stationary states of the perturbed harmonic oscillator. We find that each solution of the traditional Brillouin-Wigner perturbation theory equations gives rise to a different unitary transformation which, when operating on the unperturbed ground state, produces one or the other of the perturbed eigenstates. With any of the perturbed states able to be reached by a unitary transformation on the unperturbed ground state, we advise caution in using approximate solutions of the perturbation equations in general cases, lest an unexpected stationary state be obtained.     

The polarization phenomena of spherical molecules

The calculation of the polarizabilities of spherical molecules is discussed in the light of the average excitation energy approximation to perturbation theory. It is shown that whilst information about the energy in external fields can always be obtained from polarization phenomena, some information about the unperturbed wave function also can be obtained from magnetic susceptibility and Cotton–Mouton effect measurements. In the case of argon such information was found to agree with the results of self-consistent-field calculations. Predictions of the Cotton–Mouton constants of krypton and xenon are made.     

Acceleration of Correlation-corrected Vibrational Self-consistent Field Calculation Times for Large Polyatomic Molecules

Acceleration of the correlation-corrected Vibrational self-consistent field (CC-VSCF) method for anharmonic calculations of vibrational states of polyatomic molecules is described. The acceleration assumes pairwise additive interactions between different normal modes, and employs orthogonality of the single-mode vibrational wavefunctions. This greatly reduces the effort in computing correlation effects between different vibrational modes, which is treated by second order perturbation theory in CC-VSCF. The acceleration can improve the scaling of the overall computational effort from N ⁶ to N ⁴, where N is the number of vibrational modes. Sample calculation times, using semi-empirical potential surfaces (PM3), are given for a series of glycine peptides. Large computational acceleration, and significant reduction of the scaling of the effort with system size, is found and discussed.     

外电场对甲醛分子的结构与电子光谱的影响

采用密度泛函理论(DFT)在B3LYP/6-311++G(d,p)基组水平上,计算了不同外加电场(-8.22×10~9~8.22×10~9 V/m)下甲醛分子基态稳定构型、分子键长、电荷分布、能级分布、能隙、红外光谱、拉曼光谱和分子的总能量.在此基础上利用TDDFT/B3LYP/6-311++G(d,p)方法研究了甲醛分子由基态跃迁到前25个激发态的激发能E、谐振强度f、吸收波长λ受外电场的影响.结果表明:随着C=O连线方向外电场的增加,C=O键键长、氢原子电荷、偶极矩和能隙递增;C—H键键长、C,O原子电荷递减,总能量降低.振动频率与红外强度及拉曼强度由于不同振动有不同变化.甲醛分子UV-Vis光谱随外电场的增加,不同的吸收峰发生了不同程度的蓝移或者红移;外电场对甲醛分子的激发能、谐振强度和吸收波长的强度有一定影响,但随电场变化比较复杂.     

尿素分子振动光谱的密度泛函理论研究

用密度泛函理论方法BLYP/6-31¹⁺+G(2df,2pd)对尿素分子的平衡几何构型进行了优化,并计算了该分子的谐力场.使用Wilson的GF矩阵方法,对尿素分子的振动基频进行了理论研究.根据振动频率的势能分布对此分子的振动基频进行了理论归属,计算的振动频率和能级指认均同实验结果吻合较好.     

外电场作用下甲基乙烯基硅酮分子结构和电子光谱

采用密度泛函B3P86方法在6-311++G(d, p)基组水平上优化得到了沿分子轴方向不同外电场(0-0.04 a.u.)作用下, 甲基乙烯基硅酮分子的基态电子状态、几何结构、电偶极矩和分子总能量. 在优化构型下利用杂化CIS-DFT方法(CIS-B3P86)研究了同样外电场条件下对甲基乙烯基硅酮的激发能和振子强度的影响. 计算结果表明, 分子几何构型与电场大小呈现强烈的依赖关系, 分子偶极矩μ随电场的增加先减小后急剧增大. 电场为零时, 分子总能量为-483.5532137 a.u., 随着电场增加, 能量升高, 在F=0.02 a.u.时达到最大值-483.5393952 a.u., 此后, 继续增大电场系统总能量则开始降低. 激发能随电场增加急剧减小, 表明在电场作用下, 分子易于激发和离解.     

Perturbation calculation on the hydrogen atom in electric and magnetic fields

A generalization of a perturbation theory without wave function is developed which applies to a hydrogen atom perturbed by magnetic and electric fields. A double perturbation expansion for the Stark–Zeeman effect for parallel fields is considered and results for the states obeying |m| = l = n ? 1 in the zero field limit are presented. Other problems that can be treated this way are discussed.     

Effect of critical fluctuations on adsorption of van der Waals fluid in a spherical cavity

A recently proposed non-uniform fifth-order thermodynamic perturbation theory (TPT) is employed to investigate the adsorption of a hard core attractive Yukawa (HCAY) fluid in a spherical cavity. Extensive comparison with available simulation data indicate that the non-uniform fifth-order TPT is sufficiently reliable in calculating the density profiles of the HCAY fluid in the highly confining geometry, and generally is more accurate than a previous third-order?+?second-order perturbation density functional theory. The non-uniform fifth-order TPT is free from numerically solving an Ornstein–Zernike integral equation, and also free of any adjustable parameter; consequently, it can be applied to both supercritical and subcritical temperature regions. The non-uniform fifth-order TPT is employed to investigate critical adsorption of the HCYA fluid in a single spherical cavity – it is disclosed that the critical fluctuations near the critical point induce depletion adsorption – quantitative theoretical calculation on relationship between the critical depletion adsorption, parameters of coexistence bulk phase and the responsible external field is in agreement with qualitative physical analysis.     

Coupled dressed-states formalism for multiphoton excitation and population inversion by coherent pulses

We show how the single-mode Floquet theory, valid only for sinusoidal field problems, may be generalized to a coupled quasienergy (or dressed-) states formalism, allowing non-perturbative treatment of multiphoton excitation of multilevel quantum systems driven by non-sinusoidal coherent pulse fields. The method is illustrated by a case study of the adiabatic population inversion in a CO Morse oscillator.     

On the role of classical orbits in mesoscopic electronic systems

We discuss the semiclassical periodic orbit theory (POT) and some of its recent extensions which are applicable also to systems exhibiting a transition from integrable to chaotic behaviour. We apply the POT to give a semiclassical interpretation of shell effects in free metal clusters and semiconductor quantum dots in terms of classical periodic orbits. In particular, we study the ground-state deformations of large metal clusters and discuss the recently observed conductance oscillations in a circular quantum dot under the influence of an external magnetic field. We also predict the shell structure of a triangular quantum dot, using as models a triangular billiard and the Hénon-Heiles potential including weak magnetic fields.     

Phase diagrams of grafted molecules under external fields: A mean field model

A mean field theory is extended to investigate the phase behavior of grafted molecules under external fields. In the model, each grafted molecule contains two states, similar to the Ising model, and the applied field interacts with only one of the two states. The free energy of this model is formulated as a function of composition, field strength, and a parameter to account for the intermolecular interactions of neighboring molecules. Our calculations show that uniform fields exhibit no significant effect on phase diagrams. In contrast, linear gradient fields affect critical temperature but show no direct effect on critical composition. Under external fields with quadratic spatial gradient, both critical constants become sensitive to field direction and strength. Moreover, an analysis of field dependent critical constants suggests that quadratic fields affect miscibility and critical temperature. A brief comparison of the current model and the Ising model is also given.     

A Constant Potential Molecular Dynamics Simulation Study of the Atomic‐Scale Structure of Water Surfaces Near Electrodes

Novel and technologically important processes and phenomena arise at water surfaces in the presence of electric fields. However, experimental measurements on water surfaces are challenging, and the results are scarce and inconclusive. In this work, the constant potential molecular dynamics method, in which the electrode charges are allowed to fluctuate to keep the electric potential fixed, was implemented in the study of a near‐electrode water surface systems. This simulation system was set up with a vapor/liquid‐water/vapor slab and two electrodes under different sets of applied electrostatic potential, yielding i) a detailed characterization of the external E‐field dependent electrostatic potential/density/dipole moment density profiles, and ii) the relationship between the water surface width and the applied electrode voltage differences which has been rarely reported. The adjustments in the number density profiles in the vicinity of water surfaces due to external E‐fields were observed, while the capillary interfacial widths for the surfaces near both cathode and anode were found with different increment rates under increasing E‐fields. By examining dipole density profiles across the water surfaces, we found that external E‐field induced polarization occurs in both bulk and surface regimes, yet the surface polarization densities vary asymmetrically with respect to the increasing E‐fields. Detailed discussions were carried out to explain the correlation between water surface tension and surface widths, as well as the interplay between the surface polarization densities and the hydrogen bond network structure. We conclude that the mechanical and structural properties of the water surfaces could be tuned by both magnitude and direction of the strong external E‐fields. We also recognize that more surface properties with application value, such as dielectric permittivity tensor or surface potential, could also be regulated by the external E‐fields.     

铆接于固体表面的两性聚电解质链构象的分子动力学模拟

用分子动力学模拟研究了铆接于带电固体壁面上的两性无规共聚电解质链的构型及其随溶剂的介电常数、系统温度和带电壁面电场的变化。结果表明,聚离子链的构型取决于外电场对链节的作用、链内各链节间的静电作用和链节的热运动(温度)三者的综合作用结果。电场强度较低时,铆接聚离子链与非铆接聚离子链的构型变化类似。电场强度较高时,两性聚离子链构型更为舒展。溶剂介电常数减小,链节间静电作用增强,净电荷比较小的中性或非中性两性聚电解质链倾向于收缩,净电荷比较多的链则膨胀。温度的升高一般总是抵消电场和分子内静电作用的影响,当它占主导地位时将使聚离子链膨胀。     

Electronic structures of low-lying Bu excited states in trans-oligoenes: Pariser-Parr-Pople and ab initio calculations

Two lowest-lying excited singlets with B(u) symmetry of all-trans-oligoenes, the well-known ionic 1(1)B(u)(+) state as well as the "hidden" ionic-covalent-mixed 1(1)B(u)(-) state, are calculated within both the Pariser-Parr-Pople (PPP) model at full configuration interaction (FCI) level and ab initio methods. The vertical excitation energies as well as wavefunctions from PPP-FCI calculations are found to be in good agreement with those from high-level multi-reference methods, such as multi-reference complete active space self-consistent field (CASSCF) with second order perturbative corrections (CASPT2), multi-reference M?ller-Plesset perturbation theory (MRMP), and complete active space valence bond theory (CASVB). The oscillator strengths from PPP calculation are in good agreement with spectroscopy experiments. The relatively small oscillator strength of 1(1)B(u)(-) is due to the approximate electron-hole symmetry of this state. In addition, the bond lengths in both states are found to show remarkable relativity with the bond orders calculated with ground state geometries, which suggests a possible strategy for initial guess in geometry optimization of excited states.