Second-Order Impedance Spectroscopy of an Electroreduction Reaction with Allowance for the Frumkin Correction

A theory of second-order impedance spectroscopy is developed. The theory is good for analyzing an electroreduction reaction in surface-inactive supporting electrolytes with allowance made for the structure of the electrical double layer (the Frumkin correction). According to the theory, a measured second-order impedance contains, as a factor, an effective charge transfer coefficient. The latter's dependence on potential has a minimum connected with the diffuseness of the electrical double layer. The theoretical notions are experimentally confirmed on the basis of a real system.     

On the thermal fluctuations of free charge in the Ershler-Randles circuit

Noise method for the analyzing of thermodynamic second-order fluctuations of the electrical double layer charge in complicated electrochemical systems is developed. The method is based on the joint application of the Nyquist fluctuation-dissipation theorem and Laplace transform. Second-order fluctuations of the free charge in the electrical double layer are studied under the conditions when the weak-signal faradaic impedance of equilibrated electrode is determined by the diffusion impedance, alongside with the slow-discharge resistance. It is shown that, unlike the high-order fluctuations, the level of thermodynamic second-order fluctuations of the free charge does not depend on the mechanism of interaction of the thermodynamic system with thermostat; it fully corresponds to the conceptions of the Gibbs statistical thermodynamics.     

Physical properties of sulfur near the polymerization transition

Acoustical measurements, electron spin resonance, and Raman spectroscopy have been employed to probe sulfur over the temperature range 80-180 degrees C, which includes the polymerization transition and the supercooled liquid state. Acoustical properties (sound velocity, absorption, and impedance) have been studied with both longitudinal and transverse waves at frequencies between 500 kHz and 22 MHz. The results confirm that polymeric sulfur is a solution of long chain molecules in monomeric solvent, and that the polymerization transition is not a second-order phase transition, as was proposed theoretically. Sulfur is a viscous liquid, but not viscoelastic, both below and above the polymerization transition temperature. It is shown that the classical Navier-Stokes theory is not applicable to the sound absorption in liquid sulfur in the highly viscous state.     

Multireference composite approaches for the accurate study of ground and excited electronic states: C2, N2, and O2

A multireference analog of the correlation consistent composite approach (MR-ccCA) based on complete active space with second-order perturbation theory (CASPT2) has been utilized in an investigation of the ground and valence excited states of C(2), N(2), and O(2). The performance of different second-order multireference perturbation theory methods including second-order n-electron valence state perturbation theory, second-order multireference M?ller-Plesset, and second-order generalized van Vleck perturbation theory has been analyzed as potential alternatives to CASPT2 within MR-ccCA. The MR-ccCA-P predicts spectroscopic constants with overall mean absolute deviations from experimental values of 0.0006 A?, 7.0 cm(-1), and 143 cm(-1) for equilibrium bond length (r(e)), harmonic frequency (ω(e)), and term values (T(e)), respectively, which are comparable to the predictions by more computationally costly multireference configuration interaction-based methods.     

Second-order nonadiabatic couplings from time-dependent density functional theory: evaluation in the immediate vicinity of Jahn-Teller/Renner-Teller intersections

For a rigorous quantum simulation of nonadiabatic dynamics of electrons and nuclei, knowledge of not only the first-order but also the second-order nonadiabatic couplings (NACs) is required. Here, we propose a method to efficiently calculate the second-order NAC from time-dependent density functional theory (TDDFT), on the basis of the Casida ansatz adapted for the computation of first-order NAC, which has been justified in our previous work and can be shown to be valid for calculating second-order NAC between ground state and singly excited states within the Tamm-Dancoff approximation. Test calculations of the second-order NAC in the immediate vicinity of Jahn-Teller and Renner-Teller intersections show that calculation results from TDDFT, combined with modified linear response theory, agree well with the prediction from the Jahn-Teller/Renner-Teller models. Contrary to the diverging behavior of the first-order NAC near all types of intersection points, the Cartesian components of the second-order NAC are shown to be negligibly small near Renner-Teller glancing intersections, while they are significantly large near the Jahn-Teller conical intersections. Nevertheless, the components of the second-order NAC can cancel each other to a large extent in Jahn-Teller systems, indicating the background of neglecting the second-order NAC in practical dynamics simulations. On the other hand, it is shown that such a cancellation becomes less effective in an elliptic Jahn-Teller system and thus the role of second-order NAC needs to be evaluated in the rigorous framework. Our study shows that TDDFT is promising to provide accurate data of NAC for full quantum mechanical simulation of nonadiabatic processes.     

The restricted active space followed by second-order perturbation theory method: theory and application to the study of CuO2 and Cu2O2 systems

A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.     

A validity test of the WCA perturbation theory for two-dimensional Lennard-Jones fluids

The potential energy and pressure are obtained from molecular dynamics simulations of two-dimensional Lennard-Jones fluids over a wide range of densities and temperatures, thus testing the validity of first-order (high temperature approximation) and second-order Weeks-Chandler-Andersen theory. The pressure results, which are very important for a subsequent analysis of adsorption theories, are very much affected by that approximation, especially at low densities and, surprisingly, at very high densities. For the potential energy the effect is smaller, and the approximation gives good results at intermediate and high densities even at low temperatures. The conclusion is that the second-order term of the Weeks-Chandler-Andersen theory is needed for theoretical calculations of the pressure, except at very high temperatures and intermediate densities. Nevertheless, the first-order term gives good results for the potential energy except at low densities. All these findings are necessary for a complete analysis of the validity of the Weeks-Chandler-Andersen theory and its consequences in the study of the adsorption of rare gases onto flat surfaces.     

Density-functional theory with effective potential expressed as a direct mapping of the external potential: applications to atomization energies and ionization potentials

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Moller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods.     

多参考态微扰理论大小一致性的数值研究

采用由H2、He 和LiH分别组成的三个超分子系列, 从数值的角度研究了多参考态微扰理论和单双重激发的多参考态组态相互作用(MRSDCI)的大小一致性. 首先在模型空间中进行一个小的完全组态相互作用计算, 然后进行多参考态微扰计算. 数值结果显示, 对这三个模型体系, 我们以前提出的多参考态二级微扰公式是完全大小一致的. 和MRSDCI结果比较, 我们也对它的计算精度进行了讨论. 另外, 还对两组多参考态微扰理论的二级和三级计算结果以及MRSDCI的计算结果的大小一致性误差进行了研究和比较.     

Second-order relativistic electron capture

Starting with the impulse approximation, we analyse second-order effects in relativistic electron capture. The relation of this model with relativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theory are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord with the formulae of Moiseiwitsch for flip and nonflip transitions in the ultra-relativistic limit. This confirms that the continuum-distorted-wave model generalises to relativistic spinors, and highlights the defects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but leads to a divergent total cross section for spin-flip transitions in the second-order term. This effect, which is quite distinct from the spurious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions.     

Feynman diagrams of the first two orders for the low-lying excited levels of He

The field form of perturbation theory is applied to two-electron atomic systems for the lower excited states (1s2s and 1s2p configurations). The contributions from the first- and second-order diagrams are calculated.     

The calculation of second-order molecular properties at the CI level of accuracy. The magnetisability of LiH

The perturbation theory approach to the calculation of second-order molecular properties is amended for the case when the perturbation is a magnetic field. It is therefore possible to calculate reliably the CI contributions to molecular magnetisabilities and large basis results are presented for LiH.     

Second-order Impedance in Electrode Kinetics

The kinetics of electrode reactions with a rather severe influence of the EDL structure is studied by nonlinear second-order impedance spectroscopy. Polarization impedance spectra and potential dependences of a nonlinear impedance are obtained for the reaction of electroreduction of the ferricyanide anion on the cadmium and bismuth electrodes in surface-inactive supporting NaF and Na₂SO₄ electrolytes. The results of measurements for the reaction Eu³⁺ + e Eu²⁺ on the bismuth and mercury electrodes are presented. It is shown that such important parameters of EDL as the potential of zero charge and the second derivative of potential with respect to the charge of the electrode surface can be determined directly from experimental curves even under conditions of occurrence of a faradaic process.     

Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states

A generalization of the spin-component scaling and scaled opposite-spin modifications of second-order M?ller-Plesset perturbation theory to the approximate coupled-cluster singles-and-doubles model CC2 (termed SCS-CC2 and SOS-CC2) is discussed and a preliminary implementation of ground and excited state energies and analytic gradients is reported. The computational results for bond distances, harmonic frequencies, adiabatic and 0-0 excitation energies are compared with experimental results to benchmark their performance. It is found that both variants of the spin-scaling increase the robustness of CC2 against strong correlation effects and lead for this method even to somewhat larger improvements than those observed for second-order M?ller-Plesset perturbation theory. The spin-component scaling also enhances systematically the accuracy of CC2 for 0-0 excitation energies for pi --> pi* and n --> pi* transitions, if geometries are determined at the same level.     

The structure of the second-order reduced density matrix in density matrix functional theory and its construction from formal criteria

Some formal requirements for the second-order reduced density matrix are discussed in the context of density matrix functional theory. They serve as a basis for the ad hoc construction of the second-order reduced density matrix in terms of the first-order reduced density matrix and lead to implicit functionals where the occupation numbers of the natural orbitals are obtained as diagonal elements of an idempotent matrix the elements of which represent the variational parameters to be optimized. The numerical results obtained from a first realization of such an implicit density matrix functional give excellent agreement with the results of full configuration interaction calculations for four-electron systems like LiH and Be. Results for H2O taken as an example for a somewhat larger molecule are numerically less satisfactory but still give reasonable occupation numbers of the natural orbitals and indicate the capability of density matrix functional theory to cope with static electron correlation.     

On the relativistic theory of NMR chemical shifts

A relativistic analogue to Ramsey's theory of NMR chemical shifts is formulated. Four-component spinor one-electron wavefunctions and relativistic magnetic hamiltonians are used. In contrast to the third-order Pauli approximation theory of Nakagawa et al., the main relativistic effects are then included in the usual second-order theory.