Performance of SOPPA-based methods in the calculation of vertical excitation energies and oscillator strengths

We present two new modifications of the second-order polarization propagator approximation (SOPPA), SOPPA(SCS-MP2) and SOPPA(SOS-MP2), which employ either spin-component-scaled or scaled opposite-spin MP2 correlation coefficients instead of the regular MP2 coefficients. The performance of these two methods, the original SOPPA method as well as SOPPA(CCSD) and RPA(D) in the calculation of vertical electronic excitation energies and oscillator strengths is investigated for a large benchmark set of 28 medium-sized molecules with 139 singlet and 71 triplet excited states. The results are compared with the corresponding CC3 and CASPT2 results from the literature for both the TZVP set and the larger and more diffuse aug-cc-pVTZ basis set. In addition, the results with the aug-cc-pVTZ basis set are compared with the theoretical best estimates for this benchmark set. We find that the original SOPPA method gives overall the smallest mean deviations from the reference values and the most consistent results.     

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.     

Second-order perturbation correction to the Bogoliubov excitation spectrum

Two substantially different perturbation methods are used to obtain two equivalent exact results for the leading correction to the Bogoliubov formula for the energy spectrum of an elementary excitation in a boson fluid.     

On the use of the finite difference method in a calculation of vibration-rotation energies

The use of the finite difference method to obtain a Taylor series expansion of a potential energy function for a subsequent calculation of the rovibration energies of molecules is considered. A method is proposed that allows the stability of a finite-difference scheme to be increased against the computational inaccuracy upon numerical expansion of a multidimensional potential energy function into a high-order Taylor series. The method is based on the successive elimination of calculated expansion coefficients of a higher order in calculating the lower-order coefficients by the finite difference method. The approach is illustrated for the example of the CO and H₂S molecules.     

经式8-羟基喹啉铝的光谱与激发性质密度泛函

经式8-羟基喹啉铝(mer-Alq3)是一种光电性能优良的小分子有机半导体发光材料.本文采用密度泛函理论(DFT)B3LYP/6-31G*方法和基组对其进行结构优化,计算并研究了该分子的红外光谱、拉曼光谱和前线轨道.计算得到的红外光谱、拉曼光谱均与实验相符.前线轨道表明基态最高占据轨道(HOMO)的电子云主要集中在苯酚环,最低未占据轨道(LUMO)的电子云主要集中在吡啶环.用含时密度泛函理论(TDDFT)计算得到紫外-可见吸收光谱,采用空穴-电子分析法研究了电子激发特征.结果表明:电子从基态到激发态的跃迁,主要是8-羟基喹啉环内或环间的电荷转移,以π-π*跃迁为主,包括局域激发和电荷转移激发两种类型.本工作对mer-Alq3分子发光机理提出更深入的认识,能为进一步提高该分子发光效率和调控分子的发光范围提供一定的理论指导.     

Shell effects in a paired nucleus for finite excitation energies

Shell effects are considered as functions of the excitation energy of the nucleus. The effects of pairing are included and studied in the BCS approximation. Some numerical results, based on the single-particle spectrum of a Woods-Saxon potential, are given. In the limit of zero excitation the shell correction to the energy is compared with the results obtained by the Strutinsky method.     

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas--Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.     

7LiH分子基态及若干激发态的平衡几何及垂直激发能的从头算

使用“对称性匹配簇-组态相互作用方法”(SAC/SAC-CI),在多种基组下计算了7LiH分子X1Σ 、A1Σ 、B1Π及b3Π态的平衡几何,并将由“几何优化”得到的相应各态的平衡几何与“单点能扫描”得到的结果进行了比较。比较的结果表明,由“几何优化”得到的相应各态的平衡几何,与“单点能扫描”得到的结果存在着差异。分析的结果表明,在完全活性空间中,由“SAC/SAC-CI”方法进行“单点能扫描”得到的结果,比“几何优化”得到的结果更加合理。首次报告了使用6-311G(3df,3pd)基组进行“单点等扫描”得到的相应各态的平衡几何。其值分别是:基态(X1Σ )为0.1588 nm、单重态的第一激发态(A1Σ )为0.2487 nm、单重态的第二激发态(B1Π)为0.2434 nm、三重态的第二激发态(b3Π)为0.1958 nm。这一计算结果与实验值非常接近。还研究了从基态到上述相应各态的垂直激发能,在基态的平衡位置处,其值分别为(A1Σ ←X1Σ )3.613 eV(、B1Π←X1Σ )4.612 eV和(b3Π←X1Σ )4.233 eV。与其它理论计算结果进行比较后得出,本文的计算结果非常接近于使用很复杂的计算方法获得的结果。     

非Born-Oppenheimer近似一对双原子分子振动光谱的修正

为提高Born-Oppenheimer(BO)近似的精确度,修正BO近似所得到的令人不太满意的结果,此文在电子与原子核之间引入一个位相差,并利用小参数微扰法推导出了双原子分子核振动的波函数及红外能谱的计算公式,由修正后的结果得到的双原子分子红外振动光谱线的位置应更接近于实验观测值.     

Excitation spectrum of TTF-TCNQ: a finite temperature calculation

In this paper we study the excitation spectrum of the organic conductor tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) using finite temperature calculations. The effect of electronelectron interaction is considered within the random phase approximation (RPA). Our results show the temperature dependent plasmon and dipolar mode corresponding qualitatively to the modes obtained previously using zero temperature formalism assigned to the observed excitations at 10 meV and 0.75 eV. These modes have an essential influence on the energy-loss function. The obtained results are in good qualitative agreement with the optical and EELS data of TTF-TCNQ.     

The excitation spectrum of the one-dimensionalXY-model in a magnetic field

The exact excitation spectrum of theXY-model with a magnetic field inz-direction is considered in detail. If the exchange is exceeding the influence of the magnetic field, single fermion excitations are forbidden and at least two fermions have to be excited. The excitation spectrum is then continuous.     

One particle excitation spectrum of the Kondo-lattice

The renormalized time ordered perturbation approach for the (impurity -) Anderson model with respect to hybridization is combined with a random walk treatment of coherent scattering in order to calculate the one particle excitation spectrum of an Anderson lattice in the Kondo regime. It is found that the Kondo resonance at the Fermi-level splits into two narrow peaks. With decreasing temperature a gap develops in between these peaks due to coherence effects. These results furnish a more rigorous basis for phenomenological theories explaining experimental data in Kondo lattice systems like CeCu₂Si₂.