MRCI study on spectroscopic and molecular properties of several low-lying electronic states of the CN radical

The potential energy curves (PECs) of eight low-lying electronic states (X²Σ⁺, A²Π, B²Σ⁺, a⁴Σ⁺, D²Π, E²Σ⁺, 1²Σ⁻ and F²Δ) of the CN radical have been studied using the ab initio quantum chemical method. The calculations have been performed using the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation-consistent basis sets of Dunning and co-workers. The effects on the PECs by the core-valence correlation and relativistic corrections are taken into account. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction calculations are performed with the cc-pCVQZ basis set. The relativistic correction is carried out at the level of cc-pV5Z basis set. In order to obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The PECs are extrapolated to the complete basis set (CBS) limit by the total-energy extrapolation scheme. With these PECs, the spectroscopic parameters (T_e, R_e, ω_e, ω_ex_e, ω_eу_e, B_e, α_e and γ_e) are determined and compared with those reported in the literature. Finally, with the PECs obtained by the MRCI+Q/CV+DK+Q5 calculations, the complete vibrational states are computed for the eight electronic states by solving the ro-vibrational Schrödinger equation for the non-rotating radical, and the vibrational levels and inertial rotation and centrifugal distortion constants of the first 11 vibrational states are reported, which agree favorably with the available experimental data. The spectroscopic parameters of 1²Σ⁻ and F²Δ electronic states obtained by the MRCI+Q/CV+DK+Q5 calculations should be good predictions for future laboratory experiments.     

Effects on spectroscopic parameters of several low-lying electronic states of GeS by core-valence correlation and relativistic corrections

The potential energy curves (PECs) of six low-lying electronic states (X¹Σ⁺, a³Σ⁺, b³Π, A¹Π, 1³Σ⁻ and 1⁵Σ⁺) of GeS molecule have been investigated employing the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach with large correlation-consistent basis sets for internuclear separations from 0.08 to 2.00 nm. The effects on the spectroscopic parameters by the core-valence correlation, relativistic and nonadiabatic corrections have been discussed in detail. The core-valence correlation correction is carried out at the aug-cc-pCVTZ basis set. The nonadiabatic correction is performed at the aug-cc-pVTZ basis set. And the relativistic correction is made at the level of cc-pV5Z basis set. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian (DKH2) approximation. To obtain more reliable PECs, the Davidson modification is also included in the present study. To reduce the incomplete basis set error, the PECs of these electronic states are extrapolated to the complete basis set (CBS) limit. With these PECs, the spectroscopic parameters of these low-lying electronic states are determined. On the one hand, analyses demonstrate that the effects on the spectroscopic parameters by the core-valence correlation correction, relativistic correction and Davidson modification are very obvious, whereas the effect on the spectroscopic parameters by the nonadiabatic correction is very small. On the other hand, comparison with the RKR data shows that the two-point total-energy extrapolation could improve the quality of spectroscopic parameters. On the whole, as expected, the most accurate spectroscopic parameters of GeS molecule are determined by the MRCI+Q/CV+DK+Q5 calculations.     

Effects on spectroscopic properties for several low-lying electronic states of CS molecule by core-valence correlation and relativistic corrections

The potential energy curves (PECs) of six low-lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ⁻ and A¹Π) of CS molecule have been investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach with large correlation-consistent basis sets. Effects on the PECs by the core-valence correlation and relativistic corrections have been taken into account. And the two corrections are performed at the level of cc-pV5Z basis set. The way to consider the relativistic corrections is to use the second-order Douglas-Kroll Hamiltonian approximation. Using the CCSD(T), MRCI and MRCI with the Davidson modification (MRCI + Q), the PECs of electronic states involved are extrapolated to the complete basis set (CBS) limit. With the PECs, the spectroscopic parameters (T_e, R_e, ω_e, ω_ex_e, ω_ey_e, α_e, β_e, γ_e and B_e) of the six low-lying electronic states are determined. These parameters are in excellent agreement with the experimental data. The complete vibrational states are computed for the six low-lying electronic states when the rotational quantum number J equals zero, and the inertial rotation constants of the first 23 vibrational states are reported, which agree favorably with the RKR data. Comparison with the measurements shows that the two-point total-energy extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.     

MRCI study on spectroscopic and molecular properties of four low-lying electronic states of the BO radical

The potential energy curves (PECs) of four low-lying electronic states of the BO radical, including two ²Σ⁺ and two ²Π states, have been studied using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the cc-pV5Z basis set for internuclear separations from 0.05 to 2.0 nm. The effect on the PECs by the relativistic correction has been taken into account. With these PECs, the spectroscopic parameters (T_e, D₀, D_e, R_e, ω_e, ω_ex_e, α_e and B_e) of two main isotopologues (¹¹B¹⁶O and ¹⁰B¹⁶O) have been determined. These parameters have been compared in detail with those of previous investigations reported in the literature, and excellent agreement has been found between the available data and the present results. By solving the radial Schrödinger equation of nuclear motion, 60 vibrational states for the ¹¹B¹⁶O(X²Σ⁺), 60 for the ¹⁰B¹⁶O(X²Σ⁺), 66 for the ¹¹B¹⁶O(A²Π) and 64 for the ¹⁰B¹⁶O(A²Π) are predicted for the non-rotating molecule. For each vibrational state of the ¹¹B¹⁶O(X²Σ⁺), ¹⁰B¹⁶O(X²Σ⁺), ¹¹B¹⁶O(A²Π) and ¹⁰B¹⁶O(A²Π), the vibrational level G(υ), inertial rotation constant B_υ and centrifugal distortion constant D_υ have been determined. Comparison with the available data shows that the present molecular constants are reliable and accurate. The ro-vibrational levels have been calculated for the X²Σ⁺ and A²Π states of two main species for future laboratory research.     

Multireference configuration interaction study on spectroscopic properties of low-lying electronic states of As2 molecule

The potential energy curves (PECs) of four electronic states (X1Σ+g , e3△u , a 3 Σ-u , and d 3Πg ) of an As 2 molecule are investigated employing the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV5Z basis set. The effect on PECs by the relativistic correction is taken into account. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian approximation. The correction is made at the level of a cc-pV5Z basis set. The PECs of the electronic states involved are extrapolated to the complete basis set limit. With the PECs, the spectroscopic parameters (Te , Re , ωe , ωexe , ωeye , αe , βe , γe , and Be ) of these electronic states are determined and compared in detail with those reported in the literature. Excellent agreement is found between the present results and the experimental data. The first 40 vibrational states are studied for each electronic state when the rotational quantum number J equals zero. In addition, the vibrational levels, inertial rotation and centrifugal distortion constants of d 3Πg electronic state are reported which are in excellent agreement with the available measurements. Comparison with the experimental data shows that the present results are both reliable and accurate.     

75As32S+和75As34S+离子的光谱常数与分子常数

采用内收缩多参考组态相互作用(MRCI)方法, 结合Dunning系列相关一致基, 分别对⁷⁵As³²S⁺和⁷⁵As³⁴S⁺离子的X³Σ^-和A¹Π电子态的势能曲线进行了计算, 进一步拟合势能曲线, 得到各电子态的光谱常数与分子常数. 首先, 采用MRCI方法结合相关一致基, aug-cc-pV5Z, 对AsS⁺离子的X³Σ^-和A¹Π 电子态进行了计算, 获得相应的势能曲线; 然后, 为进一步提高势能曲线的精度, 对其进行了三种修正计算. 采用Davidson(+Q)方法修正MRCI 方法计算过程中存在的基组大小不一致缺陷; 利用二阶Douglas-Kroll哈密顿近似, 在cc-pVQZ基组水平, 修正了相对论效应对势能曲线的影响; 利用两点能量外推法, 在aug-cc-pVQZ和aug-cc-pV5Z基组水平对各能量点的势能值进行了外推, 得到完全基组极限处的势能曲线. 最后, 利用修正(包括Davidson修正、相对论修正和基组外推)后的势能曲线, 通过Vibrot程序, 求解双原子分子核运动的径向Schrödinger方程, 并进行同位素质量识别, 得到⁷⁵As³²S⁺和⁷⁵As³⁴S⁺离子两个电子态的光谱常数(T_e, R_e, ω_e, ω_ex_e, α_e 和B_e)和分子常数(G(ϒ), B_v, D_v).     

SiN自由基X2∑+, A2Π和B2∑+ 电子态的光谱常数研究

采用内收缩多参考组态相互作用(MRCI)方法, 结合价态范围内的最大相关一致基aug-cc-pV6Z, 计算了SiN自由基X²∑⁺, A²Π 和B²∑⁺电子态的势能曲线. 采用Davidson修正来避免由于MRCI方法本身的大小一致性缺陷产生的误差. 为了提高计算精度, 进一步考虑了相对论修正和核价相关修正对势能曲线的影响. 本文的相对论修正是利用二阶Douglas-Kroll 哈密顿近似在cc-pV5Z基组水平进行的; 同时核价相关修正是在cc-pCV5Z基组水平进行的. 对这些势能曲线进行拟合, 得到各种水平下三个电子态的光谱常数(T_e, R_e, ω_e, ω_ex_e, α_e和B_e), 并详细分析了Davidson修正、相对论修正和核价相关修正对光谱常数的影响. 与其他理论结果和实验数据进行比较, 可知本文的结果更精确、更完整.     

SF分子基态及低激发态势能函数与光谱常数的研究

采用含Davidson修正的内收缩多参考组态相互作用的方法和考虑相对论修正, 在价态范围内的最大相关一致基 aug-cc-pV6Z 的条件下, 对SF分子的基态²∏及几个低激发态⁴∑^-, ²∑^-, ²Δ进行了势能扫描计算. 对SF分子的势能曲线进行拟合, 得到了该分子的光谱常数R_e, ω_e, ω_eχ_e, D₀, D_e, B_e和 α_e, 通过比较发现它们与已有的实验结果较为一致. 利用SF分子的势能曲线, 通过求解双原子分子核运动的径向Schrödinger方程得到J=0 时SF分子所计算各电子态的多个振动态. 对于每一振动态, 分别计算了振动能级、惯性转动常数和离心畸变常数. 关键词： SF 势能曲线 光谱常数 分子常数     

MRCI方法计算CP和CP~-低能电子态的光谱常数

采用内收缩多参考组态相互作用(MRCI)方法结合相关一致基aug-cc-p V5Z计算了CP分子X~2Σ~+,A~2Π和B~2Σ~+和CP~-离子X~1Σ~+电子态的势能曲线.考虑了Davidson、相对论和核价相关修正对势能曲线的影响.本文的相对论修正是利用二阶Douglas-Kroll哈密顿近似在cc-p V5Z基组水平进行的;同时核价相关修正也是在cc-p V5Z基组水平进行的.为了提高计算精度,利用基组外推将能量外推至完全基组极限处,得到外推的势能曲线.对这些势能曲线进行拟合,得到各种水平下四个电子态的光谱常数(T_e,R_e,ω_e,ω_ex_e,α_e和B_e),并详细分析了Davidson修正、相对论修正和核价相关修正及基组外推对光谱常数的影响.与其它理论结果和实验数据进行比较,可知本文的结果更精确、更完整.     

MRCI方法计算CP和CP-低能电子态的光谱常数

采用内收缩多参考组态相互作用（MRCI）方法结合相关一致基aug-cc-pV5Z计算了CP分子X2Σ+,A2Π和B2Σ+和CP-离子X1Σ+电子态的势能曲线．考虑了Davidson、相对论和核价相关修正对势能曲线的影响．本文的相对论修正是利用二阶Douglas-Kroll 哈密顿近似在cc-pV5Z基组水平进行的;同时核价相关修正也是在cc-pV5Z基组水平进行的．为了提高计算精度,将能量外推至完全基组极限处,得到外推的势能曲线．对这些势能曲线进行拟合,得到各种水平下四个电子态的光谱常数(Te,Re,ωe,ωexe,αe和Be),并详细分析了Davidson修正、相对论修正和核价相关修正及基组外推对光谱常数的影响．与其它理论结果和实验数据进行比较,可知本文的结果更精确、更完整．     

CN~+离子电子结构和跃迁性质的理论研究

采用多组态参考相互作用方法和AV5Z-DK基组对CN~+离子的两个解离极限C~+(~2P_u)+N(~2D_u)和C~+(~2P_u)+N(~4S_u)下的X~1Σ~+、a~3Π、~1Δ和A~1四个电子态的势能曲线、永久偶极矩和振动能级进行了计算.为保证计算结果的精确性,在计算中考虑了Davidson修正.基于求得的势能曲线,数值求解一维径向薛定谔方程得到了各个电子态的光谱数据,并与实验值和已有的理论值吻合较好.除此之外,对A~1Π→X~1Σ~+和1~1Δ?A1~Π的跃迁性质进行了研究,同时通过跃迁的弗兰克-康登因子及辐射寿命,对CN~+离子激光冷却的可行性进行了分析.     

分子部分电子态的高阶振动能级和离解能的精确研究

鉴于K₂分子电子态的振动能谱和分子离解能D_e在实际研究和应用中的重要性,应用Sun,Ren等人提出的基于微扰理论的代数方法(AM)和基于AM的代数能量方法(AEM)研究了K₂分子的X¹Σ⁺_g,a³Σ⁺_u,0^-_g,B¹Π_{u< 关键词： 2}分子')" href="#">K₂分子 代数方法 高阶振动能级 离解能     

Na2分子部分电子态的完全振动能谱和离解能的精确研究

对于大多数双原子分子的电子态，用现代实验方法或精确的量子理论方法往往可以获得含m个振动能级的能谱子集合［Ev］，而不易得到包含最高振动能级在内的所有高振动量子态能级的完全振动能谱{Ev}.鉴于Na2分子电子态的振动能谱和分子离解能De在实际研究和应用中的重要性，使用基于微扰理论的代数方法（AM），获得了Na2分子一些电子态的振动光谱常数和完全振动能谱；使用基于AM的代数能量方法（AEM）获得了这些电子态的正确离解能.研究结果表明：AM方法能从少数精确的实验能级获得精确的分子振动光谱常数集合和正确的完全振动能谱{Ev}，AEM方法获得的分子离解能比由文献发表的振动光谱常数计算得到的近似离解能值更准确，对于难以获得分子离解能的那些电子激发态，AEM方法能给出合理的离解能数据. 关键词： Na2分子 代数方法 振动能级 离解能 电子激发态     

Electronic states and spectroscopic properties of GeSi

Electronic structure and spectroscopy of the GeSi molecule have been investigated by performing ab initio based multireference configuration interaction calculations. Potential energy curves of 29 Λ-S states of singlet, triplet, and quintet spin multiplicities have been constructed. Spectroscopic constants of 24 bound states within 36 000 cm⁻¹ are reported and compared with the available data. The calculated dissociation energy of GeSi in the ground state is 2.80 eV. Effects of the spin-orbit coupling on the spectroscopic properties of the molecule have been found to be small. However, the computed zero-field-splitting of the ground state compares well with the earlier prediction. Transitions such as 2³Σ⁻-X³Σ⁻, 3³Σ⁻-X³Σ⁻, 4³Π-A³Π, 5³Π-A³Π etc. are relatively strong. Radiative lifetimes for several dipole allowed and spin-forbidden transitions are calculated. The estimated lifetimes of the 2³Σ⁻, 3³Σ⁻, and 5³Π states are about 109, 33, and 62 ns, respectively. Dipole moments of most of the low-lying states of GeSi are also reported.     

The rotational spectrum of BiO radical in its X1Π1/2 and X2Π3/2 states

Rotational spectra have been observed for BiO produced in a DC discharge through a low pressure mixture of O₂, Ar, and Bi vapor. Because of the highly non-thermal distribution of states, it has been possible to observe spectra arising from the X₁²Π_1/2 level up to v = 9 and for the X₂²Π_3/2 level up to v = 5 near 10 538 cm⁻¹. Precise rotational and hyperfine parameters have been determined for the observed states. By using available near infrared (NIR) data in a merged fit, the 0-0 and 1-1 fine structure intervals have been more precisely determined. Although the quality of the fit is very good, the interpretation of the hyperfine constants is complicated by relativistic effects and the interaction of the X₂ state with A₁⁴Π_3/2 state. The magnetic and quadrupole coupling constants will be compared with those of the Bi atom and related molecules.     

On the high resolution spectroscopy and intramolecular potential function of SO2

Two weak stretching bands, ν₁ + 3ν₃ and 3ν₁ + ν₃, of the sulfur dioxide molecule have been recorded at high resolution and analyzed for the first time with using a Fourier transform Bruker IFS-120 HR interferometer. About 1000 transitions with J^max. = 51, , and 900 transitions with J^max. = 53, have been assigned to the bands ν₁ + 3ν₃ and 3ν₁ + ν₃, respectively. Analysis of the recorded spectra was made using the model of isolated vibrational states. Parameters obtained from the fit reproduce the initial experimental ro-vibrational energies with the rms deviation of 0.0006 and 0.0012 cm⁻¹ for the bands, 3ν₁ + ν₃ and ν₁ + 3ν₃, respectively. The problem of determination of the intramolecular potential function of SO₂ is discussed.     

The optical properties of Dy-doped NaY(MoO4)2 crystal

The Dy³⁺-doped NaY(MoO₄)₂ single crystals were grown successfully by the Czochralski technique. The main spectroscopic properties (absorption, luminescence, decay curve) of Dy³⁺-doped NaY(MoO₄)₂ have been determined for both the σ and π polarizations. By using the Judd-Ofelt theory, the measured room temperature absorption spectra were applied to determine the intensity parameters, spontaneous transition probabilities, branching ratios, and radiative lifetimes of Dy³⁺ transitions. The results show that the Dy³⁺-doped NaY(MoO₄)₂ crystal may realize the yellow laser operation.     

Phase stability and electronic structure of Si2Sb2Te5 phase-change material

On the basis of an ab initio computational study, the present work provide a full understanding on the atomic arrangements, phase stability as well as electronic structure of Si₂Sb₂Te₅, a newly synthesized phase-change material. The results show that Si₂Sb₂Te₅ tends to decompose into Si₁Sb₂Te₄ or Si₁Sb₄Te₇ or Sb₂Te₃, therefore, a nano-composite containing Si₁Sb₂Te₄, Si₁Sb₄Te₇ and Sb₂Te₃ may be self-generated from Si₂Sb₂Te₅. Hence Si₂Sb₂Te₅ based nano-composite is the real structure when Si₂Sb₂Te₅ is used in electronic memory applications. The present results agree well with the recent experimental work.     

Si2O2 molecule: structure of ground state and the excited properties under different external electric fields

Geometry and vibrational frequencies of the ground state of Si 2 O 2 molecule are studied using density function theory (DFT) at the level of cc-pvtz and 6-311++G.It is found that the optimizing value by B3lyp/cc-pvtz is closer to the experimental data.The excited properties under different external electric fields are also investigated by the time-dependent-DFT method.Transitions from the ground state of Si 2 O 2 molecule to the first singlet state under different external electric fields can take place more easily.The corresponding absorption spectral line is about 360 nm in wavelength and the excitation energy is about 3.4 eV.     

Spectroscopic studies of interfacial structures of CeO2-TiO2 mixed oxides

We have investigated the geometric and electronic structures of the cerium oxide (CeO₂)-titanium dioxide (TiO₂) mixed oxides with various Ce/TiO₂ weight ratios prepared by the sol-gel method in detail by means of X-ray diffraction (XRD), high-resolution X-ray photoelectron spectroscopy (XPS), Raman spectroscopy excited by 325 and 514.5 nm lasers, and scanning electron microscope (SEM). Existence of cerium effectively inhibits the phase transition of TiO₂ from the anatase phase to the rutile phase. XRD peaks of TiO₂ anatase attenuate continuously with the increasing amount of CeO₂ in the mixed oxide, but the XRD peaks of cubic CeO₂ appear only after the weight ratio of Ce/TiO₂ reaches 0.50. The average crystalline sizes of TiO₂ anatase and cubic CeO₂ in CeO₂-TiO₂ mixed oxides are smaller than those in the corresponding individual TiO₂ anatase and cubic CeO₂. Raman spectroscopy excited by the 514.5 nm laser detects CeO₂ after the weight ratio of Ce/TiO₂ reaches 0.70 whereas Raman spectroscopy excited by the 325 nm laser detects CeO₂ after the weight ratio of Ce/TiO₂ reaches 0.90. XPS results demonstrate that Ti exists in the form of Ti⁴⁺ in the CeO₂-TiO₂ mixed oxide. Ce is completely in the form of Ce³⁺ in the mixed oxides with a 0.05 weight ratio of Ce/TiO₂. With the increasing weight ratio of Ce/TiO₂, Ce⁴⁺ dominates. On basis of these results, we proposed that CeO₂ initially nucleates at the defects (oxygen vacancies) within TiO₂ anatase, forming an interface bridged with oxygen between CeO₂ and TiO₂ anatase. At the interface, Ce species cannot substitute Ti⁴⁺ in the lattice of TiO₂ anatase whereas Ti⁴⁺ can substitute Ce⁴⁺ in the lattice of cubic CeO₂. The decreasing concentration of oxygen vacancies, the Ti-O-Ce interface, and the decreasing average crystalline size of TiO₂ anatase act to inhibit the phase transformation of TiO₂ anatase. With the increasing amounts of CeO₂, the CeO₂ clusters continuously grow and form cubic CeO₂ nanocrystals. Spectroscopic results strongly demonstrate that the surface region of CeO₂-TiO₂ mixed oxide is enriched with TiO₂.