多参考CI方法研究KH激发态B1Π态的势能函数与光谱参数

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本文主要探讨了钾氢（KH）分子B1Π激发态的分析势能函数及其光谱参数的计算方法。研究者采用多参考配置交互(Multi-reference Configuration Interaction, MRCI)技术来生成钾氢分子B1Π状态的势能曲线(PECs)，这种方法旨在精细捕捉核心-价电子间的关联效应。为了考虑到不同类型的电子关联和不同的作用空间，研究团队设计了五种策略，分别考虑了不同组合的关联电子以及不同的活性轨道空间。 MRCI是一种强大的量子化学计算方法，它结合了单参考近似中的自旋-轨道相互作用和多参考波函数的精确性，能够处理复杂的电子结构问题。通过这种方法得到的势能曲线被进一步拟合为解析势能函数(Associative Potential Energy Functions, APEFs)，这些函数在理论化学中常用于精确描述分子的能量行为和振动特性。在对B1Π状态进行分析后，作者获得了包括转动-振动能级以及跃迁频率在内的光谱参数。这些参数对于理解分子的结构、动力学以及与实验数据的对比至关重要。实验数据和先前的理论预测为比较提供了基准，通过这样的对比，研究者能够评估他们的计算结果的准确性和可靠性。本文还涉及到分子性质的讨论，如振动频率、红外和紫外吸收线的强度，以及可能的非辐射跃迁。通过这些参数，科学家可以深入理解钾氢分子在特定能量下的动态行为，这对于化学反应机理的研究、分子光谱学以及潜在的应用如量子信息处理等领域都有重要意义。该研究不仅展示了多参考配置交互在处理复杂分子系统中的有效性，而且还提供了关于钾氢B1Π状态精确势能函数和光谱参数的关键信息，为未来对该系统以及其他类似分子的研究奠定了基础。

COL 9(12), 120201(2011) CHINESE OPTICS LETTERS December 10, 2011

Analytical potential energy function and spectroscopy

parameters for B

Π state of KH

Jingjuan Liang (ùùùµµµïïï)

, Chuanlu Yang (DDD´´´)

2∗

, Lizhi Wang (ááá)

1,2

, and Qinggang Zhang ( ÜÜÜfff)

College of Physics and Electronics, Shandong Normal University, Jinan 250014, China

Scho ol of Physics, Ludong University, Yantai 264025, China

∗

Corresp onding author: yangchuanlu@263.net

Received June 17, 2011; accepted August 8, 2011; posted online October 18, 2011

Multi-reference configuration interaction is used to produce potential energy curves (PECs) for the excited

Π state of KH molecule. To investigate the correlation effect of core-valence electrons, five schemes are

employed which include the different correlated electrons and different active spaces. The PECs are fitted

into analytical potential energy functions (APEFs). The spectroscopic parameters, ro-vibrational levels,

and transition frequencies are determined based on the APEFs and compared with available experimental

and theoretical data. The molecular properties for B

Π obtained in this letter, which are better than

those available in literature, can be reproduced with calculations using the suitable correlated electrons

and active space of orbitals.

OCIS codes: 020.2070, 300.6390.

doi: 10.3788/COL201109.120201.

Potassium hydrides have been studied extensively

through experimental measurements and theoretical

research. Yang et al.

[1]

showed isotopically combined

spectroscopic constants obtained by Rydeberg-Klein-Ree

(RKR) potential energy curves (PECs) up to ν

= 4 and

= 26 for the X

and A

states. Giroud et al.

calculated the X

RKR potential curve for KH to ν

[2]

. Hussein et al. extended the RKR potential curve

of the X

state to ν = 23

[3]

. Zemke et al. constructed

a potential energy curve for the ground state of KH

and determined that D

=14 772.7±0.6 cm

−1[4]

. Jeung et

al. proposed the perturbative treatment of core-valence

correlation effects. Results show that the valence cor-

relation slightly diminishes the core-valence correlation

which plays a very important role in the spectroscopy

of KH for the ground state

[5]

. To test the iterative

difference dedicated configuration interaction metho d,

Garc´ıa et al. calculated the three lowest Σ

potential

curves of KH at the level of CAS-MP2 and obtained

the spectroscopic parameters within 0.1 eV which differs

with the experimental values

[6]

. Lee et al. calculated the

and

states of KH which were dissociated into

the 4s-6p states of K at the level of the configuration

interactions and found that most of states show the un-

dulating potential curves

[7]

. Khelifi et al. performed ab

initio adiabatic and diabatic studies of the KH molecular

for all the states below the ionic limit [i.e., K(4s, 4p, 5s,

3d, 5p, 4d, 6s, and 4f)+H(1s)] in

and

symme-

tries at the level of full valence CI approaches

[8]

. They

presented the spectroscopic constants for the states and

obtained seven vibrational levels of B

Π.

In contrast to the intense interest in Σ

states, rela-

tively minimal attention has been accorded on B

Π state.

Recently, Lee et al. observed the B

Π excited state for

the first time

[9]

and obtained several ro-vibrational lev-

els and spectroscopic constants which could be used as a

reference standard for theoretical calculation. The theo-

retical results in literature clearly deviate from the new

experimental values. This implies that there is still space

to perform high-level calculations for the state. Thus,

in this letter, PECs for the B

Π state are calculated

using multi-reference configuration-interaction method

(MRCI)

[10,11]

and large basis set. The large active space

effect of core-valence correlation is emphasized. The

PECs are fitted to the analytical potential energy func-

tions (APEFs) for further analysis. The quality of the

APEFs is evaluated by comparing the vibrational levels

and the spectroscopic properties determined based on

them with the available experimental values.

The PECs of B

Π of KH are calculated with the inter-

nal contracted MRCI method. This is preceded by multi-

configuration self-consistent-field calculations

[12,13]

us-

ing C

symmetry. The basis sets ECP10MDF

[14]

for K,

which means that the electrons of 1s

are described

with pseudopotential, and the electrons of 3s

are

described with basis sets (11s11p5d3f). For H, aug-cc-

pVQZ basis set is used

[15]

To obtain high accurate interaction energy, three cor-

relation schemes are performed for K. The first scheme

includes the core electrons 3s

. The second includes

the core electrons 3p

, and the third includes only the va-

lence 4s

. Two different sets of active spaces (including

3d orbitals) are used. To show the calculation schemes

clearly, we have listed the options for the two sets in

Table 1. All calculations are performed using the MOL-

PRO 2009.1 program package

[16]

Each PEC includes 200 ab initio points with inter-

nuclear distances from 0.12 to 1.115 nm and a step of

0.005 nm. The PECs are subsequently fitted into the

APEFs in the form of Murrell-Sorbie (MS) potential

energy function

[17]

. The general MS function, formula-

tions of the ro ot mean square (RMS) error, and spec-

troscopic parameters, such as the equilibrium rotational

constant (B

), are the harmonic and anharmonic con-

stants (ω

and ω

) and the vibration-rotation coupling

constant (α

) that can be found in previous works

[18−26]

The vibrational levels are obtained by solving the radial

Schr¨odinger equation for the bound and quasibound lev-

els. The calculations are realized using the Le Roy’s level

1671-7694/2011/120201(4) 120201-1

° 2011 Chinese Optics Letters

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