MRCI方法下BO分子X2Σ+与2Π态的势能曲线与解析势能函数研究

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本文主要探讨了多参考配置交互（MRCI）方法和邓宁的关联一致基集在BO分子X2Σ+和2Π状态的势能曲线（PECs）计算中的应用。MRCI是一种高级量子化学计算技术，它结合了单参考方法的优点并考虑了多个参考态的影响，特别适用于处理包含强烈电子相关性的系统，如BO分子的双自旋多重性态。研究者利用MRCI方法获取了BO分子的Σ+和Π对称态下的PECs，这些状态涉及双电子的精细结构，因此对于理解分子的振动、旋转以及光谱特性至关重要。通过使用Dunning的关联一致基集，能够获得高精度的势能数据，这些基集在描述分子的电子结构时表现出良好的收敛性和准确性。进一步，文中介绍了解析势能函数（Analytical Potential Energy Functions, APEFs）的构建过程。作者采用了Murrell-Sorbie（MS）函数和最小二乘法来拟合这些数据，这是一种常用的数据拟合方法，能够提供一种简单而直观的方式来描述复杂的势能行为。通过对PECs的分析，研究人员得以确定这两个状态的光谱常数，这些常数包括振动能级间隔、转动惯量等关键参数，它们与理论预测和实验测量结果进行了比较，验证了MRCI方法和基础设置的计算精度和可靠性。根均方误差（Root Mean Square Error, RMS）被用来评估拟合结果与基础理论计算之间的偏差，这是一项重要的指标，因为它反映了模型的准确度。低RMS值通常表明模型的性能良好，能够精确地再现实验数据。这篇论文不仅提供了BO分子X2Σ+和2Π状态的详细势能曲线，而且还展示了如何通过MRCI方法和数据分析得到可靠的解析势能模型，这对于理解和预测这类分子系统的动态行为以及设计相关的实验和理论研究具有重要意义。

August 10, 2009 / Vol. 7, No. 8 / CHINESE OPTICS LETTERS 663

MRCI potential energy curves and analytical potential

energy functions for the X

and

Π states of BO molecule

Xinqiang Wang (

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), Chuanlu Yang (

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, Tao Su (

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Fengjuan Bai (

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Department of Physics and Electronic Engineering, Ludong University, Yantai 264025, China

∗

E-mail: yangchuanlu@263.net

Received December 1, 2008

The potential energy curves (PECs) of BO molecule, including Σ

and Π symmetries with doublet spin

multiplicities, are obtained employing multi-reference conﬁguration interaction (MRCI) method and Dun-

ning’s correlation consistent basis sets. The analytical potential energy functions (APEFs) are ﬁtted using

the Murrell-Sorbie (MS) function and the least square method. Based on the PECs, the spectroscopic

constants of the states have been determined and compared with the theoretical and experimental results

available to aﬃrm the accuracy and liability of the calculations. The root-mean-square (RMS) errors be-

tween the ﬁtted results and the ab initio values are too little in comparison with the chemical accuracy

(349.755 cm

−1

). It is shown that the present APEFs are accurate and can display the interaction between

the atoms well. The present APEFs can be used to construct more complicated APEF or do some dynamic

investigations.

OCIS codes: 020.0020, 300.6390.

doi: 10.3788/COL20090708.0663.

Boron clusters and boron-rich materials are very im-

portant species and have been widely used in industry

and technology, including thermally and chemically sta-

ble insulators and high modulus boron-ﬁber composites.

Currently, the studies of this system are very active in

both experiment and theory. Langhoﬀ et al.

[1]

reported

the spectroscopic par ameters of B

molecule with multi-

reference conﬁguration interaction (MRCI) method

[2,3]

Yang et al. have performed investigations for the po-

tential energy curves (PECs) and spectroscopic proper-

ties of B

ion at the quadratic single and double exc ita-

tion conﬁguration interaction (QCISD) level, and ﬁtted

the analytical potential energy functions (APEFs) with

least square method

[4]

. They also studied the geometri-

cal and electronic properties of B

+[5]

and B

+[6]

clusters.

Very r e c e ntly, the ground and low-lying excited states of

have been studied by Zhang et al. employing MRCI

method

[7]

. The spectroscopic properties and APEFs o f

four metastable sta tes have been reported in their work.

The determination of accurate data fo r bond disso-

ciation energies as well as spectroscopic properties is

very important for the interpretation of many spectro-

scopic and chemical phenomena. The tasks considering

the chemical bonding in elemental boron alloy clusters

on this system have also been completed over the past

few ye ars

[8−9]

. Niu et al. studied some ions of boron

and boron-rich clusters with the Becke 3-parameter

(exchange), Lee, Yang, and Parr (correlation; density

functional theory) (B3LYP) method and Moller-Plesset

(MP

) method with the basis sets (10s, 5p, 1d/3s, 2p,

1d). In 2004, ab initio methods with 6-311G* and cc-

pVTZ basis sets have been used to c alculate the equilib-

rium geometries and vibrational properties of nine elec-

tronical states of MgB

molecule by Yang et al.

[11]

. They

distinguished the ground state from the

and

states successfully and gave a preferred dissociation chan-

nel in their work.

Boron monoxide is the simplest boron oxide and has

attracted persistent interest over the past four decades,

primarily due to their roles in the combustion of boron

and bo ranes. In 1981, Nemukhin et al.

[12]

calculated

the ground state and some low-lying excited electroni-

cal states (

2,4

Σ,

2,4

Π, and

2,4

∆) of BO molecule by using

the complete active space self-consistent-ﬁeld (CASSCF)

method in conjunction with the basis s e ts of contracted

Gaussian-type orbitals (CGTOs). PECs and some spec-

troscopic constants of these states were reported in their

work. However, limited by the c alculation level, the

sp e ctroscopic parameters deviated from the expe rimen-

tal data signiﬁcantly. Taking the ground state as an ex-

ample, the percentage error of the dissociation energy

was larger than 4.5 % and the diﬀerence for the har -

monic frequency ω

was 23 cm

−1

compared with the

exp erimental value. In 2001, the theoretical study of

the ground state of BO molecule was implemented by

Papakondylis et al. using coupled cluster calculations

(CCSD(T)) method in conjunction with a series of ba-

sis sets

[13]

. As we all know, the APEFs are an eﬀective

way to research the spectrosc opic properties of diatomic

molecules

[14,15]

. However, bo th Nemukhin et al.

[12]

and

Papakondylis et al.

[13]

only paid attention to the spec-

troscopic constants, and the APEFs of the excited states

were not considered in their studies.

In this letter, valence internally contracted MRCI in-

cluding those conﬁguration state functions (CSFs) that

contribute mo st sig niﬁcantly to the correla tio n energy, is

employed in our calculation to obtain PECs of the ground

state X

and one excited state

Π. The MRCI calcula-

tions are prece ded by the CASSCF calculations, in which

all valence molecular orbitals are optimized and it is

1671-7694/2009/080663-04

 2009 Chinese Optics Letters

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