{"title":"N $$ N $$ -耦合态双原子系统绝热和非绝热表示的精确振动等效","authors":"Ryan P. Brady, S. N. Yurchenko","doi":"10.1002/jcc.70181","DOIUrl":null,"url":null,"abstract":"<p>The Born–Oppenheimer approximation assumes nuclear motion evolves on single, uncoupled potential energy surfaces, widely used to solve the time-independent Schrödinger equation for atomistic systems. However, for near-degenerate same-symmetry electronic states, avoided crossings in the potential energy curves occur and non-adiabatic couplings (NACs) become significant. In such cases, the adiabatic approximation is unsuitable for high-resolution spectroscopy. A unitary transformation to the diabatic representation can eliminate NACs, resulting in smooth molecular property curves that may cross. Computing this adiabatic-to-diabatic transformation (AtDT) is desirable but non-analytic for multi-state coupled systems, necessitating numerical solutions. It remains unclear if current methods yield numerically exact AtDTs ensuring rovibronic energy level equivalence between adiabatic and diabatic pictures. We demonstrate (for the first time) numerically exact equivalence of adiabatic and diabatic representations for <span></span><math>\n <semantics>\n <mrow>\n <mi>N</mi>\n </mrow>\n <annotation>$$ N $$</annotation>\n </semantics></math>-state diatomic molecules using ab initio data for <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mi>N</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ {N}_2 $$</annotation>\n </semantics></math>, CH, and a model 10-state system. We show how the equivalence can be efficiently used to assess the importance of non-adiabatic effects and the impact of omitting them when computing rovibronic energies of diatomic molecules. 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However, for near-degenerate same-symmetry electronic states, avoided crossings in the potential energy curves occur and non-adiabatic couplings (NACs) become significant. In such cases, the adiabatic approximation is unsuitable for high-resolution spectroscopy. A unitary transformation to the diabatic representation can eliminate NACs, resulting in smooth molecular property curves that may cross. Computing this adiabatic-to-diabatic transformation (AtDT) is desirable but non-analytic for multi-state coupled systems, necessitating numerical solutions. It remains unclear if current methods yield numerically exact AtDTs ensuring rovibronic energy level equivalence between adiabatic and diabatic pictures. 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引用次数: 0
摘要
玻恩-奥本海默近似假设核运动在单个,不耦合的势能表面上演变,广泛用于解决原子系统的时间无关Schrödinger方程。然而,对于近简并的同对称电子态,势能曲线上出现了避免交叉,非绝热耦合(NACs)变得重要。在这种情况下,绝热近似不适用于高分辨率光谱学。对非绝热表示的幺正变换可以消除NACs,从而得到光滑的可能交叉的分子性质曲线。计算这种绝热到绝热的转换(AtDT)是可取的,但对于多态耦合系统是非解析的,需要数值解。目前尚不清楚目前的方法是否能产生精确的atdt,以确保绝热和绝热图像之间的振动能级等效。我们首次用从头算数据证明了N $$ N $$ -态双原子分子的绝热和非绝热表示在数值上的精确等价$$ {N}_2 $$, CH,以及一个10州系统模型。我们展示了等效性如何有效地用于评估非绝热效应的重要性,以及在计算双原子分子的振动能量时忽略它们的影响。光谱模型的绝热和非绝热表示,包括所有耦合项,已在双原子代码Duo中实现。
Exact Rovibronic Equivalence of the Adiabatic and Diabatic Representations of
N
$$ N $$
-Coupled State Diatomic Systems
The Born–Oppenheimer approximation assumes nuclear motion evolves on single, uncoupled potential energy surfaces, widely used to solve the time-independent Schrödinger equation for atomistic systems. However, for near-degenerate same-symmetry electronic states, avoided crossings in the potential energy curves occur and non-adiabatic couplings (NACs) become significant. In such cases, the adiabatic approximation is unsuitable for high-resolution spectroscopy. A unitary transformation to the diabatic representation can eliminate NACs, resulting in smooth molecular property curves that may cross. Computing this adiabatic-to-diabatic transformation (AtDT) is desirable but non-analytic for multi-state coupled systems, necessitating numerical solutions. It remains unclear if current methods yield numerically exact AtDTs ensuring rovibronic energy level equivalence between adiabatic and diabatic pictures. We demonstrate (for the first time) numerically exact equivalence of adiabatic and diabatic representations for -state diatomic molecules using ab initio data for , CH, and a model 10-state system. We show how the equivalence can be efficiently used to assess the importance of non-adiabatic effects and the impact of omitting them when computing rovibronic energies of diatomic molecules. The adiabatic and diabatic representations of the spectroscopic model, including all coupling terms, have been implemented in the diatomic code Duo.
期刊介绍:
This distinguished journal publishes articles concerned with all aspects of computational chemistry: analytical, biological, inorganic, organic, physical, and materials. The Journal of Computational Chemistry presents original research, contemporary developments in theory and methodology, and state-of-the-art applications. Computational areas that are featured in the journal include ab initio and semiempirical quantum mechanics, density functional theory, molecular mechanics, molecular dynamics, statistical mechanics, cheminformatics, biomolecular structure prediction, molecular design, and bioinformatics.