Langhoff P W, Boatz J A, Hinde R J, Sheehy J A
San Diego Supercomputer Center, University of California, La Jolla, California 92093-0505, USA.
J Chem Phys. 2004 Nov 15;121(19):9323-42. doi: 10.1063/1.1794634.
Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive methods which avoid explicit construction the metric matrix and do not require storage of the full Hamiltonian matrix to isolate the antisymmetric subspace of the spectral-product representation. Calculations of the lowest-lying singlet and triplet electronic states of the covalent electron pair bond (H(2)) illustrate the various theorems devised and demonstrate the degree of convergence achieved to values obtained employing conventional prior antisymmetrization. Concluding remarks place the atomic spectral-product development in the context of currently employed approaches for ab initio construction of adiabatic electronic eigenfunctions and potential energy surfaces, provide comparisons with earlier related approaches, and indicate prospects for more general applications of the method.
本文报道了用于从头计算分子及其他原子聚集体的绝热（玻恩 - 奥本海默）电子波函数和势能面的理论方法。采用了从长程相互作用的微扰理论处理中熟知的原子本征态完备集的外积作为表示基，而无需事先强制聚集体波函数的反对称性。文中指出了这种原子光谱积基的性质和属性，给出了反对称态表示的完备性证明，确立了在此基下薛定谔本征态的收敛性，并描述了该理论的计算实现策略。得到了一个类似非绝热哈密顿矩阵的表示，它在原子能矩阵和成对原子相互作用能矩阵中是可加的，为基于原子组成部分的（库仑）相互作用进行分子计算提供了基础。光谱积基被证明仅一次且唯一地包含聚集体电子坐标置换对称群的完全反对称不可约表示，但也跨越了其他（非泡利）对称群表示，已知这些表示包含非物理离散态及相关连续区，而物理上有意义的薛定谔本征态通常嵌入其中。通过用从显式反对称化光谱积基的度量矩阵得到的酉变换来隔离哈密顿矩阵的物理块，从而避免了这些非物理表示。在光谱闭包极限下，给出了收敛的形式证明，即对于采用常规事先反对称化得到的波函数和能量面，无需将哈密顿矩阵元作为显式反对称聚集体基态上的积分进行重复计算即可确定。该理论的计算实现采用了高效的递归方法，避免了显式构建度量矩阵，并且不需要存储完整的哈密顿矩阵来隔离光谱积表示的反对称子空间。对共价电子对键（H₂）的最低单重态和三重态电子态的计算说明了所设计的各种定理，并展示了与采用常规事先反对称化得到的值相比所达到的收敛程度。结束语将原子光谱积的发展置于当前用于从头构建绝热电子本征函数和势能面的方法背景下，与早期相关方法进行了比较，并指出了该方法更广泛应用的前景。
