Direct INDO/SCI Method for Excited State Calculations AIME ´ E TOMLINSON, DAVID YARON Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received 5 December 2002; Accepted 13 June 2003 Abstract: Intermediate neglect of differential overlap (INDO) is the most commonly utilized semiempirical technique for performing excited state calculations on large organic systems such as organic semiconductors and fluorescent dyes. The calculations are typically done at the singles-configuration interaction (SCI) level. Direct methods provide a more efficient means of performing configuration interaction (CI) calculations, and the computational trade offs associated with various approaches to direct-CI theory have been well characterized for ab initio Hamiltonians and high-order CI. However, the INDO and SCI approximations lead to a new set of trade offs. In particular, application of the electron-electron interactions in the atomic basis leads to savings in computational time that scale as the number of atomic orbitals, which for a large organic system can be two to three orders of magnitude. These savings are largest when only a few low-lying excited states are generated and when a full SCI basis, which includes excitations between all filled and empty molecular orbitals, is used. In addition, substantial memory savings are achieved in the direct method by avoiding the evaluation of the two electron integrals in the molecular orbital basis. The method is demonstrated by calculating the absorption spectrum of a poly(paraphenylenevinylene) oligomer containing 16 phenyl rings. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1782–1788, 2003 Key words: INDO; direct CI; SCI; excited states; PPV Introduction Intermediate neglect of differential overlap (INDO) 1 is a widely utilized semiempirical model for the excited states of large organic systems, such as conjugated polymers and fluorescent dyes. 2–4 Within INDO, the excited states are typically obtained at the singles-configuration interaction (SCI) level. This work develops a direct method for INDO/SCI calculations that provides a more efficient approach to these computations. Roos and Siegbahn 5–7 first introduced the direct configuration interaction (direct-CI) method, which was instrumental in making CI applicable to large systems. The computational trade offs associated with various approaches to direct-CI theory have been well characterized for ab initio Hamiltonians 8,9 and high-order CI. 10 However, the INDO and SCI approximations lead to a new set of trade offs. Most importantly, the evaluation of electron-electron interactions in the atomic basis provides a considerable savings in INDO theory, whereas it is not advantageous in ab initio theories. 11 For direct INDO/SCI, the computational savings relative to nondirect ap- proaches are on the order of the number of atomic basis functions in the calculation, which can be two to three orders of magnitude for large organic systems. In CI theory, the electronic wave function is written as a linear combination of many-body functions, which are obtained as exci- tations from the Hartree-Fock ground state. In SCI, the excited states include only singly excited electronic configurations: |  =  r,a c r,a |  a r  (1) For singlet excited states, |  a r  is given by |  a r  = 1  2  a r, † a a, + a r, † a a,  | HF (2) where | HF is the restricted Hartree-Fock ground state, and a a,  † ( a a,  ) is the creation (destruction) operator for an electron in molecular orbital (MO) a with spin . Throughout this article, a, b . . . are used for MOs that are occupied in the Hartree-Fock ground state, and r , s . . . are used for unoccupied MOs. The coefficients, c r, a of eq. (1), are determined variationally. This is equivalent to finding the eigenfunctions of the N  N Hamiltonian matrix within the SCI basis, where N is the number of singly excited configurations. We will refer to methods that ex- plicitly create the Hamiltonian matrix as “traditional methods.” For full diagonalization of this N  N matrix, the computational effort scales as N 3 , and gives all eigenvalues and eigenstates. An alter- Correspondence to: D. Yaron; e-mail: yaron@chem.cmu.edu Contract/grant sponsor: National Science Foundation; contract/grant number: CHE9985719 Contract/grant sponsor: Dreyfus Foundation © 2003 Wiley Periodicals, Inc.