INDO

(This keyword was written by Prof. Rebecca L. M. Gieseking, Brandeis University)

The INDO/S method is to be used. The default parameters are Zerner’s INDO/S parameters (also known as ZINDO/S). Other parameters can be read in from an external file using EXTERNAL. Since the INDO/S parameters were developed exclusively for spectroscopic (excited-state) properties, calculations involving energy gradients (geometry optimizations, transition states, frequencies, etc.) are not available.

Advantages of adding INDO/S

The INDO/S Hamiltonian (or equivalently, ZINDO/S),¹ has parameters designed specifically to reproduce vertical excited-state energies using a configuration interaction ( C.I.) approach with single excitations (CIS). In benchmarking studies, INDO/S has performed significantly better than traditional NDDO-based semiempirical methods for singlet excited states. For a set of 103 excited states of prototypical π-conjugated organic molecules, the mean absolute error at the INDO/S level is 0.51 eV, versus 1.35 eV at the MNDO level, 1.19 eV at the AM1 level, and 1.41 eV at the PM3 level.²

The solvatochromic shifts computed using INDO/S and the COSMO solvent model are in good agreement with experimental results and comparable to the accuracy of typical DFT functionals. For a series of 24 donor-acceptor substituted polyenes, the computed solvatochromic shift between toluene and ethanol at the INDO/CIS level has a root mean square error of 0.087 eV versus experimental results.  This can be compared with the 0.077 eV at the ωB97XD/6-31G* level and 0.116 eV at the B3LYP/6-31G* level.³

The INDO/S Hamiltonian has also shown success in understanding excited states with large double-excitation character using either single and double excitations (CISD) or a multi-reference approach (MRCI); these calculations have been particularly important in understanding the nonlinear optical properties of several classes of π-conjugated organic molecules.^4–7 The INDO/S Hamiltonian also provides good agreement with Time-Dependent Density Functional Theory (TD-DFT) for the optical properties of noble metal clusters^8,9 and is to date the only semiempirical method to yield physically reasonable ground-state electronic structures for these clusters.¹⁰
 

(1)      Ridley, J.; Zerner, M. An Intermediate Neglect of Differential Overlap Technique for Spectroscopy: Pyrrole and the Azines. Theor. Chim. Acta 1973, 32, 111–134. https://doi.org/10.1007/BF00528484.

(2)      Silva-junior, M. R.; Thiel, W. Benchmark of Electronically Excited States for Semiempirical Methods: MNDO, AM1, PM3, OM1, OM2, OM3, INDO/S, and INDO/S2. J. Chem. Theory Comput. 2010, 6 (5), 1546–1564. https://doi.org/10.1021/ct100030j.

(3)      Gieseking, R. L.; Ratner, M. A.; Schatz, G. C. Implementation of INDO/SCI with COSMO Implicit Solvation and Benchmarking for Solvatochromic Shifts. J. Phys. Chem. A 2016, 120, 9878–9885. https://doi.org/10.1021/acs.jpca.6b10487.

(4)      Pierce, B. M. A Theoretical Analysis of Third-Order Nonlinear Optical Properties of Linear Polyenes and Benzene. J. Chem. Phys. 1989, 91, 791–811. https://doi.org/10.1063/1.457132.

(5)      Meyers, F.; Marder, S. R.; Pierce, B. M.; Bredas, J. L. Electric Field Modulated Nonlinear Optical Properties of Donor-Acceptor Polyenes: Sum-over-States Investigation of the Relationship between Molecular Polarizabilities (Alpha, Beta, and Gamma) and Bond Length Alternation. J. Am. Chem. Soc. 1994, 116, 10703–10714. https://doi.org/10.1021/ja00102a040.

(6)      Geskin, V. M.; Lambert, C.; Brédas, J. L. Origin of High Second- and Third-Order Nonlinear Optical Response in Ammonio/Borato Diphenylpolyene Zwitterions: The Remarkable Role of Polarized Aromatic Groups. J. Am. Chem. Soc. 2003, 125, 15651–15658. https://doi.org/10.1021/ja035862p.

(7)      Gieseking, R. L.; Ensley, T. R.; Hu, H.; Hagan, D. J.; Risko, C.; Van Stryland, E. W.; Brédas, J.-L. Nonlinear Optical Properties of X(C 6 H 5 ) 4 (X = B – , C, N + , P + ): A New Class of Molecules with a Negative Third-Order Polarizability. J. Am. Chem. Soc. 2015, 137, 9635–9642. https://doi.org/10.1021/jacs.5b04377.

(8)      Shapley, W. A.; Reimers, J. R.; Hush, N. S. INDO/S Parameters for Gold. Int. J. Quantum Chem. 2002, 90, 424–438. https://doi.org/10.1002/qua.10058.

(9)      Gieseking, R. L.; Ratner, M. A.; Schatz, G. C. Semiempirical Modeling of Ag Nanoclusters: New Parameters for Optical Property Studies Enable Determination of Double Excitation Contributions to Plasmonic Excitation. J. Phys. Chem. A 2016, 120, 4542–4549. https://doi.org/10.1021/acs.jpca.6b04520.

(10)    Gieseking, R. L. M.; Ratner, M. A.; Schatz, G. C. Benchmarking Semiempirical Methods To Compute Electrochemical Formal Potentials. J. Phys. Chem. A 2018, 122, 6809–6818. https://doi.org/10.1021/acs.jpca.8b05143.

Details to be aware of when using INDO

Normally only model RHF systems. UHF is not implemented and although ROHF is implemented its SCF convergence behavior may be poor.

The default active space for single excitations is all M.O.s. The number of excitations included in the CI matrix is controlled by MAXCI, so it is possible to generate a large number of single excitations within an active space of hundreds of M.O.s.

Within INDO, the active space indicated by the C.I. keyword applies only to single excitations; if CISD is specified, the active space for double excitations must be specified by C.I.D. The configurations are automatically spin-adapted, so only electron configurations of a single spin are included. By default, only configurations with the lowest possible spin are included (singlet for a closed-shell system or doublet for an odd-electron system). Higher spins can be selected using TRIPLET or QUARTET.

See also: C.A.S., C.I.D., MAXCI, MRCI, TDIP, WRTCI, and WRTCONF.