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Volumn 106, Issue 22, 1997, Pages 9213-9226

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken-Hush and block diagonalization methods

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EID: 4243234418     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.474023     Document Type: Article
Times cited : (453)

References (87)
  • 2
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    • edited by J. Jortner and M. A. Ratner (Blackwell Science, in press)
    • (b) M. D. Newton and R. J. Cave, in Molecular Electronics, edited by J. Jortner and M. A. Ratner (Blackwell Science, in press).
    • Molecular Electronics
    • Newton, M.D.1    Cave, R.J.2
  • 14
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    • and references cited therein
    • (a) M. D. Newton, J. Phys. Chem. 95, 30 (1991), and references cited therein;
    • (1991) J. Phys. Chem. , vol.95 , pp. 30
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    • (b) 99, 1182 (1995).
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    • (b) 97, 3199 (1993).
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    • Modern Theoretical Chemistry, edited by H. F. Schaefer, III Plenum, New York
    • (a) I. Shavitt, in Modern Theoretical Chemistry, Vol. 3 Methods of Electronic Structure Theory, edited by H. F. Schaefer, III (Plenum, New York, 1977), p. 189;
    • (1977) Methods of Electronic Structure Theory , vol.3 , pp. 189
    • Shavitt, I.1
  • 34
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    • footnote 5 of Ref. 18(a), "2√β" should be replaced with the correct expression, "√2β"; the GMH model is an extension of the earlier two-state Mulliken-Hush model (Refs. 18(c)-18(f))
    • (a) R. J. Cave and M. D. Newton, Chem. Phys. Lett. 249, 15 (1996); (b) in footnote 5 of Ref. 18(a), "2√β" should be replaced with the correct expression, "√2β"; the GMH model is an extension of the earlier two-state Mulliken-Hush model (Refs. 18(c)-18(f));
    • (1996) Chem. Phys. Lett. , vol.249 , pp. 15
    • Cave, R.J.1    Newton, M.D.2
  • 45
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    • (d) T. Pacher, L. S. Cederbaum, and H. Köppel, Adv. Chem. Phys. 84, 293 (1993); see also V. Sidis, ibid. 82, 73 (1992).
    • (1992) Adv. Chem. Phys. , vol.82 , pp. 73
    • Sidis, V.1
  • 49
    • 85033292672 scopus 로고    scopus 로고
    • Additional comparative studies are currently underway for systems which include through-bond (TB) coupling of D-A sites via superexchange mechanisms (Ref. 1)
    • Additional comparative studies are currently underway for systems which include through-bond (TB) coupling of D-A sites via superexchange mechanisms (Ref. 1).
  • 57
    • 85033322009 scopus 로고    scopus 로고
    • note
    • An alternative method for the formulation of diabatic orbitals entails use of the GMH method. Given a set of adiabatic states spanning the localized (diabatic) states of importance for the processes in question, one first performs a GMH analysis to obtain the GMH diabatic states. Formation of the natural orbitals (based on the one-electron density) for each of the GMH diabatic states yields, in the CASSCF active space, localized natural orbitals. The localized natural orbitals from one of the states may be used directly as reference diabatic orbitals in the BD procedure, or it may be that the active spaces from two or more GMH diabatic states need to be combined in order to span the set of localized orbitals required to describe the system.
  • 58
    • 85033309102 scopus 로고    scopus 로고
    • note
    • ZnZn. Projection of these multiconfigurational zeroth-order states onto the adiabatic CI vectors at a given geometry is performed analogously to the single-CSF case; (b) For doublets involving three half-filled orbitals there are two linearly-independent spin eigenfunctions, and hence two CSFs which are included in the projector.
  • 60
    • 85033294049 scopus 로고    scopus 로고
    • note
    • Since the adiabatic states are obtained as eigenvectors of a CI matrix, the P and Q spaces are automatically orthogonal, independent of any rotations done within the P space.
  • 62
    • 85033282730 scopus 로고    scopus 로고
    • note
    • In cases where the active space canonical molecular orbitals obtained from the nSA/CASSCF procedure (at points of high symmetry or large D-A separation) are adequately localized on the sites of interest, they could be substituted for the ANO's and serve equally well as reference diabatic orbitals.
  • 63
    • 0003985620 scopus 로고
    • University of Lund, Sweden, R. A. Blomberg and P. E. M. Siegbahn, University of Stockholm, Sweden, V. Kello, J. Noga, and M. Urban, Commenus University, Slovakia and P.-O. Widmark, IBM, Sweden
    • MOLCAS versions 2 and 3, K. Andersson, M. P. Fülscher, R. Lindh, P.-A. Malmqvist, J. Olsen, B. O. Roos, and A. J. Sadlej, University of Lund, Sweden, R. A. Blomberg and P. E. M. Siegbahn, University of Stockholm, Sweden, V. Kello, J. Noga, and M. Urban, Commenus University, Slovakia and P.-O. Widmark, IBM, Sweden, 1991.
    • (1991) MOLCAS Versions 2 and 3
    • Andersson, K.1    Fülscher, M.P.2    Lindh, R.3    Malmqvist, P.-A.4    Olsen, J.5    Roos, B.O.6    Sadlej, A.J.7
  • 70
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    • note
    • 2.
  • 71
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    • to be published
    • ab) and other energetics, will be reported elsewhere, R. J. Cave, Y.-P. Liu, and M. D. Newton (to be published).
    • Cave, R.J.1    Liu, Y.-P.2    Newton, M.D.3
  • 73
    • 85033293762 scopus 로고    scopus 로고
    • note
    • p′ (in each case the members of a given pair differed by <10%).
  • 76
    • 85033292567 scopus 로고    scopus 로고
    • note
    • (a) Other formulations similar in spirit to the BD method employed here (Refs. 19 and 20) have been reported by Ruedenberg and co-workers (Refs. 44(b)-44(d)). We thank Professor Ruedenberg for supplying us with a copy of Ref. 43(d) prior to publication, and also for a number of helpful discussions;
  • 87
    • 85033315530 scopus 로고    scopus 로고
    • to be published
    • Use of the BD transformation of the adiabatic nSA/CASSCF Hamiltonian matrix yields diabatic states as in the present application. Once one has obtained the CASSCF diabatic Hamiltonian matrix, the diagonal Hamiltonian matrix elements can be augmented with correlation energies obtained at a geometry where the diabatic states are noninteracting (e.g., a point of high symmetry or large distance). Rediagonalization of the augmented Hamiltonian matrix yields new adiabatic states based on the above diagonal dressing of the diabatic states. This procedure has been used to study the interaction of the low-lying triplet states of pyrazine as a function of bending, R. J. Cave (to be published).
    • Cave, R.J.1


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