Richard D. Harcourt

Rate expressions for excitation transfer. II. Electronic considerations of direct and through–configuration exciton resonance interactions

The electronic interactions which promote singlet–singlet and triplet–triplet electronic excitation (energy) transfer (EET) are investigated in detail. Donor and acceptor locally excited configurations, ψ1(A*B) and ψ4(AB*), respectively, are each allowed to mix with bridging ionic configurations, ψ2(A+B−) and ψ3(A−B+) to form the new donor and acceptor wave functions ΨR=ψ1+λψ2+μψ3 and ΨP=ψ4+μψ2+λψ3. Use of the latter wave functions leads to the establishment of the matrix element TRP= 〈ΨR‖H−E1‖ΨP〉≊T14−(T12T24+T 13T34)/A, with Tij=〈ψi‖H−E1‖ψj〉 and A=E2−E1, as the exciton resonance interaction term for EET. Introduction of the Mulliken approximation shows that the ‘‘direct’’ exciton resonance interaction term (T14) contributes primarily a Coulombic interaction, for singlet–singlet EET, while the ‘‘through–configuration’’ exciton resonance interaction term [−(T12T24+T13T34)/A] replaces the Dexter exchange integral (which is a component of H14) as the primary source of short‐range orbital overlap‐dependent EE...

Rate expressions for excitation transfer. III. An ab initio study of electronic factors in excitation transfer and exciton resonance interactions

A detailed theory for electronic aspects of electronic excitation (energy) transfer (EET) for sandwich dimers was derived in paper II of this series [J. Chem. Phys. 101, 10 521 (1994)]. In II, the electronic transfer matrix element for EET was evaluated, then simplified to various levels of approximation. The results of ab initio molecular orbital calculations on an ethene sandwich dimer are reported here in order to test and quantify the theory of II. The calculations were undertaken using a STO‐6G basis set and localized molecular orbitals, with separations of 4, 5, and 6 A between the molecules. It is demonstrated that the important electronic factors contributing to EET are the Coulombic interaction (for direct singlet–singlet transfer) and, for both singlet–singlet and triplet–triplet EET, orbital overlap‐dependent interactions. The dominant orbital overlap‐dependent terms arise from through‐configuration interaction, which involves successive one‐electron transfers mediated via bridging ionic config...

Configuration interaction and the theory of electronic factors in energy transfer and molecular exciton interactions

The theory established in J. Chem. Phys. 101, 10521 (1994), for electronic factors which promote interchromophore electronic energy transfer, exciton interactions and which provide the stabilization of excimers, is extended; first so as to include the possible contribution of doubly excited configurations. It is ascertained that there is a resultant effect upon the (interchromophore orbital overlap‐dependent) through‐configuration interaction, and a significant correction to the simple expression obtained previously for the Coulombic interaction. These CI effects are admitted to the general theory of the previous work and the cases of nonidentical, identical, and orthogonal donor and acceptor are discussed. Second, a description of superexchange effects is admitted to the theory. Two possible formalisms are developed and discussed.The theory established in J. Chem. Phys. 101, 10521 (1994), for electronic factors which promote interchromophore electronic energy transfer, exciton interactions and which provide the stabilization of excimers, is extended; first so as to include the possible contribution of doubly excited configurations. It is ascertained that there is a resultant effect upon the (interchromophore orbital overlap‐dependent) through‐configuration interaction, and a significant correction to the simple expression obtained previously for the Coulombic interaction. These CI effects are admitted to the general theory of the previous work and the cases of nonidentical, identical, and orthogonal donor and acceptor are discussed. Second, a description of superexchange effects is admitted to the theory. Two possible formalisms are developed and discussed.

Increased-valence formulae for nitro and nitroso compounds

Abstract Some earlier molecular orbital studies of the electronic structure of N2O4. are briefly reviewed. For ten mobile σ-electrons, the molecular orbital wave-function may be expressed as ψ(covalent)+ψ(ionic). The ψ(covalent) involves nine electrons in bonding to each nitrogen atom, and therefore generates “increased-valence” formulae. Such formulae may also be constructed by three other methods. Using these methods, increased-valence formulae for various nitro and nitroso compounds are described, and are shown to be compatible with measured bond lengths. Some theories of the “pentavalent nitrogen atom” are briefly discussed; the most satisfactory representation for such an atom is considered to be that which pertains to the increased-valence formulae of the present study.

Ab initio valence bond calculations and the spin-paired diradical character of sulfur nitride dimer (S2N2)

Calculs VB (STO-6G en negligeant les orbitales 3d de S): structure de Lewis primaire de type diradicalaire (a liaisons longues). Mecanisme de la polymerisation thermique de S 2 N 2 en (SN) x et de la conduction electronique de (SN) x

On the “pentavalent” nitrogen atom and nitrogen pentacoordination

Abstract Hydrazoic acid (HN3) is an example of a molecule whose bond lengths suggest hat the central nitrogen atom is apparently pentavalent, as indicated in the classical valence bond structure (I). However, unless the nitrogen atom expands its valence shell, the π bonds of this structure are fractional electron-pair bonds. The increased-valence structure (II) with fractional electron-pair π and π′ bonds, and 1-electron π and π′ bonds, also involves an apparent pentavalence. Some of the properties of these two VB structures are used to restate the nature of the origin of the apparent electronic pentavalence for nitrogen, namely appreciable contributions of Dewar-type structures such as (III) to the component Lewis structure resonance scheme. It is shown that although the valence of the central nitrogen atom of structure (II) is able to exceed a value of 4, it can never attain a value of 5. Increased-valence structures for the C2 isomer of N6 are also presented, and the bond lengths that are associated with the most stable of these structures are in accord with those calculated using ab initio techniques. The results of some ab initio VB calculations, with minimal basis sets, are reported for: (a) N2, to demonstrate the effect of variation in σ bond atomic orbital hybridization on the lengths of the N″N‴ bonds of HN3 (as HN′N″N‴) and the NN bond of N2; (b) trigonal bipyramidal NH3F2 and PH3F2, to suggest that the unwillingness of nitrogen to form stable pentacoordinate compounds is associated with some reluctance by nitrogen to participate in the formation of axial 4-electron 3-centre σ bonding units.

On the origin of matrix elements for electronic excitation (energy) transfer

The origin of electronic energy transfer (EET) between two chromophores (D and A) is explored further for several molecular situations that may be encountered in experiment—namely, nonoverlapping active‐space orbitals of the D and A chromophores, forbidden electronic excitations for both chromophores, and an allowed and a forbidden electronic excitation for the D and A chromophores, respectively. The theory is illustrated via the results of calculations of the EET matrix elements for model systems with both four–eight active‐space electrons and all of the electrons included explicitly. In each case, it is found that any overlap contribution to these matrix elements is associated much more with charge‐transfer and penetration terms rather than it is with the Dexter exchange integral. The calculated magnitude of the latter integral is always smaller than that of the Coulomb integral.

The origin of the long N-N bond in N2O2: an ab initio valence bond study

Abstract The results of some ab initio valence bond calculations, with an STO-5G basis set, are reported for the Ca2v isomer of N2O2. The existence of a very long N-N bond in this isomer is calculated to be associated mostly with the nature of the hybridization and the orientation of the lone-pair atomic orbitais on each nitrogen atom. The optimum forms of the two orbitais have a large 2s component, and overlap appreciably when the N-N internuclear separation is close to that of a normal single bond. The associated strong non-bonded repulsions that exist between the nitrogen lone-pair electrons lengthen the N-N bond. At N-N distances close to the equilibrium value (2.237 A), the orbitals that form the N-N σ bond are almost entirely 2p in character, and oriented at right angles to the N-O bond axes. Although some delocalization of oxygen lone-pair electrons of the Lewis structure does occur, thereby generating a fractional N-N σ bond, this effect produces only a small lengthening of the N-N bond.

Wavefunctions for “4-electron, 3-centre” bonding units

The simplest type of triatomic electron-excess system is one which involves four electrons distributed amongst three overlapping atomic orbitals on three adjacent atoms. If Y, A and B are the three atoms, and Y and B are symmetrically equivalent atoms, wavefunctions for the following types of valence formulae are constructed and compared: (i) delocalized molecular orbital [graphic omitted], (ii) standard valence-bond Ÿ A—B ↔ Y—A B, (iii) non-paired spatial orbital Y · A · B, (iv) increased-valence Y—A · B ↔ Y · A—B, and (v) Y—A—B with 2-centre non-orthogonal bondorbitals, each of which is doubly occupied.Where appropriate, a different spatial orbital is used for each of the bonding electrons in (ii)-(v). When 2-centre bond-orbitals are used as wavefunctions for both the one-electron bonds and the two-electron bonds of (iv), the resulting “increased-valence” wave-function with three different bondorbital parameters is equivalent to the complete configuration interaction wave-function.For (i)-(v), energies are calculated for the four π-electrons of HCO–2, NO–2 and C3H–5, and also for the four bonding σ-electrons of XeF2. For each of these systems, the non-paired spatial orbital and increased-valence wave-functions generate low energies. The importance of the “long bond” canonical structure [graphic omitted] is discussed.

The interconversion of N12 to N8 and two equivalents of N2

Abstract Ab initio MO computations have been performed at HF/6-31G(d) and electron correlated MP2/6-311G(d) levels of theory for N 12 (diazobispentazole, N 5 –N N–N 5 , C 2 h ), N 10 (pentaazopentazole, N 5 –NNNNN, C 1 ), N 8 (azidopentazole, N 5 –N 3 , C s ) and the two transition states connecting (i) N 12 and N 10 +N 2 (TS1, C 1 ); and (ii) N 10 and N 8 +N 2 (TS2, C 1 ). In addition, a qualitative valence bond (VB) mechanism has been suggested for the interconversion of (i) N 12 →N 10 +N 2 ; and (ii) N10→N 8 +N 2 .