Quantitative valence bond computation of a curve crossing diagram for

Jul 1, 1989 - A VB/MM View of the Identity SN2 Valence-Bond State Correlation Diagram in Aqueous Solution. Avital Sharir-Ivry and Avital Shurki. The J...
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J . Phys. Chem. 1989, 93, 5661-5665

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Quantitative Valence Bond Computation of a Curve Crossing Diagram for a Model S,2 Reaction, HCH,H’ HCH, H’-

+

+

Cjergji Sini,la Sason S. Shaik,**lbJean-Michel Lefour,la Gilles Ohanessian,lB and Philippe C. Hiberty*?l8 Laboratoire de Chimie ThPorique,’ Brit. 490, UniversitP de Paris-Sud, 91405 Orsay Cedex, France, and the Department of Chemistry, Ben-Gurion University of the Negec, Beer-Sheua, 84105, Israel (Received: October 12, 1988; In Final Form: March 20, 1989)

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A quantitative avoided crossing diagram for the model SN2reaction, HC + CH3H, HICH3+ H;, is computed by using a V B method based on local fragment orbitals. The essential parameters of curves are quantified at the 6-31G*+D level. The vertical electron-transfer energy gap, G , is 174 kcal/mol. The height of the crossing point (relative to H- + CH4) is 42% of G. The quantum mechanical resonance energy of the transition state, Le., the avoided crossing interaction, is 15.9 kcal/mol. The barrier of 56.8 kcal/mol is computed as the difference between the height of the crossing point and the avoided crossing interaction. All these parameters show insignificant basis set dependence and support previous estimations of these parameters which formed the crucial hypotheses for the use of the avoided crossing model to discuss reactivity trends.

Introduction Curve crossing diagrams2 have been used in recent years to discuss reactivity patterns in a variety of organic reaction^,^.^ notably the SN2r e a ~ t i o n . ~The ~ . ~diagrams have proved to be useful also for understanding the stability patterns in small clusters such as X3, X3-, and X,.6 All these applications have been essentially qualitative with reliance on thermochemical quantities for estimating the various parameters of the diagram, the avoided crossing interaction ( B ) , the curves’ energy gaps (G) and the curves’ curvatures Though some quantitative diabatic curves, of other types, have appeared,’ the quantitative counterpart of the qualitative curve crossing d i a g r a ~ n ~is~still q ~ largely absent. What appears to be missing is a critical examination of the validity of the model a t the state-of-the-art level of quantum mechanical computations. Specifically, (i) do the quantitatively determined G , and B parameters, of the curve crossing diagram, follow the trends, or estimations, suggested by the qualitative consideration^?^^-^ (ii) Can the curves in the model be reproduced rigorously and meaningfully? (iii) Can their avoided crossing, if computed, reproduce a quantitative potential surface? This paper tries to answer these questions by investigating a model SN2reaction, the hydride exchange in the equation y ) . 3 d 9 5

HY

+ CH3H, * HICH3 + H F

A Qualitative Curve Crossing Model The curve crossing diagram for reaction 1 is shown in Figure 1 ,3d,5 The diagram consists of two curves, I and 11, which are anchored a t two ground states and two charge-transfer states of reactants and products. The avoided crossing of these two curves generates the adiabatic ground-state curve. The ground states of the two curves I and I1 are the Lewis structures 1 and 2, where electrons are represented by heavy dots, H

I

1

Y

3

4

5

represented by a line connecting the heavy dots. The upper anchor points of the curves I and I1 in Figure 1 are valence-type charge-transfer states, which are composed of an H’ and a radical anion, CH4-, in which the charge is equally distributed over the four identical C-H linkages. To generate the charge-transfer states, e.g., Hl’/(CH3H,)-, we mix the H - L component of the Lewis structure 1 (in which HI and C are now infinitely distant) with two additional structure types which are shown in 6 and The symmetry-adapted structure 7 is 7.3d3S

Y

s~nglet-paired

6

(1)

where H I and H, are the two interchanging hydrogen atoms.

H

3-5. Here, the spin-paired electrons in the H-L bond in 3 are

2

bonds are represented by lines, and H , and H, are the left- and right-hand-side hydrogens of the interchanging C-H bonds. These latter bonds are called hereafter “active”, while the other three C-H bonds are called “inactive”. Each Lewis structure represents an optimized mixture of a Heitler-London (H-L) and two ionic configurations. These constituents, for the left-hand Lewis structure, 1, are shown in ‘The Laboratoire de Chimie ThEorique is associated with the CNRS(UA 506).

0022-36S4/89/2093-5661$01.50/0

s ~ n g l e -t p a i r e d

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generated from 6 by simply promoting an electron from the (1) (a) UniversitE De Paris-Sud. (b) Ben-Gurion University. (2) [a) Shaik, S . S. J . Am. Chem. Soc. 1981, 103, 3692. (b) Shaik, S. S. in New Concepts for Understanding Organic Reactions; Bertran, J . , Ed.;

Reidel: Amsterdam, 1989. (3) (a) Pross, A.; Shaik, S . S . Arc. Chem. Res. 1983, 16, 361. (b) For a recent review of the models see: Lowry, T. H.; Richardson, K . S. Mechanism and Theory in Organic Chemistry; Harper and Row: New York, 1987; pp 218-222, 354-360. (c) Pross, A . Ada. Phys. Org. Chem. 1985, 21, 99. (d) Shaik, S . S . Prog. Phys. Org. Chem. 1985, IS, 197. (4) (a) Shaik, S . S . J . Org. Chem. 1987, 52, 1563. (b) Buncel, E.; Shaik, S. S.; Um, I . H.; Wolfe, S . J . Am. Chem. Soc. 1988, 110, 1275. (c) Cohen, D.; Bar, R., Shaik, S. S . J . A m . Chem. Soc. 1986, 108, 231. (5) (a) Shaik, S. S.; Pross, A.; J . Am. Chem. Soc. 1982, 104, 2708. (b) Shaik, S. S . J . Am. Chem. Soc. 1984, 106, 1227. (c) Mitchell, D. J.; Schlegel, H. B.; Shaik, S. S.; Wolfe, S. Can. J . Chem. 1985, 63, 1642. (6) (a) Shaik, S. S.; Hiberty, P. C.; Lefour, J.-M.; Ohanessian, G.J . Am. Chem. Sac. 1987, 109, 363. (b) Shaik, S. S.; Hiberty, P. C.; Ohanessian, G.; Lefour, J . M. J . Phys. Chem. 1988, 92, 5086. ( c ) Shaik, S. S.; Bar, R. N o w . J . Chim. 1984, 8, 411. (7) (a) Sevin, A.; Hiberty, P. C.; Lefour, J. M . J . Am. Chem. Soc. 1987, 109, 1845. (b) Bernardi, F.; Robb, M . A. J . Am. Chem. Soc. 1984, 106, 54. (c) Kabbaj, 0. K.; Volatron, F.; Malrieu, J . P. Chem. Phys. Lett. 1988, 147, 353. (d) Sevin, A,; Chaquin, P.; Hamon, L.; Hiberty. P. C. J . Am. Chem. Soc. 1988, 110, 353. (e) Bernardi, F.; Olivucci, M.; McDouall, J. J. W.; Robb, M. A. J . Am. Chem. Soc. 1987, 109, 544. (f) Robb, M. A,; Bernardi, F. I n New Concepts for Understanding Organic Reacfions; Bertran, J . , Ed.; Reidel: Amsterdam, 1989.

62 1989 American Chemical Society

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The Journal of Physical Chemistry, Vol. 93, No. 15, 1989

T

fG

1 I

-H H

+Hi

H

Figure 1. A two-curve avoided crossing diagram for reaction 1 The adiabatic curve which is obtained from the mixing of the curves I and I 1 is shown by the heavy line. The values on the energy scale are computed with the V B method by use of the 6-31G*+D basis set (see the Theoretical Methods section). The geometries indicated on the various species are taken from ref 20b; AE* is the barrier, whilefG represents the height of the crossing point, and B is the avoided crossing interaction which is also the quantum mechanical resonance energy (QMRE).

carbon’s atomic orbital (or hybrid) which participates in active bond to the a* orbital (of a l symmetry) of the central C H 3 group. In between the anchor points, each curve in Figure 1 is composed of a mixture of an optimized Lewis structure and structures 6 and 7, with the latter two gradually vanishing as the ground state, e.g., HICH3/H;, is a p p r o a ~ h e d . ~ ~ . ~ The curve crossing diagram can be characterized by three quantities. The first quantity is the vertical charge-transfer energy gap G given by the difference between the ionization potential ( I ) and the valence electron affinity ( A ) of the corresponding species: G = I H - ACH4 The second quantity is the height of the crossing point (AE,) which can be simply expressed as a fraction U, of the gap G; that is

Sini et al. to reproduce various potential wells of diatomics and reaction barriers within a few kilocalories per mole, with respect to the best MO-CI calculations in the same basis sets. An additional satisfactory test is provided by the adiabatic ground-state surface computed in the present work. Each VBF is a linear combination of Slater determinants constructed out of local fragment orbitals (FO’s) which are spin-coupled so as to represent a bonding scheme between electrons in specified FO’s. Each FO is associated with a single fragment, which can be in the present case H I , the central CH, fragment, or H,. The FO’s are not allowed to delocalize themselves onto neighboring fragments. Such a delocalization is generally used, in other VB methods, for partially or totally orthogonalizing the FO’s,’’ or for eliminating the ionic VBFs as in the generalized valence bond (GVB)” or spin-coupled valence bond (SCVB)12 methods, and results in considerable savings of computer time. By waiving this computational convenience, we ensure in return the interpretability of the VB wave function; indeed each VBF is unambiguously associated with a particular bonding scheme, since each F O belongs to a single fragment without delocalization tails of any kind.13 The VB description of the bonds explicitly takes into account the intrapair correlation of the corresponding electron pairs. Here only the active bonds, HI-C and C-H,, are described this way, while the three inactive bonds of C H 3 are left uncorrelated and treated in a Hartree-Fock ( H F ) manner; i.e., the corresponding electron pairs are frozen into doubly occupied MO’s of the central fragment. Thus, one makes the approximation that this lack of electron correlation only brings a constant error throughout the potential surfaces and uniformly shifts the energy curves. The same philosophy has guided the method of Das and Wahl14 and the correlation-consistent C I of Carter and Goddard.lS The VB calculations described above have been performed by using a program written by FlamentI6 and one of us (J.M.L.), and utilize the Prosser and Hagstrom transformatioq” for calculating the minors of the overlap matrix. The H F calculations have been performed with the MONSTERGAUSS program.I8 W e have used two basis sets composed of initial 6-31G and 6-31G* setslg both augmented with diffuse orbitals (D), with exponents 0.036, on the axial hydrogens. Some H F calculations of the reaction barriers for the system investigated here have shown that the 6-31G*+D basis set, which is still relatively small, is sufficient to reproduce the results of the best calculations of this reaction.*O The geometries used are those optimized by Baybutt.*Ob A . Optimization of the Atomic Orbitals. In basis sets larger than minimal the FO’s are optimized in stages. Initially the FO’s

( I O ) McDouall, J . J. W.; Robb, M. A. Chem. Phys. Lett. 1986, 132, 319. ( 1 I ) Bobrowicz. F. B.: Goddard 111, W. A. In Methods of Electronic Structure Theory; Schaefer, H. F., Ed.; Plenum: New York, 1977; pp 79-127. (12) Cooper, D. L.; Gerratt, J.; Raimondi, M. A&. Chem. Phys. 1987, 59, 319. (13) Ohanessian, G.; Hiberty, P. C. Chem. Phys. Lett. 1987, 137, 437. (14) (a) Das, G.; Wahl, A. C. J . Chem. Phys. 1967, 47, 2934. (b) Das, G.: Wahl, A . C. J . Chem. Phys. 1972, 56, 1769, 3532. (c) Stevens, W. J.; Das. G.; Wahl, A. C.; Krauss, M.; Neumann, D. J . Chem. Phys. 1974, 61, 3686. (15) Carter, E. A,; Goddard 111, W. A. J . Chem. Phys. 1988, 88, 3132. (16) Flament, J. P. DCMR. Ecole Polytechnique, 91 128 Palaiseau, France. (17) Prosser, F.; Hagstrom, S. Int. J . Quant. Chem. 1967. I . 88: J . Chem. hE’= f G - B (4) Phys. 1968, 48, 4807. (18) Peterson, M.;Pokier, R. MONSTERGAUSS; Department of Chemistry, Let us turn now to the quantitative counterpart of this section. University of Toronto, Canada, 1981. (19) Francl, M. M.: Pietro, W . J.; Hehre, W. J.; Binkley, J. S.; Gordon, Theoretical Methods M. S.; DeFrees. D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. Gordon, The quantitative valence bond method (VB) that we use is M. S.; Binkley, J. S.; Pople, J. A.;Pietro, W. J. J . A m . Chem. Soc. 1982, 104, usually referred to as “multistructure valence b ~ n d ’ ’ . ~ It~ is ~ * ~ ~ 2797. Pietro, W . J.; Francl, M. M.;Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J . A m . chem. SOC.1982, 104, 5039. a nonorthogonal C I among VB configurations that we call here(20) See for example: (a) Dedieu, A,; Veillard, A . J . Am. Chem. Soc. after valence bond functions (VBFs) to avoid confusion with 1972, 94, 6730. (b) Baybutt, P. Mol. Phys. 1975, 29, 389. (c) Keil. F.; MO-CI methods. Some guiding principles to use the VB method Ahlrichs, R . J . A m . Chem. SOC.1972, 94, 6730. (d) Wolfe, S.; Mitchell, D. J.; Schlegel, H. B. J . A m . Chem. Soc. 1981, 103, 7694. (e) Reed, A. E.; in a reliable way are described in detail e l s e ~ h e r eand ~ , ~will only Schleyer, P.v.R. Chem. Phys. Lett. 1987, 133, 553. (f) Leforestier, C. J . be briefly summarized here. The method has already been shown9 Chem. Phys. 1978, 68, 4406. (9) Dedieu, A,; Veillard, A,; Roos, B. Proceedings of the 6th Jerusalem Symposium on Quantum Chemistry; Israel (8) Hiberty, P. C.; Lefour, J.-M. J. Chim. Phys. 1987, 84, 607. Academy of Science; Jerusalem, 1974. ( h ) Cremer, D.; Kraka, E. J . Phys. Chem. 1986, 90, 33. ( i ) Kost, D.; Aviram, K. Tetrahedron Lett. 1982, 23, (9) Maitre, P.; Lefour, J. M.; Ohanessian, G.; Hiberty, P. C., submitted for publication 4157. 0)Ritchie, C. D.; Chappell. G. A . J. A m . Chem. SOC.1970, 92, 1819.

AE,=fG c f < 1) (3) The fraction parameter depends on the curvature of the two curves I and The third quantity in the figure is the degree of avoided crossing, B. This is in fact also the quantum mechanical resonance energy (QMRE) of the CH,- transition ~ t a t e . ~ ~ , ~ , ~ The reaction barrier can be expressed in terms of these three quantities and reads: 11.3d9s

Curve Crossing Diagram for a Model SN2Reaction

The Journal of Physical Chemistry, Vol. 93, No. 15, 1989 5663

are optimized, through H F calculations of the separated fragments, at each calculated point of the potential surface, and vary smoothly from the reactants to the products so as to follow the distortion of the system. These F O s are used to construct a set of elementary VBFs, each corresponding to one of the various VB structures involved in the reaction. To further improve the HF-optimized FO’s, to take the effect of the neighboring axial hydrogens into account, the FO’s should be modified in three ways: rehybridization, polarization, and relaxation of their diffuse c h a r a ~ t e r . ~ . ~ These three effects can be retrieved by adding systematically generated complementary VBFs to the elementary ones, the former being generated from the latter by single excitations from a HF-optimized FO to a virtual one (see later, Table I), within the same fragment. The complementary VBFs involve one, two, or more such excitations and thereby represent terms of first order, second order, etc. with respect to the elementary VBFs. In the present study the expansion has been limited to second order. Thus, each VB structure is described by several VBFs, whose coefficients are variationally calculated. Two points are noteworthy: (i) The complementary VBFs must have relatively small coefficients, which ensures that the FO’s used in the elementary VBFs are not too far from optimal and that truncating the expansion to second order is a good approximation. (ii) If the latter condition is fulfilled, the energy is invariant to first-order variations in the HF-optimized FOs. So defined, the complete set adds to a total of 220 VBFs of the elementary and complementary types throughout all regions of the potential surfaces, in the 6-3 l G + D basis set. Note that the effect of the diffuse orbitals (denoted by a double prime) on the axial hydrogens are recovered through VBFs corresponding to electron excitations from sIand s, orbitals to respectively s? and s i ’ in elementary VBFs. A similar procedure has been used to properly take into account the effect of the polarization orbitals in the calculations using the 6-3 1G*+D basis set, thus leading to a set of 305 VBFs. It should be noted that the polarization orbitals are already present in the HF-optimized FO’s in the 6-3 IG*+D calculation. However, the polarization so obtained is not optimal for an FO involved in a bond, and the correct polarization must be retrieved through complementary structures. The above discussed set of complementary VBFs defines a coherent minimal space of VBFs necessary to mimick the optimization of the FO’s in the elementary VBFs. In other words, the wave function one gets after C I in this space is in principle equivalent to a much more compact one, reduced to a linear combination of elementary VBFs only, but in which each determinant would have its own set of optimized orbitals, different from one determinant to the other. Starting now from the above-defined set of VBFs, we have discarded some of them for the sake of reducing computer time, after some computational tests showing that this simplification had no important effect on the calculated energies: (i) the Hentity, in the geometry of the reactants, is only described by two VBFs, s2 and ss”. A full C I calculation shows that this results in an error of only 1 kcal/mol. (ii) The VBFs which proved inefficient in the 6-3 l G + D basis set have been removed before using the more costly 6-31G*+D basis set. This results in an energy rise less than 1 kcal/mol. The VBFs which are kept after this simplification are displayed later in Table I with their coefficients in the CHS- ground state, as calculated in 6-31G+D basis set, and add to 138, vs 174 in the 6-31G*+D basis set. B. The Relationship between VBFs and VB Structures. In a minimal basis set, or one which derives from an effective Hamiltonian,2’ a single function represents an FO and if we suppose that the FO’s need not be rehybridized, then the VBFs and their number will be identical with the chemical structures (effective configuration^^^.^) described in the qualitative section. However, since we use extended basis sets that are composed from at least two components (double [ D, and also polarization in

+

(21) (a) Malrieu, J. P.; Maynau, D.; J . Am. Chem. Sor. 1982, 104, 3021, 3029. (b) Malrieu, J. P.; Maynau, D.; Daudey, J. P. Phys. Rev. 1984, B30, 1817.

TABLE I: VBFs Used for the Calculation’ of the Adiabaticb CH, and Its Diabatic Components structure structure typec VBF coeff typec VBF coeff 0.1156 6 sIsrp2u2 0.0054 1 s,s:pu2 0.0140 sls,pp’u2 0.0406d sI’s:pu2 sIsip2:22 0.0130 sIs,s,’pu2 0.019gd sls,‘pp u 0.0037d sIs,s/pu2 0.4483d sls,p2uu* 0.1938d sIsi2pu2 0.0144 7 sls,pu2u* 0.1685d s(s,s,)pu2 0.0021d s s u2u*’ 0.0447d s(s,s/pu2 0.0044d s,’si2pu2 0.0015 VI rrP, P IJ2 01, 0.0055d s,’s,pu2u* 0.003 I d sIs,2p’u2 0.0089 ~ ~ s , ) ~ p u ~0.0052d r~*’ sIs,s,)p’u2 0.0097d s s s ” ’ 6 2 0.0159d s,‘srp’u2u* 0.0010d si$ip!u: 0.0026 s(s,)pu2u* 0.0009d 0.0029 sIs:u2u* 0.0288 0.0004 s,’s,2u2u* s12s’2Y 0.0171 i:sp’p2u2 0.0270 sIs,s~u2u* 0.0065d sIsrs/u2u* 0.0219d s,zppfu2 0.0104 sIs/pp’u2 0.0125‘ s I s ~ u 2 u * ’ 0.0 177 s?s;q2 0.0720 s,’s,2u2u*’ 0.0045 sI2s,s, u 0.0080 sI’srs,‘uzu* 0.0003d s12s,s/u2 0.1804 s,’s,s/u2u* 0.0030d s , ~ s , ’ ~ ~ J ~ 0.0226 sIs,s,‘u2u*’ 0.0025d sIs,’srs,u 0.0042d sIsrs,I’u2u*’ 0.0024d s1s,”s,s,”u2 0.0931d s:pu2u* 0.0074 s?s:uu* 0.0036 s,s,”pu2u* 0.0151d sIs(‘s,2uu* 0.0950

“The calculations refer to the 6-31G+D basis set. *The coefficients in the table are results for the adiabatic CH5-. ‘In each case we show only one of the two symmetry-related VBFs (e.g., 1 instead of 1 and 2). this V B F both spin coupling schemes have been used but only the largest coefficient is shown. 6-31G*+D), the number of VBFs exceeds the number of chemical structures. In fact, each chemical structure is described by several VBFs with coefficients that are determined variationally. For example, the H-L structure 3 will be composed of many VBFs which obey the same electronic distribution as in 3, Le., with a “lone pair” (and a negative charge) on H, and an H-L spin pair connecting C H 3 to HI. One of the VBFs will involve the HF-optimized F O s , while others will involve electrons in the diffuse, or virtual FO’s, and so on. Since this linear combination of VBFs is determined variationally, the entire combination is equivalent to a single structure with localized FO’s which would be optimized for this particular VB s t r u c t ~ r e . This ~ - ~ enables ~~ to retain a simple picture in terms of a few chemical structures, while allowing to reach any desired level of quantitative accuracy. C. Valence Bond Structures f o r Reaction 1. The important points along the reaction coordinate are the reactants, products, and the D3,, C H < species. Let us exemplify the arguments with the latter species. The elementary FO’s of the active bonds (the axial H,.-M.-H, portion) and the u-type M O s of the inactive bonds (the equatorial C H 3 portion), both having al’ symmetry, are labeled by letters that signify their nature. The virtual counterparts of these orbitals carry the same label but with a prime, e.g., s,’ vs sI, while the diffuse orbitals carry a double prime. Out of all the FO’s of the equatorial C H 3 linkages, only the u* FO of al’ symmetry belongs to the active set as this FO is singly occupied in structures of the type 7 . Table I lists the VBFs and their coefficients in the optimized wave functions of CHS-. The VBFs are organized according to their structural types. All the above VBFs types are used also in the calculations of the ground states H-/CH4 and the charge-transfer states.

Results A . Adiabatic Ground-State Surfaces. Comparison with Previous Works. A number of theoretical studies of the CHssystem have been published.*O The bond lengths of the various structures are very similar for the different basis sets (which are

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The Journal of Physical Chemistry, Vol. 93, No. 15, I989

TABLE II: Total Energies (in hartrees) of Ground States, Valence Charge-Transfer Pseudostates, and the CH< (D,,,) Ground State, and Curve Crossing Parameters for Reaction 1" 6-3 IG+D basis set H Fb CH,/H:(CH,)-/H' CH,AE*

G'

f

B

VB

-40.66756 -40.703232 -40.431 549 -40.435472 -40.56460 -40.61 1246 64.6 57.7 I48 I68 0.44 15.6

6-31G*+D basis set H F'

VB

-40.681513 -40.444391 -40.579954 63.7 149

-40.715821 -40.438941 -40.625260 56.8 174 0.42 15.9

" T h e reaction barrier LE*,B , and G a r e in kcal/mol. I, is computed with inclusion of diffuse orbitals in the basis set for H'. ACH4is calculated without diffuse orbitals. The open-shell species in both cases a r e calculated with R H F theory. 'G = E ( ( C H J / H ' ) - E(CH,/H-). This quantity corresponds to the gap in Figure 1.

all a t least split valence). The energetics show slight method dependency. At the H F level, C H < is found to lie 63.6,20c61 .2,20b and 63.020e kcal/mol over the constituent species, H- and CH,. Most interesting is the effect of electron correlation. It has been estimated by Keil and Ahlrichs20Cby means of the CEPA method2* to reduce the barrier in reaction 1 by 7.2 kcal/mol. Our own H F and VB calculations are displayed in Table 11. At the H F level the two basis sets gave barriers of 64.6 and 63.7 kcal/mol, respectively, for reaction 1. Thus, the 6-31G*+D basis set reproduces the H F value of the most recent studies" with a reasonable accuracy despite its small size. Including the electron correlation correction as estimated by Keil and Ahlrichs,20c one would expect to get correlated barriers of 57.4 and 56.5 kcal/mol for reaction 1 with our two basis sets. Indeed the VB calculations in Table I1 provide values very close to these estimations: 5 7 . 7 and 56.8 kcal/mol. These results, together with some previous test^,^,^ show that the VB method is able to provide quantitative energetics which, within the limitations of the basis sets used, are comparable to those of reliable MO-CI computations. B. Computed Curve Crossing Diagram f o r Reaction 1 . The reactants, products, and crossing point (Figure 1) are unique and do not depend on the details of the reaction coordinate. Therefore, each curve can be constructed meaningfully by calculating its energy a t the ground state, the crossing point, and the chargetransfer state. As mentioned in the qualitative section the charge-transfer (pseudo) states in the two-curve model (as in Figure 1) correspond to vertical valence states. Thus, the CH4- species in these states accepts the electron into orbitals made up of the same AO's which constitute the C-H bonds of the ground-state molecule. This means that the CH4- species that is faithful to the model is the one that uses the same basis set as CH4, without diffuse orbitals. Inclusion of diffuse orbitals would be irrelevant, as their best exponent, which minimizes the energy of the unbound chargetransfer state, would be infinitely small. The removal of the diffuse orbitals is done by simply discarding the complementary VBFs involving diffuse AO's. It should be noted that the latter VBFs do not anyway mix into the ground anchor states, for reasons of orthogonality. The closest physical analogues of our CH4- species are the unbound dissociative temporary species (5 s) which are observed as scattering states in the electron transmission experiment.23s24 This perhaps gives some physical justification not to fully optimize our vertical CH4- species. It is important to mention in this sense the work of Heinrich et al.25who showed that basis sets like 3-21G and 6-31G* reproduce trends in the experimental electron affinities. However, inclusion of diffuse functions (6(22) Kutzelnigg, W. In Methods of Electronic Structure Theory; Schaefer, H. F., Ed.; Plenum: New York, 1977; pp 160-182. (23) Jordan, K. D.; Burrow, P. D. Acc. Chem. Res. 1978, 1 1 , 341. (24) Giordan, J . C.; Moore, J. H.; Tossell. J . A. Ace Chem. Res. 1986, 19, 28 I. (25) Heinrich, N.: Koch, W.; Frenking, G. Chem. Phps. Lert. 1986, 124, 20.

Sini et al. 31+G*) leads to a break down in the correlation between theory and experiment. The conclusion of Heinrich et aL2' is similar to ours that diffuse orbitals are not appropriate for the description of anions with negative electron affinity (unbound). It must be emphasized though that the specific nature of the charge-transfer states does not affect either the height of the crossing point or the adiabatic state. Thus, both the adiabatic state and the two resonating forms of the crossing point are separately computed and are themselves variational wave functions. The adiabatic state is variational over the entire set of VBFs, while each of the resonating forms of the crossing point is variational over the subset of VBFs that define a single bonding scheme (Le., a single Lewis structure together with the secondary configurations, structures 6 and 7, that can mix into it). Figure 1 is drawn with this definition, and the corresponding G, A and B quantities of the curve crossing, as defined in eq 4, are summarized in Table 11. Let us discuss at first thef factor. In the original qualitative p a p e r a~ largef ~ ~ ~ factor ~ was predicted for this reaction because of the very delocalized nature of the odd electron in CH4-, owing to the equivalence of the four atoms linked to carbon and the unavailability of this electron on the carbon center (for the particular direction of attack). Indeed the VB calculation shows that the odd electron density on carbon, in the active bond, is 1 0 . 2 9 . Thus, as argued u ~ u a l l y ,the ~ bond coupling of the charge-transfer state, e.g., H,'/(CH3H,)-, is rather weak and its descent is shallow. This produces a high-energy crossing point, which is equivalent to saying that the energy of the crossing point is a large fraction of the gap CfG in eq 4); that i s f i s a large quantity. The validity of this argument has been tested and retrieved in the present study. Thus, by use of only Lewis curves where no delocalization is present, one obtains anfvalue of 0.27, a s compared to the value of 0.42 for the full curves I and I1 (Figure I , Table 11). The electron-transfer energies (G) are calculated also a t the H F level, and it is apparent that these estimations are quite good. It should be noted that the individual errors in the H F values of IH: and ACH4,due to lack of electron correlation, cancel out, as the gap G is given by their difference, I,: - A C H (eq ~ 2). Thus, the H F estimation may provide a quick and easy access to such values. The VB-computed G factor is 168 and 174 kcal/mol, depending on the basis set. Both of these values are comparable to the range of experimental estimations, 133-190 kcal/mol, based on the known ionization potential of H-, and the vertical electron affinity of CH4.26 In previous paper^,^^^^^^' G has been estimated by use of a thermochemical equation that required calculation of one quantity, the three-electron repulsion energy in the (C-H)linkages (Figure I ) . This quantity has been found to depend largely on the level of approximation and provided a G value of 163 kcal/mol a t the best The B factor is an important property of the CH5- transition state: its quantum mechanical resonance energy (QMRE).2a,4,6 A s apparent by the VB makeup of CH,- in Table I, this Q M R E is contributed by delocalizing four electrons primarily over three orbitals (si, s,, and p) in analogy with the delocalization in species like H3-, allyl anion, etc. Owing to the significance of B, it is important to devise methods for calculating it as accurately and uniquely as possible. In this respect we note that a satisfying feature of our calculations is the (26) (a) I": = 17.5 kcal/mol. Chen, E. C. M.; Wentworth, W. E. J . Chem. Educ. 1975, 52, 486. (b) ACH4 = -(5-7.5) eV. See discussions in Lindholm, E.; Li, J . J . Phys. Chem. 1988, 92, 1731. See also ref 24. ( 2 7 ) A value of 81 kcal/mol is obtained by neglecting the C-H A 0 overlap in the normalization constants of the VB wave functions, and using a standard overlap s = 0.5 to estimate the VB matrix element (see ref 3d,5). The value of 163 kcal/mol is obtained by retaining the overlap. In this latter manner, the repulsion energy is larger than the corresponding quantity with neglect of overlap by a factor of ( 1 + s2)/( I - s2), and therefore the estimated G value is also larger. For a discussion, see: Shaik, S. S.; Mitchell. D. J . ; Schlegel, H . B.: Wolfe, S. Theoretical Physical Organical Chemistry. Application To the S,v2 Transition State; monograph in preparation. to be published by Wiley.

J . Phys. Chem. 1989, 93, 5665-5672 small variance of this property with changes in the basis set and the curve types. Indeed using only Lewis curves (structures 1 and 2), the resulting avoided crossing quantity is 15.8 and 16.1 kcal/mol, respectively, in the 6-31G+D and 6-31G*+D basis sets, both values being close to the respective B values in Table 11, 15.6 and 15.9 kcal/mol. All of these B values are close to the value of 14 kcal/mol proposed for this quantity in the previous qualitative

discussion^.^^^^ The smallness of the B value is an important condition for the model to be useful. This means that the final adiabatic curve stays close to the two curves which participate in the avoiding crossing (Figure I ) . With this condition fulfilled, one can deduce the energetics of the adiabatic curve from knowledge of the behavior of the crossing curves. In this sense, the present V B method provides a simple and ultimately useful picture of the curve crossing model. While the curve crossing diagram can be generated by other methods, the resulting picture may not be as simple as in the present study. Thus, for example, using orthogonalized A O s raises very much the energy of the crossing point and produces unrealistically large G values that can be as much as 80 k ~ a l / m o l . ’ ~ W e believe that, for a fundamental property such as B, one must use its unique definition as the energy difference between variational adiabatic state and crossing point and rely as much as possible on VBFs based on FO’s without delocalization tails.

5665

Otherwise, the interpretation of such quantities, which are not adiabatic, is uncertain.

Conclusion The present study indicates that avoided crossing diagrams2” can now be computed with a satisfactory degree of accuracy that is comparable to H F computations with an extended basis set followed by a good CI treatment. The ultimate goal of these diagrams though is still interpretative. In this sense, the combination of qualitative and quantitative applications is important. Thus, while the qualitative approach provides the models, the quantitative applications can reveal subtle new features and details. Thinking about reactivity problems in terms of avoided crossing diagram appears to be useful. Thus, a two-curve model like Figure 1 can serve to discuss sN2 reactivity.3d Here the barrier (eq 4) is a balance of the energy that is required to achieve crossing and quantum mechanical resonance energy, due to avoided crossing ( B ) . The energy of the crossing point is proportional to the gap ( G ) , and the proportionality factor,f, is larger when the electrons are more delocalized in the charge-transfer ~ t a t e . 3 4The ~ computed diagram (Table I1 and Figure 1) provides support for this kind of thinking. Further computations will reveal whether other qualitative ideas, such as the quasiconstancy of the QMRE ( E ) , in sN2 reaction can be maintained or will have to be abandoned for a more refined picture.

Optical Spectroscopic Studies of the Antitumor Drug 1,4-Dihydroxy-5,8-bis[ [2-[ (2-hydroxyethyl)amino]ethyl]amino]-9,1O-anthracenedione (Mitoxantrone) B. S. Lee and Prabir K. Dutta* Department of Chemistry, The Ohio State University, 120 W . 18th Avenue, Columbus, Ohio 43210 (Received: November 11, 1988; In Final Form: February 14, 1989)

The absorption, emission, and vibrational spectra of the novel antitumor drug mitoxantrone and its complex with DNA have been examined. The structure of this drug molecule is derived from anthraquinone. Spectral assignments for the electronic spectra have been made on the basis of solvent effects. A quantitative analysis of the fluorescence emission intensity has provided a measure of the dimerization and trimerization constants: 2.7 X lo4 M-’ and 7 X lo4 M-2, respectively. By use of the molecular exciton model, a geometrical arrangement of the dimeric aggregate of the drug molecule in solution has been proposed. These molecules are stacked upon one another, with the angle between transition dipoles calculated to be 22’ and with a 6.2-A separation between them. A normal-coordinate calculation of 1,4-diaminoanthraquinoneas a model for mitoxantrone has been carried out, and vibrational assignments for bands observed in the resonance Raman spectra of mitoxantrone have been made. The strongly enhanced resonance Raman band in the visible is found to have significant C-N character, in support of the assignment to an amino to ring charge transfer for the -660-nm band. Hypochromic effects were observed in the resonance Raman spectra of the drug-nucleic acid complex, indicating an environmental effect only on the excited state.

-

OH

0

NdHCH&H*NHCH&H20H

Biochem. Pharmacol. 1981, 30, 231. ( 6 ) Islam, S. A,; Neidle, S.; Gandecha, B. M.; Patridge, H.; Patterson, L. H.; Brown. J. R. J . Med. Chem. 1985, 28, 857.