2190
J. Phys. Chem. 1981, 85,2190-2194
Intermolecular Potentials in the Dimer, the Exclmers, and the Dimer Ions of Ethylene E. Joy Padma Malar and Asish K. Chandra" DepaHment of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560 0 12, India (Received: July 3, 1980; I n Final Form: March 20, 198 1)
Calculations are reported on the interaction energies in the dimer, the excimers, and the dimer ions of ethylene. The various a- and u-electron terms for different conformations of the dimeric species are determined by using the exchange perturbation method. The results predict that the singlet excimer and the dimer cation are stable primarily because of the large magnitude of the exciton-resonance and charge-resonance terms, respectively, while the neutral dimer, the triplet excimer, and the dimer anion are weakly stable. The variations of the various energy terms with conformations suggest that these dimeric species cannot have identifical structure.
Introduction Ethylene is the simplest a-electron system. A detailed study of interactions in the van der Waals dimer, the singlet and triplet excimers, and the cation and the anion of ethylene dimer is expected to provide valuable information about the nature of the molecular interactions between two neutral molecules, between a neutral molecule and its excited partner, and between a neutral molecule and its ion. Although the formation of dimer cation in ?r-electron systems has been k n ~ w n , l the - ~ formation of dimer anion has so far not been reported. The theoretical treatment of Badger and Brocklehurst4 suggests that the binding energies of the dimer cation and the dimer anion of an aromatic hydrocarbon should be nearly the same. Recently ab initio calculations within the framework of a supermolecule have been performed on the ground-state dimer5 and the dimer ions6 of ethylene. More recently, Suzuki and Iguchi' have obtained the intermolecular potential of the ground-state dimer of ethylene by means of the perturbation method employing the CNDO wave functions. The results of ab initio calculation^^^^ reveal that the ethylene dimer cation is stable with a binding energy of 16.14 kcal/mol while the dimer anion and the groundstate dimer of ethylene are very weakly stable. No calculations are reported on excimers of ethylene. The object of this investigation is to understand the nature of interactions in the groun-state dimer, the excimers, and the dimer ions of ethylene. The rigorous ab initio calculations within the framework of a supermolecule do not however provide any detailed insight into the nature and the relative importance of the various kinds of forces that operate in the molecular interactions. In this paper we follow the exchange perturbation method8i9 which determines, term by term, the contributions of the various forces to the potentials of these dimers and hence provides an informative picture of the (1) T. Ichikawa and P. K. Ludwig, J. Am. Chem. SOC.,91,1023 (1969). (2) B. Badger and B. Brocklehurst, Trans. Faraday SOC.,65, 2576, 2582, 2588 (1969). (3) A. Kira, M. Imamura, and T. Shida, J . Phys. Chem., 80, 1445 (1976). (4) B. Badger and B. Brocklehurst, Trans. Faraday SOC.,66, 2939 (1970). (5) P. E. S. Wormer and A. van der Avoird, J . Chem. Phys., 62,3326 (1975). (6) J. Almlof, A. Lund, and K. A. Thuomas, Chem. Phys. Lett., 32,190 (1975). (7) K. Suzuki and K. Iguchi, J . Chim.Phys. P h y s X h i m . Biol., 75,779 (1978). (8) J. N. Murre11 and G. Shaw, J. Chem. Phys., 46, 1768 (1967). (9) J. I. Musher and A. T. Amos, Phys. Reu., 31, 164 (1967).
0022-3654/81/2085-2190$01.25/0
important interactions in these dimers. We have investigated a variety of different conformations of the dimers and chosen a parameter such that our calculated interaction potential of the ground-state ethylene dimer of the perfect sandwich structure fits with the ab initio results5 for the same structure. Thus, the premise of our paper is based on our faith in the ab initio results because hardly any experimental data are available to us to check our findings. The advantage of using a perturbative method is that the various interaction terms which can be given physical meaning are obtained directly, and hence their relative importance can be assessed immediately. Besides, our previous calculations on naphthalenelo and pyrenel' excimers using a similar procedure show that the binding energies of the singlet excimers are in reasonably good agreement with the experimental findings.
Theory and the Computational Procedure In dealing with the various interaction terms we treat the ?r- and the a-electron terms separately. The total intermolecular potential is then obtained by summing all of the interaction terms. The zero-order functions \ko for the ground-state dimer and \kd for the excimers and the dimer ions are given by eq 1and 2, where A is the intermolecular antisymmetriser,
4oAis the wave function of the ground state of the neutral molecule A, and 4oA*stands for either the wave function of the lowest singlet or triplet excited state or the ground state of the cation and anion of A as the case may be. The coordinates of the electrons are so chosen that the states with the (+) combination in eq 2 refer to the lowest energy state. The first-order energy in a ground-state neutral dimer is made up of electrostatic and first-order exchange (or overlap repulsion) terrns.l2 For excimers and dimer ions, the first-order energy involves, in addition to these two terms, a resonance term defined as resonance term = ( A~oAr#)oB*lVI~OA*~OB) (3) where V is the interaction perturbation. For excimers this may be called the exciton-resonance1° and for dimer ions the charge-resonance term. (10) E. J. Padma Malar and A. K. Chandra, Theor. Chim. Acta., 55, 153 (1980). (11) E. J. Padma Malar and A. K. Chandra, unpublished results. (12) A. K. Chandra and B. S. Sudhindra, Mol. Phys., 28, 695 (1974).
0 1981 American Chemical Society
The Journal of Physical Chemisty, Vol. 85, No. 15, 1981 2191
Intermolecular Potentials in Ethylene Species
In dealing with the second-order terms, we ignore the exchange of electrons and obtain the charge-transfer, induction, and dispersion energies. The detailed application of this approach has been discussed for hydrocarbon dimers and excimers in our previous papers.1°J2 a-Electron Terms. The important first-order and second-order a-electron terms for the dimer, the excimers, and the dimer ions are as follows. a-n overlap repulsion energy (first-order exchange energy): EoR(G) = -4Snn‘~nnt (4)
EoR(S)= EoR(T)= -2(Snn/Vnnt + SnmtVnrnJ)
(5)
EoR(C) = -2Snn‘~nnl
(6)
EoR(A) = - 4 S n n l ~ n n l - 2 S n r n ~ ~ n r n ~ (7) Exciton-resonance energy (in singlet and triplet excimers): EER(S,T) = Snn~qmml + Smmqnnt- (nmln’m’) 7 (nmln’m’) - [((mmlnn’) + Smm1(nnln’n) + SnnJ(rnmlnh’))7 (Snnt(mnIm’n’) S,,,(nmln’n’))] (8)
+
Charge-resonance energy (in the cation and the anion of the dimers): EcR(C) = qnn‘ (9) EcR(A) = Vmm’
(10)
Charge-transfer energy: EcT(G) = - 4 ~ n m ’ ~ / ( e m j En)
(11)
+ Vmm02/(Jnm - Knm K n m ) (12) EcT(C) = -[qnm41 + 2 S n n ~ ) I 2 / ( c r n-~H n n ) (13) EcT(A) = 2 [ ~ n m 4 + 1 2 S m m O 1 2 / ( ~ m-~en + J m m ) ( 1 4 )
EcT(S,T) = -(Vnn/
dispersion energy: EJ;,“(G) = -4(nmln’mm’)2/(t, - e,, T-T
+ 2Kn, - J,, + c, tnt
Ea;:@) = -4(nmln’m’)2/(c,
- E,
+ 2K,,
-
+ 2Knr,,
Jn,
-
-
JnJm,)(15)
+ ern[ - e,!
-
Jnl,O (16)
EI;:(T) = 0 EJi,“(C) = Edi,(A) = - 2 ( n m l n , m ’ ) 2 / ( c , - t, - Jn,
(17)
+ 2Kn, + H,I,I
- H,,!,I)
(18) where G, S, T, C, and A inside the parentheses denote respectively the ground-state dimer, the singlet excimer, the triplet excimer, the cation, and the anion of the dimer. n and m refer respectively to the occupied and unoccupied n-electron molecular orbitals in molecule A while n’and m’refer to those of molecule B. These spatial orbitals are assumed to be the same for the cation, the anion, and the ground and excited states of the neutral molecule. The upper and lower signs in eq 8 and 12 refer to the singlet and triplet excimers, respectively. The various integrals appearing in eq 4-18 are defined as Snm,= (nlm’) (19) Vnm‘
(nmlp’q’) =
=
(nlvlm’)
1J n ( i ) p’(j)(ez/rij)m(i)4’0’)dui duj E,,,
= H,,
+ 2J,,
- K,,
(20) (21) (22)
J,, =
K,, =
s s
H m m = (mIH*coreIm)
(23)
s n ( i ) m(j)(e2/rij)n(i) mG) dvi dv, ( 2 4 ) s n ( i ) n(j)(e2/rLj)m(i)m(j) dui dvj (25)
We have employed the SCF carbon 2p, orbital13 to calculate all of the intermolecular integrals. The two electron integrals involving differential overlap are calculated by using Mulliken’s approximation.14 The atomic integrals required for calculating the intramolecular quantities appearing in the above equations are computed by using the Slater value of the orbital exponent. The integral V&, appearing in eq 4-14 is assumed to be proportional to the overlap, i.e., Vik! = Ksikt (26) For the present study, we obtain the value of K by fitting the total interaction energy of the ethylene dimer of symmetric sandwich geometry, obtained by the method outlined above, with the ab initio values for the same structure for a wide range of intermolecular separations. For fitting the interaction energies, one has the choice of both ab initio SCF LCAO values or ab initio multistructure valence bond resulk5 We have chosen the latter because of the obvious reason that in the former results the stabilizing contribution arising from the dispersion interaction is missing, while the latter and our calculations take into account explicitly the attractive dispersion term. By the above procedure we obtain the value K = -3.7 eV. It may be noted that this value is very close to one used by Salem (K = -3 eV)15for the calculation of the orbital interaction in conjugated systems. a-Electron Terms. The important a-electron interaction10J2terms are electrostatic, nonbonded repulsion and a-CTdispersion terms. Haugh and HirschfelderlGconclude that the U-T dispersion interaction in small a systems such as ethylene is not negligible. Therefore, we have included the a-a dispersion term in the present study. We assume that the a core of the excimers and the dimer ions is the same as in the ground-state dimer. Hence, the a-electron interaction terms are the same for all of the dimeric species considered in the present study. The electrostatic energy is computed by using the point charge model and the a charges.17 In the case of dimer ions one gets, in addition, a finite a-n electrostatic energy since the n charges on the molecular ions are not zero. The nonbonded H-H and C-H repulsions are calculated by using the expressions given by Banerjee and Salemlg while the C-C repulsions are estimated by using the exponential function B exp(-CR) where R is the nonbonded C-C distance. The values of the parameters B and C are given by Kitaigorod~ky.’~~~~ We have followed the bond polarizability approximation developed by Rein et alaz1to compute the a-a and a-n dispersion interactions. The a-bond polarizabilities of C-C and C-H bonds are taken from the literature.18i22 (13) R. B. Hermann, J . Chem. Phys., 42, 1027 (1965). (14) R. S. Mulliken, J. Chim.Phys. Phys.-Chin. Biol., 46,497 (1949). (15) L. Salem, J . Am. Chem. SOC.,90, 543 (1968). (16) E. F. Haugh and J. 0. Hirschfelder, J. Chem. Phys., 23, 1778 (1955). (17) R. Hoffmann, J. Chem. Phys., 39, 1397 (1963). (18) K. Banerjee and L. Salem, Mol. Phys., 11, 401 (1966). (19) A. I. Kitaigorodsky, J . Chim. Phys. Phys.-Chim. Biol., 63, 6 (1966). (20) A. I. Kitaigorodsky, “Molecular Crystals and Molecules”, Academic Press, New York, 1973. (21) R. Rein, P. Claverie, and M. Pollak, Int. J . Quantum Chem., 2, 129 (1968). (22) K. G. Denbigh, Trans. Faraday SOC.,36, 936 (1940).
2192
The Journal of Physical Chemistry, Vol. 85, No. 15, 1981
Malar and Chandra
GZ X
Flgure 1. Relative orientations of two monomers and the definition of the parameters to describe different conformations of the ethylene dimer.
I 2.5
I
3.0
3.5
4.0
L.5
Dill
Flgure 3. Variation with D (A) a-a overlap repulsion, (b) excitonresonance, (c) charge-transfer, (d) T-A dispersion, and (U) total interaction energies for the symmetric sandwich structures of the singlet (S) and triplet (T) exclmers of ethylene.
2.5
3.0
1
I
I
3.5
4.0
L5
D lil Flgure 2. Variation with D (A) of (a) electrostatic, (b) a-a overlap repulsion, (c) nonbonded repulsion, (d) T-T dispersion, (e) a-a dispersion, (f) u-a dispersion, and (U) total interaction energies (all in kcal/moi) for the symmetric sandwich structure of the ethylene dimer.
Results and Discussion Figure 1 shows the coordinates of the two ethylene monomers. The different conformations of the dimer can be derived either by varying a , P, or 6 keeping D, the distance between the centers of the two C-C bonds, fixed or by translating one monomer relative to the other along the x or y axis. Dimer and Excimers. Figures 2 and 3 show the variation with D of the different interaction terms in the ethylene ground-state dimer and excimers, respectively, of the symmetric sandwich geometry. The charge-transfer term for the ground-state dimer vanishes for this structure while the u--R dispersion term is small. The total interaction potential, U , of the ground-state dimer does not show a minimum with D in agreement with the ab initio r e ~ u l t s . ~ , ~ Figure 3 shows that the exciton resonance stabilization is quite high for the singlet excimer. It is to be noted that the nonbonded repulsion PU and cr-a dispersion terms are the same as those in the ground-state dimer. On adding all of the component terms, we find that the singlet excimer shows a minimum in the total energy curve for D
-
The Journal of Physical Chemistry, Vol. 85,
Intermolecular Potentials in Ethylene Species
No. 15, 1981 2193
TABLE I: Equilibrium Geometries and Binding Energies of Ethylene Ground-State Dimer, Singlet and Triplet Excimers, and Dimer Ions
equilibrium structure
binding energy, kcal/mol
Ground-State Dimer T-shaped structure ( p = go", 0.42 CY = e = 0", D = 4.2 A ) 12.11 CNDOZ4 symmetric sandwich (D = 2.25 A , C Y =p = e = 0") CNDO' symmetric sandwich (D = 0.23 2.8 A , CY = p = e = 0") a b initio S C F T-shaped structure (D = 0.36 LCAO s t u d y S 5.20 A , p = go", a = 8 = 0") a b initio VB s t u d y S T-shaped structure (D = 0.21 5.67 A , p = go", a = e = present s t u d y
0")
exptl13 present s t u d y
8 S,D - 2 E A
present s t u d y
-12
20
LO
60
present s t u d y
Figure 5. Variation with 0 or a: (degrees) of the total interaction energies In the ground-state dimer (G) and the singlet (S) and triplet (T) excimers of ethylene for the fixed values of D. The solid and dashed lines refer to the variation with a: and 0, respectively.
Singlet Excimer tilted structure (D = 2.8 A , CY = 40", e = p = 0")
10.98
Triplet Excimer T-shaped structure (D = 4 . 2 A , p = go", ~i = e = 0")
0.42
Dimer Cation symmetric sandwich (D= 3.0 a , CY = p = e = 0") symmetric sandwich (D = 2.75 A , CY = p = e = 0")
80
d or B [ in degrees1 --t-
0.41
a b initio s t u d y 6
Dimer Anion T-shaped structure (D = 4.2 A , p = go", 01 = e = 0")
present s t u d y a b initio study6
dispersion and nonbonded terms, respectively. The minimum in the potential energy curve appears for D = 4.2 A with a binding energy of 0.42 kcal/mol. When one of the component molecules is rotated by 8 (Figure l),there is a gradual decrease in the magnitude of the attractive and repulsive terms. Consequently the total interaction potential of the ground-state dimer and the triplet excimer do not change much with 8. In the case of the singlet excimer, the exciton-resonance term drops markedly; hence, the singlet excimer experiences a large barrier with rotation. We have observed a similar phenomenon for naphthalene excimer.1° In Figure 5 are also shown the variations of the total energy with a. When one of the molecules is tilted by a keeping D fixed, we note that the exciton-resonance term does not decrease as rapidly with a as with 8. Hence, a minimum appears in the singlet excimer potentials of the tilted structure for D = 2.8 A. We have noted that the variations of the total energy with fl do not give a minimum for any value of D. We obtain the equilibrium conformations and the binding energies of the dimer and the excimers of ethylene by minimizing the total interaction energies for all conformations that can be derived from Figure 1. The results are summarized in Table I. The experimental value of the intermolecular potential in the ethylene dimer is obtained from the viscosity or second virial coefficient in which a certain rotational average is done.23 The estimated experimental value of the binding energy in ethylene dimer is 0.41 kcal/mol, which is less than the thermal energy at room temperature. This indicates that two ethylene molecules have no ability to form a stable ~~~~
~
(23) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids", Wiley, New York, 1954. (24) M. Hashimoto and T. Isobe, Bull. Chem. SOC.Jpn., 46, 2381
(1973).
13.00 16.14
0.73 unstable
I
I
2.5
,
\
I
3.0
/
I
I
3.5
L.0
D i81 Figure 0. Variation with D (A) of (a) total electrostatic, (b) a-a overlap repulsion, (c) charge-resonance, (d) a-a dlspersion, and (U)total interaction potential energies in the cation (C) and the anion (A) of the ethylene dimer of the syrnmetrlc sandwich structure.
dimer at room temperature. Our results agree with this. Our results further predict that the equilibrium structures of the singlet and triplet excimers are different. The large binding in the singlet excimer is primarily due to the large magnitude of the exciton-resonance term. The next dominating terms that contribute to the difference in the singlet and triplet excimer potentials are the a-a chargetransfer and T-a dispersion energy terms. The stabilization arising from these terms in the triplet excimer is negligible; hence, the triplet excimer prefers a T-shaped
J. Phys. Chem. 1981, 85,2194-2199
2194
structure as the ground-state dimer where the origin of the attractive and repulsive forces lies entirely in a electrons. Cation and Anion of Dimer. In Figure 6 we present the total electrostatic term and the different a-electron interaction terms of the cation and the anion of ethylene dimer as a function of D , for the symmetric sandwich structure. The a-electron terms for the ions are the same as those for the ground-state dimer and are reported in Figure 2. In Figure 6 are also shown the total potentials U for the cation and the anion of ethylene dimer against D. It is noted that the electrostatic energy is attractive in the dimer cation and repulsive in the dimer anion. The charge-resonance term is quite high in the dimer cation and dominates the total potential of the dimer cation for D > 3 A. For D < 3 A, the a-a overlap repulsion and the u-u nonbonded repulsion terms are dominant. Consequently a minimum appears in the total interaction potential of the dimer cation at D = 3.0 A,with a net binding energy of 13.0 kcal/mol. In the case of the dimer anion it is seen that the attractive charge-resonance term is small and is almost cancelled by the repulsive electrostatic term for all values of D. The total potential is dominated primarily by the a-a overlap repulsion and is therefore repulsive in the dimer anion of symmetric sandwich geometry. For the T-shaped structure (Le., /3 = 90°, CY = 8 = O O ) , as in the case of the ground-state dimer and the excimers, the a-electron terms vanish in the dimer ions because of the symmetry. Hence, the dominating attractive and repulsive terms are the a-electron terms which are nearly identical with the ground-state dimer of ethylene except for a finite contribution arising from the a-T electrostatic energy in the dimer ions. The other probable conformations that are examined for the ground-state dimer and
the excimers are also examined for the dimer ions. Our results reveal that the charge-resonance term decreases markedly for any distortion from the perfect sandwich conformation and hence the dimer cation is most stable in the perfect sandwich conformation while the dimer anion is unstable because of its lower magnitude of the charge-resonance term and larger value of the overlap repulsion term. The lower value of the charge resonance is understandable as the vacant a orbital of ethylene which is occupied in the anion has a node between the two carbon nuclei. Since the charge-resonance term is unimportant for all conformations of the dimer anion, the equilibrium structure and binding in the dimer anion are controlled primarily by the u electronic forces as in the ground-state dimer and the triplet excimer. Hence, a difference in equilibrium conformations of the dimer cation and the anion is also expected. The results for the cation and the anion are summarized in Table I. In summary, the results of this investigation lead to the following major conclusions: (1)The lowest singlet excimer and the ground state of the dimer cation of ethylene are stable primarily because of the large magnitude of the exciton-resonance and charge-resonance terms, respectively. (2) Since the exciton-resonance and the chargeresonance terms are unimportant in the triplet excimer and the ground state of the dimer anion, respectively, the binding and the equilibrium conformations of these species are controlled by the weak van der Waal's forces as in the corresponding ground-state neutral dimer.
Acknowledgment. We thank the Computer Center, Indian Institute of Science, Bangalore, India, for providing a DEC 1090 computer and the U.G.C. (Government of India) for support.
Resonance Raman Spectra of Adsorbed Species at Solid-Gas Interfaces. 3. Analysis of the Raman Excitation Profiles for Molecules Adsorbed on Semiconductor Oxide Surf aces James F. Brazdilt and Ernest B. Yeagel* Case Laboratories for Electrochemlcal Studies and the Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44 106 (Received: July 17, 1980; In Final Form: April 20, 1981)
The resonance Raman excitation profiles for p-nitroso-N,N-dimethylaniline(p-NDMA) and p-(dimethylamino)azobenzene (p-DMAAB) molecules adsorbed on ZnO and TiOz surfaces were determined by using argon ion laser radiation. The excitation profiles for the Raman bands of ZnO and TiOpwere also measured. These substrate bands were found to undergo preresonance enhancement as the exciting frequency approached that of their respective band gaps. The resonant states were calculated to lie at -33800 A for ZnO and at -4100 8,for TiOz. At low surface coverages, the Raman bands of the adsorbates undergo enhancement due to a coupling to the electronic states in the semiconductor substrate. A mechanism is proposed for this phenomenon involving a collective scattering from the strongly coupled adsorbent-adsorbate system and a nonradiative transfer of excitation between the two.
Introduction In the previous papers,l the resonance Raman spectra of p-nitroso-N,N-dimethylaniline(p-NDMA) and p-(dimethylamino)azobenzene O-DMAAB) adsorbed on ZnO, SnOz, and "ioz surfaces were discussed in detail, This tSohio Research Center, Cleveland, OH 44128.
paper discusses the observed excitation profiles for these adsorbent-adsorbate systems. The oxides used in this study are intrinsic n-type semiconductors. AS Such, they have unique optical, electronic, and catalytic properties which have been extensively in(1) J. F. Brazdil and E. Yeager, J.Phys. Chem., 85, 995, 1005 (1981).
0022-3654/81/2085-2194$01.25/0 0 1981 American Chemical Society
