Per H Thrane-Nielsen

 

Allene - Small Molecule Paper

 

 

BIBLIOGRAPHY

Mahapatra, S.; Cederbaum, L.S.; Köppel, H. "Theoretical investigation of Jahn-Teller and pseudo-Jahn-Teller coupling effects on the photoelectron spectrum of allene." J.Chem.Phys. Volume111, Number 23, 1999. American Institute of Physics. 10452-10463.

Mebel, A.M.; Hayashi, M.; Liang, K.K.; Lin, S.H. "Ab Inito Calculations of Vibronic Spectra and Dynamics for Small Polyatomic Molecules: Role of Duschinsky Effect." J.Phys.Chem. Volume103, Number 50, 1999. American Chemical Society. 10674-10690.

Atkins, Peter. Physical Chemistry. 6th ed. Oxford: Oxford University Press, 1999.

Pouchert, Charles J. The Aldrich Library of FT-IR Spectra, 1st Ed.: FT-IR Vapor Phase Vol.3. Aldich Chemical Company Inc. Milwaukee, 1989.

Herzberg, Gerhard. Molecular Spectra and Molecular Structure: III Electronic Spectra and Electronic Structure of Polyatomic Molecules. D.VanNostrand Companies Inc. Princeton, 1966.

Herzberg, Gerhard. Molecular Spectra and Molecular Structure: II Infrared and Raman Spectra of Polyatomic Molecules, 12th printing. D.VanNostrand Companies Inc. Princeton, 1966.

http://www.pci.uni-heidelberg.de/tc/usr/lenz/ (biographical information)

 

SUMMARY AND DISCUSSION OF SELECTED ARTICLES

 

S. Mahaptra, L.S. Cederbaum, H. Köppel:

Theoretical investigation of Jahn-Teller and pseudo-Jahn-Teller coupling effects on the photoelectron spectrum of allene

The paper deals with modeling the effects of vibronic coupling as it applies to the allene molecule. Vibronic coupling is the interaction of electronic potential energy surfaces caused nuclear motion. It leads to the breakdown of the Born-Openheimer approximation, initiating new mechanisms in molecular dynamics responsible for a variety of spectroscopic phenomena such as conical intersections of potential energy surfaces. Jahn-Teller (JT) coupling and pseudo-Jahn-Teller (PJT) coupling are two subclasses of conical intersections, the latter dealing with interactions of degenerate and non-degenerate electronic states.

Allene is a member of the D_2d point group, and since it has an odd number of carbons it possesses both non-degenerate and doubly degenerate electronic states and vibrational modes, making it ideal for the study of JT and PJT interactions. Allene is a non-linear molecule with two perpendicular p orbitals and 15 normal vibrational modes. The ground and first excited ionic states are orbitally degenerate and belong to the ²E type. The totally symmetric A₁ modes n1, n2 and n3 cannot destroy the degeneracy of the ²E electronic manifold and is a special situation where non-degenerate vibrational modes are involved in JT activity, forming progressions in the photoelectron band. Allene has 1 vibrational mode of B₁ symmetry, the torsional mode n4 and 3 of B₂ symmetry, the antisymmetric bending and stretching modes n5, n6, n7. The degenerate modes n8, n9, n10, n11 do not participate other than allowing us to couple the energetically close B²B₂ and A²E ionic states in the first order, a PJT interaction.

Experimental work recording the He I excited photoelectron spectrum of allene has been done by Turner et al., pointing out JT activity in the ground ionic state, as well as Thomas and Thompson, who improved resolution and found that the JT activity is mainly caused by n4. Theoretical work reproducing the results of Turner et al. was performed by Cederbaum et al., revealing that the regular progression in the photoelectron band at low energies is caused mainly by n4 and that the antisymmetric stretching mode destroys the regular progression at higher frequencies. Further experimental work was done by Yang et al., Baltzer et al. and Bawagan et al. Theoretical work by Woywod and Domcke confirmed that progressions in the X²E photoelectron band of the allene ion are mainly caused by the JT active vibrational modes n4 and n6 and that the progression of the main lines in the A²E band at low energies are formed by n2 and n7, pointing out that the diffuse structure at higher energies could be caused by PJT interaction of the A²E and B²B₂ ionic states via the degenerate vibrational modes n8-n11.

The current paper seeks to study the dynamical JT and PJT coupling effects in the A²E and B²B₂ interacting manifold of the allene ion by constructing a model diabatic Hamiltonian within the linear vibronic coupling scheme, calculating relevant coupling parameters by ab initio quantum chemical methods, complementing experimental work by Baltzer et al. At low energies the results match those of Woywod and Domcke, with the progression of the photoelectron band mainly to be caused by n2 and n7, with the weak progression of n4 being quenched by n5. At high energies the PJT activity of the degenerate vibrational modes n8-n10 are found to cause the demolition of these progressions, contributing to the diffuseness of the photoelectron band.

The photoelectron dynamics is described as a Franck-Condon transition from the electronic ground state of allene to the A²E and B²B₂ electronic manifold of the cation, accomplished by ejecting an electron from the 1e or the 3b₂ orbital of allene. Since the energetically close A²E and B²B₂ electronic states may strongly interact via the vibrational modes of proper symmetry, the Born-Openheimer approximation may no longer be used. Instead one makes use of a diabatic electronic representation, where the elements of the vibronic Hamiltonian are weakly varying functions of the nuclear coordinates and the states are coupled through the electronic part of the Hamiltonean instead of the nuclear part. Initially the vibrational motion is treated as harmonic and the change in electric potential energy upon exitation is expanded in a Taylor series.

Calculation of the photoelectron spectrum

Fermi's golden rule:

P(E)=S_n | <y_n | T | y₀ > |² d ( E - E_n + E₀ )
| y₀ > initial vibrational and electronic ground state of allene w/ energy E₀
| y_n > final A²E and B²B₂ vibronic state of the allene radical cation
E_n vibronic energy
T transition operator describing interaction of the valence 1e and 3b₂ electrons

is applied and the photoelectron spectrum is calculated by solving the eigenvalue equation numerically by representing the vibronic Hamiltonian in a direct product basis of harmonic oscillator eigenstates. The oscillator basis is suitably truncated in the numerical calculations for each vibrational mode, and the maximum level of excitation for each mode is approximately estimated from their coupling strength.

Ab initio calculations

The electronic structure calculations are carried out using the GAUSSIAN program package. The results are similar to those from the theoretical investigation of Woywod and Domcke, but differ considerably from the experimental results for the symmetric C-H stretching (n1), antisymmetric C-H stretching (n5) and degenerate antisymmetric C-H stretching (n8) vibrations.

Coupling constants

The coupling constants k_i and l_i are defined as the gradients of the potential energy of the A²E state of the allene radical cation with respect to the dimentionless normal coordinate Q_i of the vibrational mode n_i, evaluated at the equilibrium geometry of allene. The other coupling constants were calculated in a similar manner. Using GAUSSIAN the electronic structure calculations were carried out as a function of displacements along the dimensionless normal coordinate Q_i=0.5 and 1.0 for the 15 vibrational modes. He calculations were made using the OVGF method and the cc-pVTZ basis set. The results differed significantly from those of Woywod and Domcke, who applied the DZP basis set, especially for the n1 and n5 modes.

Results

Adiabatic potential energies are obtained by diagonalizing the electronic part of the diabatic Hamiltonian matrix. The 3 totally symmetric vibrational modes n1-n3 cannot lift the degeneracy of the A²E ionic manifold, but they can shift the potential energy minimum considerably away from the equilibrium geometry of the neutral and display tuning activity in the photoelectron spectrum, which allows crossing of the A²E and B²B₂ ionic states.

• n1 is symmetric C-H stretching, but it is negligible in the photoelectron band.
  
• n2 represents symmetric H-C-H bending motion. The potential gradients at Q₂=0 are substantial for both the A²E and B²B₂ ionic states and are of opposite sign. The ionic states cross at Q₂=1.0, and remembering the presence of the PJT coupling modes, the crossing represents a triple intersection of the potential energy surfaces.
  
• n3 is of C=C stretching and H-C-H bending character, but is as with Woywod and Domcke ignored in the dynamical treatment although the coupling constant is significant.
  
• The torsional mode n4 is a JT active mode and distortion along this mode causes lifting of the degeneracy of the A²E manifold. The mode causes a large splitting of the electronic degeneracy in the X²E ionic manifold. The splitting is small for the A²E ionic manifold since it is only weakly JT active. n5-n7 of B₂ symmetry are JT active in the A²E manifold.
  
• n5 is represents antisymmetric C-H stretching motion, and although it causes large splitting of the degeneracy of the A²E ionic manifold, the vibrational frequency suppresses the possibility of any noticeable excitation in the photoelectron spectrum.
  
• n6 is of antisymmetric C=C stretching and H-C-H bending character and causes only weak splitting of the degeneracy in the A²E manifold and is therefore negligible when it comes to JT activity in the photoelectron spectrum.
  
• n7 represents antisymmetric H-C-H bending and causes large splitting in of the degeneracy in the A²E ionic manifold. It has the smallest vibrational frequency among the B₂ modes and is therefore the strongest JT active mode in the manifold. The B²B₂ ionic state undergoes crossing with the upper diabatic cone of the A²E electronic manifold along all vibrational modes of B symmetry.
  
• n8 represents antisymmetric C-H stretching motion and causes significant splitting of the electronic degeneracy of the A²E ionic manifold. Large vibrational frequency prevents significant excitation in the photoelectron spectrum.
  
• n9-n11 describe CH₂ wagging. Vibrational frequencies of n9 and n10 are small and their coupling strength is large. n9 is expected to be strongly excited in the photoelectron spectrum. n11 has very small coupling strength and its effect on the dynamics is negligible.

In the 21.218 eV He I excited photoelectron band Baltzer et al. reported well resolved structures in the 14-15 eV electron binding energy range and highly diffuse structures in the 15-17 eV electron binding energies. At low energies the structure is attributed to the A²E ionic manifold while the diffuse structure at higher energies is attributed to the B²B₂ ionic state. The progression of lines at low energies are similar to those resulting from the theoretical work of Yang et al. who assigned the progressions in terms of the symmetric vibrations n2 and n3, ignoring the effect of JT effects in the A²E ionic manifold. Woywod and Domcke later emphasized the presence of strong JT effects and assigned the progression of lines in terms of the symmetric mode n2 and the JT active mode n7.

In the absence of PJT modes the nuclear dynamics of the B²B₂ ionic state is governed by 3 totally symmetric vibrational modes. When considering n2, n4, n5, n7 in calculating the ExB JT spectrum of the A²E ionic manifold progression along the main lines can be assigned only in terms of the two modes n2 and n7. The experimental spectrum revealed line spacings of 167meV and 128meV as well as combinations of the two and the frequencies of n2 and n7 were therefore changed to match those values, respectively. The coupling constant of n7 was found to large and changed to 0.267eV. n4 is only weakly excited in the photoelectron band and is further quenched by n5. n4 and n5 are found to modulate the relative intensities of the peaks in the photoelectron band and n5 causes a shifting of the origin of progression by 0.1eV down the energy scale. The degenerate modes n8, n9 and n10 show considerable excitation in the photoelectron band, while n11 is very weakly excited. A careful study shows that progression at higher energy is predominately caused by n9 while n8 and n10 participate to destroy the progression and make the photoelectron band highly diffuse. Since their vibrational frequencies are nearly equal, n9 and n10 are joined into a single effective mode. The final theoretical calculation includes the nondegenerate modes n2, n4, n5 and n7 in addition to the degenerate modes n8 and n_eff. To better correlate with experimental results, the ab initio coupling constants for the degenerate modes n8-n10 have been decreased by 10%. Despite some minor detail the overall agreement between experimental and theoretical spectra is excellent. The spectral envelope at low energies predominately corresponds to the progression of the A²E ionic manifold caused by the nondegenerate vibrational modes, while the diffuse structures at high energies is caused by the B²B₂ ionic state via PJT activity of the degenerate vibrational modes.

Reference

1. D.W. Turner, C. Baker, A.D. Baker, C.R. Brundle, Molecular Photoelectron spectroscopy (Wiley, New York, 1970)
   
2. R.K. Thomas, H.W. Thompson, Proc.R.Soc.London, Ser.A 339, 29 (1974)
   
3. L.S. Cederbaum, W. Domcke, H. Köppel, Chem.Phys. 33, 319 (1978)
   
4. Z.Z. Yang, L.S. Wang, Y.T. Lee, D.A. Shirley, S.Y. Huang, W.A. Lester Jr., Chem.Phys.Lett. 171, 9 (1990)
   
5. P. Baltzer, B. Wannberg, M. Lundqvist, L. Karlsson, D.M.P. Holland, M.A. MacDonald, W. von Niessen, Chem.Phys. 196, 551 (1995)
   
6. A.D.O. Bawagan, T.K. Ghanty, E.R. Davidson, K.H. Tan, Chem.Phys.Lett. 287, 61 (1998)
   
7. C. Woywod, W. Domcke, Chem.Phys. 162, 349 (1992)

The paper and the theoretical work presented within it is a valuable addition to the understanding of experimental photoelectron spectra of molecules. It compliments earlier research and gives a more complete understanding of experimental data as it includes a thorough look at the contributions of the different vibrational modes and the Jahn-Teller and pseudo-Jahn-Teller effects that occur. Although a lot of theoretical research had been done prior to the publication of this paper, the results presented in the paper verifies theoretical interpretations at the lower end of the photoelectron spectra and gives a clear understanding of the effects contributing to the high end of the spectra.

 

 

A.M. Mebel, M. Hayashi, K.K. Liang, S.H. Lin:

Ab Initio Calculations of Vibronic Spectra and Dynamics for Small Polyatomic Molecules: Role of Duschinsky Effect

Ab initio molecular orbital calculations of potential energy surfaces for excited electronic states are becoming an increasingly powerful tool in studies of molecular spectroscopy and photochemistry. Advanced ab initio are applied to perform the complex task of accurately calculating the excited state surfaces. Most theoretical studies of excited electronic states only consider vertical excitation energies in the Franck-Condon region although behavior of excited states beyond this region is relevant to spectroscopy and dynamics of photochemical reactions. An ab inito approach for calculating the vibronic spectra of polyatomic molecules includes accurate calculations of the potential energy surfaces of the ground and excited states which provide information about vertical and adiabatic excitation energies, oscillator strength for different transitions, equilibrium geometries, vibrational frequencies and normal coordinates for ground and excited states and transition matrix elements. From these calculations the position and intensities of various peaks (Franck-Condon factors) in the vibronic spectra are calculated. Most spectral inensity calculations use ad hoc model potentials that include 1 or 2 degrees of freedom. Computing the Franck-Condon factors from first principles would be a more general approach, but is very complex since normal modes in an excited state can be mixed with eachother (alteration of the character of a normal mode) in addition to being displaced (displacement of a local minimum on the potential energy surface) and distorted (change of vibrational frequencies reflecting a change of the surface shape).

The mode mixing in the excited electronic state with respect to the ground state was first described by a Russian scientist in 1937 and is generally called the Duschinsky effect. The Duschinsky effect is one of the main reasons for dissymmetry between emission and absorption spectra and the appearance of combined transitions as only normal mode X is optically active and normal mode Y is mixed with X in the excited state. The Duschinsky effect scrambles the occupation of the normal modes and leads to unusual intensity distributions. The effect has been observed in absorption and emission spectra of benzene, naphthalene, styrene and others. In addition to playing a role in absorption and emission spectra it can also be observed in fluorescence, in resonance Raman spectra and in sum frequency generation spectra. The mode mixing can effect rates of internal conversion between different electronic states though alteration of the Franck-Condon factor.

Calculations of vibronic peak intensities taking into account the Duscinsky effect requires computation of multidimensional vibrational overlap integrals.

• One of the first attempts of a quantitative analysis was made by Coon, DeWames and Loyd, suggesting an approximate method for calculating 2 dimentional integrals specifically for non-linear triatomic systems.
  
• Atabek, Bourgeois and Jacon computed Franck-Condon factors taking into account two-mode mixing for a special class of symmetric triatomic molecules.
  
• Smith analyzed the effect of strong Duschinsky mixing of 2 normal coordinates Q1 and Q2 on the intensity in nontotally symmetric vibrations in electronic spectra using a Fermi resonance type theory.
  
• Sharp and Rosenstock as well as Smith and Warsop developed a more general approach in which a generating function was derived and the Franck-Condon integrals were obtained as coefficients in the expansion of this function in a multiple-power series of dummy variables.
  
• Kupka and Cribb continued the development of the generating function method and derived the multidimentional integrals by means of a multivariable generating function that incorporated both the transformation of the normal coordinates between 2 electronic states and their frequency changes.
  
• Faulkner and Richardson used a linear transformation of the normal coordinates to remove the Duschinsky rotation, expressing the multidimentional Franck-Condon integrals as sums of factorizable integrals in the new intermediate nuclear coordinates.

The authors of the article derived a closed form expression for the 4-dimentional vibrational overlap integral that is evaluated in terms of products of Hermite polynomials. The expression is valid for vibrationless ground electronic state and takes into account distortion, displacement and normal mode mixing of up to 4 modes. This approach was then applied to compute the vibronic spectrum of multiple polyatomic molecules.

Applications - Model System

The absorption spectra does not depend on the sign of the angle of Duschinsky rotation, j, in the case where the system has only distorted and rotated harmonic potential surfaces. The absorption spectra will exhibit a strong sign dependence once the potential is displaced. An absorption spectra of a system consisting of displaced, distorted and rotated harmonic potentials will in the case of a negative angle yield an absorption spectra that is broader toward the high energy region but without change in the lower energy region compared to the spectra of j=0. A positive angle will yield a spectra that shows drastic broadening towards both lower and higher energy regions.

Applications - Real Molecular Systems

p - > p* electronic transitions in small organic molecules represent an important example of the systems where the Duschinsky rotation between ground and excited electron states is extremely large. Some molecules that experience this behavior are allene, ethylene and other linear unsaturated hydrocarbons with p bonds. The absorption bands corresponding to the p - > p* transitionin allene have a weak, broad, featureless character, starting at 38000 cm^-1 and spreading to 52000 cm^-1 with eventual increase of intensity. For allene, 2 symmetry-forbidden ¹A₂ < - ¹A₁ and ¹B₁ < - ¹A₁ p-p* transitions can contribute through an intensity-borrowing mechanism from the allowed ¹E < - ¹A₁ (p-3s) and ¹B₂ < - ¹A₁ (p-p*) transitions. Recent measurements of 2-photon absorption spectra of allene show the presence of the underlying continuum band at energies as high as 60000 to 75000 cm^-1.

Theoretical ¹B₁ < - ¹A₁ ( p < - p* ) Absorption Spectra of Allene

In the allene D_2d symmetry the 2 CH₂ groups are twisted with respect to each other by 90^o and the excited p-p* ¹B₁ state is stabilized by D₂ torsion. The doubly occupied 2e and virtual 3e* MO's in D_2d symmetry are split into in plane s and out of plane p components with energies such that b_3u(p) < b_2g(p) < b_2u(s*) < b_3u(p*) for the D_2d - > D₂ - > D_2h transformation. The s* A_u state is the stabilized form of the B₁ Franck-Condon state, but because B₁ collapses to the totally symmetric representation at intermediate D₂ geometries, the ground state ultimately correlates with the open-shell ¹A_u state and the excited ¹B₁ state with the closed-shell excited state ¹A_g. Except for the CH₂ twisting, the other geometric changes from ¹A₁ to ¹A_g are minor. According to MRCI calculations, the adiabatic excitation energy for S₁ is only 3.02eV, about 3eV lower than the vertical excitation energies for ¹A₂ and ¹B₁ at D_2d symmetry.

Density functional calculations show a significant distortion of normal modes from the ground to the excited state.

Mode		Component	From (cm-1)	To (cm-1)
n12, n13	Out of plane CH2 wagging	1Ag (decrease)	833	148
n10, n11	In the plane CH2 wagging	b2 (unchanged)
		b3 (decrease)	978	490
n14, n15	CCH bending	b3 (increase)	357	502
		b2 (decrease)		Decrease about 60cm-1
n2	CH2 symmetric scissoring	1Ag (decrease)		Decrease about 150cm-1
n6	CC asymmetric stretch	1Ag (decrease)		Decrease about 150cm-1
n7	CH2 asymmetric scissoring	1Ag (decrease)		Decrease about 150cm-1

Normal mode displacement occurs only for the modes Q₁-Q₄. Q₄ corresponding to CH₂ is displaced the greatest, followed by Q₁ symmetric CH stretching and Q₂ symmetric CH₂ scissoring.

When it comes to mode mixing, only Q₁ (CH stretch) and Q₄ (CH₂ twisting) are heavily mixed. In symmetry b₁ there is some rotation of Q₅ (CH stretch) and Q₇ (CH₂ asymmetric scissoring), while Q₆ (CC asymmetric stretch) is not mixed with other modes. In symmetries b₂ and b₃, the CH asymmetric stretch Q₈ and Q₉ mixes with CH₂ out of plane wagging Q₁₂ and Q₁₃ and to a lesser extent with CH₂ in the plane wagging Q₁₀ and Q₁₁. Duschinsky matricies for symmetries a, b₂ and b₃ are unitary; the sum of squares for each row and column are equal to 1. The Duschinsky matrix for b₁, however, is not unitary.

Calculated normal mode displacements, distortions and rotations are then used to compute the absorption spectra of allene.

These results were then used to compute the temperature dependence of the absorption spectrum for the
¹B₁ < - ¹A₁ (p-p*) transition of allene.

Reference

1. J.B. Coon, R.E. DeWames, C.M. Loyd, J.Mol.Spectrosc. 8, 285 (1962)
   
2. O. Atabek, M.T. Bourgeois, M. Jacon, J.Chem.Phys. 87, 5870 (1987)
   
3. O. Atabek, M.T. Bourgeois, M. Jacon, J.Chem.Phys. 84, 6699 (1986)
   
4. W.L. Smith, J.Mol.Spectrosc. 176, 95 (1996)
   
5. W.L. Smith, J.Mol.Spectrosc. 187, 6 (1998)
   
6. T.E. Sharp, H.M. Rosenstock, J.Chem.Phys. 41, 3453 (1964)
   
7. H. Kupka, P.H. Cribb, J.Chem.Phys. 85, 1303 (1986)
   
8. T.R. Faulkner, F.S. Richardson, J.Chem.Phys. 70, 1201 (1979)

The article delves into the complexities of spectroscopy trying to further understand and interpret the features of the spectra that we so far lack a clear understanding of. More specifically the article looks at the absorption spectra of small polyatomic molecules, such as allene, in order to develop mathematical methods in which the absorption spectrum can be calculated in better agreement with experimental results, taking into effect displacements, distortion and the mixing of various modes. Normal mode mixing or rotation is alteration of the character of the normal mode after excitation and is generally called the Duschinsky effect. For the selected molecules the mathematical calculations of these effects combine to give a spectra that indeed corresponds well with experimental results, showing the importance of the Duschinsky effect in order to properly understand experimental spectra and correctly calculate potential energy surfaces.

 

Biographical Information

Cederbaum, Lorenz S. (o.Prof.) 1970 Diplom Physik (Universität München) 1972 Dissertation (Techn. Universität München) 1976 Habilitation (Techn. Universität München) 1976 Professor Universität Freiburg 1979 Cornell University (USA) since 1979 Professor Universität Heidelberg Member of the International Academy of Quantum Molecular Science http://www.pci.uni-heidelberg.de/tc/usr/lenz/

 

The Allene Molecule

H2C=C=CH2

Point group analysis:

D2d	E	2S4	C2	2C2'	2sd
A1	1	1	1	1	1		x2 + y2, z2
A2	1	1	1	-1	-1	Rz
B1	1	-1	1	1	-1		x2 - y2
B2	1	-1	1	-1	1	z	xy
E	2	0	-2	0	0	(x, y);(Rx, Ry)	(xz, yz)
G3N	21	-1	-3	-1	5	3A1+A2+B1+4B2+6E
Gtrans	3	-1	-1	-1	1	B2+E
Grot	3	1	-1	-1	-1	A2+E
Gvib	15	-1	-1	1	5	3A1+B1+3B2+4E
Gstr	6	0	2	0	4	2A1+2B2+E
Gbend	9	-1	-3	1	1	A1+B1+B2+3E

Symmetry elements:
3 C₂ (at right angles), 1 S₄ (coincident with one C₂), 2 s_d (through S₄)

Raman and Infrared Spectra:

Assignment	Raman(liquid) Dnvacuum (cm-1)	Infrared(gas) nvacuum (cm-1)
n11 (e) (C=C=C bending)	353 (m.)
2n11 (A1, B1, B2)	705 (w.)
n4 (b1) (twisting)	820
n10 (e) (C=C=C bending)	838 (m.)
n10 (e) (C=C=C bending)		852 (v.s.)
n9 (e) (CH2 rocking)		1031 (m.)
n3 C=C (a1)	1071 (v.s.)
n4 + n11 (E)		1165 (v.w.)
n7 CH2 (b2)		1389 (s.)
n2 CH2 (a1)	1432 (s.)
2n10 (A1, B1, B2)	1684 (w.)	1700 (m.)
n6 C=C (b2)	1956 (v.w.)	1980 (s.)
n7 + n9 (E)		2420 (w.)
2n2 (A1)	2858 (w.)
n5 CH (b2)		2960 (m.)
n1 CH (a1)	2993 (v.s.)
n8 CH (e)	3061 (s.)	overlapped
n3 + n8 (E)		4200 (v.w.)
3n5 (B2)		8739.0 (w.)
2n1 + n5 (B2)		8776.6 (w.)
?		8922 (v.w.)
2n8 + n5 (B2)		8978 (w.)
2n8 + n1 (B2)		9012 (w.)
3n8 (E, E)		9076.7 (w.)
?		9718 (v.w.)
?		10420 (v.w.)
2n5 + n1+ n6 (B2)		10710 (v.w.)
3n5 + 2n7 (B2) 3n8 + n7+ n9 (B2, B2)		11418 (w.)
5n5 (B2)		13904 (v.w.)

Aldrich Library of FT-IR Spectra:

WebMO using Gaussian94:

	Frequency (cm-1)	Reduced Mass (AMU)	Force Constant (mDyne/A)	IR Intensity (KM/Mole)	Raman Scattering Activity (A4/AMU)	Raman Depolarization Ratio
1	409.9483	2.4986	.2474	4.2341	4.2733	.7500
2	409.9486	2.4986	.2474	4.2341	4.2733	.7500
3	950.8037	1.0078	.5368	.0000	19.0366	.7500
4	998.4197	1.3063	.7672	63.0805	.9936	.7500
5	998.4211	1.3063	.7672	63.0804	.9936	.7500
6	1123.7241	1.5282	1.1369	.3144	.8579	.7500
7	1123.7245	1.5282	1.1369	.3143	.8579	.7500
8	1193.4028	2.5075	2.1041	.0000	78.0606	.3120
9	1567.8077	1.0823	1.5674	.0481	.2492	.7500
10	1631.6148	1.3802	2.1648	.0000	14.0138	.6906
11	2214.4795	8.9774	25.9386	80.0352	.0917	.7500
12	3327.4614	1.0628	6.9331	6.2407	52.0669	.7500
13	3330.2059	1.0588	6.9184	.0000	272.4437	.0450
14	3407.2480	1.1168	7.6390	5.4343	103.1621	.7500
15	3407.2505	1.1168	7.6390	5.4342	103.1619	.7500

Bond Length:

	Hyperchem 6 (AbInitio 6-31G*)	PC Spartan Pro 1.05
C-H	1.07573 Å	1.076 Å
C-C	1.2959 Å	1.296 Å

Bond Angles:

	Hyperchem 6 (AbInitio 6-31G*)	PC Spartan Pro 1.05
H-C-C	121.154o	121.18o 121.18o 121.17o 121.18o
C-C-C	180o	179.98o
H-C-H	117.693o	117.65o 117.65o
Dihedral	89.9999o 90.0001o	89.80o 89.90o

Normal Modes of Vibration (HyperChem 6 SemiEmpirical AM1):

	Frequency (cm-1)	IR Intensity	Symmetry	Degeneracy
n1	375.35	3.176	1E	2
n2	376.48	3.180	1E	2
n3	741.23	0	1B1	1
n4	1012.21	1.774	2E	2
n5	1012.32	1.673	2E	2
n6	1024.43	25.652	3E	2
n7	1024.47	25.581	3E	2
n8	1235.91	0	1A1	1
n9	1377.30	2.252	1B2	1
n10	1483.94	0	2A1	1
n11	2272.59	3.254	2B2	1
n12	3155.83	7.624	4E	2
n13	3155.84	7.616	4E	2
n14	3198.22	38.128	3B2	1
n15	3202.10	0	3A1	1

Hyperchem 6 calculations will yield frequencies that are about 10% high.

 

PC Spartan Pro 1.05

Electron density with electrostatic potential

HOMO

HOMO - 1

LUMO

LUMO + 1

 

Hyperchem 6

HOMO

HOMO -1

LUMO

LUMO + 1

n1

n2

n3

n4

n5

n6

n7

n8

n9

n10

n11

n12

n13

n14

n15