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SEMI-EXPERIMENTAL EQULIBRIUM

STRUCTURES; RESULTS FROM DIFFERENTCALULCATIONS OF ALPHAS AND

COMPARISON WITH THEORY

NORMAN C. CRAIG, Department of Chemistry and Biochemistry, Oberlin College,

Oberlin, OH 44074, USA Norm.Craig@oberlin.edu

DAVID FELLER, Department of Chemistry, Washington State University, Pullman, WA99164-4630

PETER GRONER, Department of Chemistry, University of Missouri-Kansas City,

Kansas City, KS 64110-2499

DONALD C. MCKEAN, School of Chemistry, University of Edinburgh, Edinburgh EH9

3JJ, U. K.

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Semi-Experimental Equilibrium Structures

Ground state (GS) rotational constants from high-resolution IR or MW spectra.

Vibration-rotation consts. (Es) from quantum chemical

force fields (Gaussian 03) asa) scaled (s. f.) harmonic, unscaled cubic>VIBROTb) scaled harmonic (m. f.) computed by ASYM40,unscaled cubic >VIBROT

c) computed by Gaussian 03 with no scalingGS rot. consts. Es> equilibrium rot. consts.Structure fit globally to equil. rot. consts. for isotopomers

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Computing Be,kfrom B0,k

Be, k

} B0, k1/ 2 E

k,M

i !1

n

where i indexes vibrational fundamentals and k is forthe a, b, and cdirections of the principal axes ofrotation.At most, the alpha sums contribute a 1% adjustment

to the ground state rotational constants. Thus, atriple-zeta level of theory is sufficient to compute thealpha contributions.

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re

Structures for Butadiene

s-trans 90r Twisted

Semi-expt.Lit.a

Semi-expt. G03dcc alphasb

CCSD(T)extrapol.

CCSD(T)extrapol.

r(C=C)/ 1.338 1.338 1.338 1.333c

r(CC)/ 1.454 1.455 1.455 1.482d

r(CHE)/ 1.085 1.084 1.085 1.085r(CH c)/ 1.082 1.082 1.082 1.082

r(CH t)/ 1.079 1.080 1.080 1.081

E(C=CC)/deg 123.6 123.6 123.5 123.8

E(C=CHE)/deg 119.9 119.7 119.8 119.3

E(C=CHc)/deg 121.0 120.8 121.0 120.2

E(C=CHt)/deg 121.5 121.5 121.5 121.2

a N.C. Craig; P. Groner; D.C. McKean, J. Phys. Chem. A 2006, 110, 7461.b B3LYP/cc-pVTZ model (dcc) with no scaling of harmonic force constants.c Compare with ethylene, re = 1.330 .d Compare with estimate of sp2sp2 = 1.470 estimated from near-equilibriumstructures of ethane and propene.

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90r twist butadiene (transition state)

Boat form of cyclooctatetraene

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Semi-experimental re

Structures for Ethylenea

Lit.b

G03 E'sc

B3LYP/6-311++G**

G03 E'sc

B3LYP/cc-pVTZ

G03 E'sc

MP2/6-311++G**

G03 E'sc

MP2/cc-pVTZ

Ave.(srange)

r(C=C)/ 1.3305 1.3316 1.3318 1.3312 1.3308 1.3314(6)

r(C-H)/ 1.0805 1.0804 1.0805 1.0812 1.0809 1.0808(4)

E(HCH)/ 117.10 117.22 117.22 117.02 117.14 117.1 (1)

E

(CCH)/ 121.45 121.39 121.39 121.49 121.43 121.42(7)

a Ground state rotational constants from MW and IR spectra, as reviewed byN.C. Craig; P. Groner; D.C. McKean, J. Phys. Chem. A 2006, 110, 7461.

bAs reported by CGM, using harmonic force constants fit with multiple scalefactors to compute harmonic contributions to E's with program ASYM40(Mills-Hedberg) and unscaled cubic contributions with program VIBROT(Groner).cAs computed by G03 with no scale factors for force constants.

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1,1-Difluorocyclopropane

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re Structures for 1,1-DifluorocyclopropaneMultiple scalefactorsa

Single ave.scale factorb

G03 with noscalingc dcc

CCSD(T)extrapol.a

r(C-F)/ 1.343 1.343 1.344 1.344r(C-H)/ 1.078 1.078 1.078 1.079

r(C1-C4)/ 1.470 1.470 1.469 1.469

r(C4-C5)/ 1.546 1.546 1.547 1.548

E(FCF)/deg 109.5 109.5 109.3 109.4

E(FCC)/deg 119.4 119.4 119.5 119.4

E(C4C1C5)/deg 63.4 63.4 63.6 63.6

E(C1C4C5)/deg 58.3 58.3 58.2 58.2

E(HCH)/deg 116.7 116.7 116.8 116.6

E(HC4C1)/deg 117.4 117.4 117.4 117.4E(HC4C5)/deg 117.1 117.1 117.1 117.2

a QC force constants fitted to observed (anharmonic) frequencies ford0, d2,and d4 isotopomers for harmonic contributions to alphas. N.C. Craig; D. Feller:H.Y. Hsin; D.C. McKean; D.J. Nemchick J. Phys. Chem .A 2007, 111, 2498.b Single average scale factor from (a) applied to harmonic force constants.

c From G03 with B3LYP/cc-pVTZ model (dcc) with principal axis system for allisotopomers.

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re structure results for3,3-difluorocyclopropeneare comparable to thosereported for cyclopropene.

Semi-Experimental re

Structures for Cyclopropenea

GeometricParameter

G03 E'sb

dccG03 alphasc

4 QC modelsVIBROTalphasd

r(C-C)/ 1.5066 1.5063(4) 1.5056(6)r(C=C)/ 1.2937 1.2936(4) 1.2931(6)

r(-C-H)/ 1.0850 1.0852(3) 1.0851(2)

r(=C-H)/ 1.0723 1.0725(3) 1.0726(4)

E(H-CH)/deg 114.57 114.45(11) 114.44(11)

E(C-C-C)/deg 50.85 50.86(1) 50.86(1)

E(C-C-H)/deg 119.27(5) 119.27(5)

E(=C-H)/deg 149.89 149.90(2) 149.90(2)a Ground state rotational constants for parent and 4 13H and 2Hisotopomers refit with quartic centrifugal distortion constants from

G03 (B3LYP/cc-pVTZ). W.M. Stigliani; V.W. Laurie; J. C. Li J. Chem.Phys. 1975, 62, 1890.bAlphas from G03 calculations without force constant scaling, androt. consts. constants from SLL. B3LYP/cc-pVTZ model (dcc). S.V.Krasnoshchekov; N.F. Stepanov Russ. J. Phys. Chem. 2006, 80, 1448.cAlphas from four QC models: B3LYP and MP2 with cc-pVTZ and6-311++G** basis sets. Average value with range in parentheses.dAlphas from VIBROT program. Harmonic force constants scaled bya single factor. Average value with range in parentheses.

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ConclusionsSemi-experimental re structures are in good agreement with high-level ab initio

structures.

High-level QC calculations for 90r-twisted butadiene give the first reliablelength for the sp2-sp2 bond free of the effect ofT-electron delocalization.

Quickie semi-experimental equilibrium structures are good to s0.002 ands0.2 deg for triple-zeta QC models andwith care taken to calculate rotationalparameters with G03 in the PAS (with work-around).

If the Cartesian coordinates passed to the vib-rot module of G03 are not in thePAS, then the computed alphas (and centrifugal distortion constants) may be

grossly in error. This failure is particularly acute in G03 for molecules likebutadiene, for which the locations of some principal rotational axes are notfixed by symmetry. Compare to a molecule like 1,1-difluorocyclopropane, forwhich symmetry aligns all three principal rotation axes.

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Support

Dreyfus Foundation

National Science Foundation

Oberlin College

Washington State University