SECOND (PLANAR) MOMENTS AND THEIR APPLICATIONS IN SPECTROSCOPY Robert K. Bohn 1, John A. Montgomery, Jr. 2, H. Harvey Michels 2, Jason Byrd 2 1. Univ.

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SECOND (PLANAR) MOMENTS AND THEIR APPLICATIONS IN SPECTROSCOPY Robert K. Bohn 1, John A. Montgomery, Jr. 2, H. Harvey Michels 2, Jason Byrd 2 1. Univ. of Connecticut, Dept. of Chemistry 2. Univ. of Connecticut, Dept. of Physics. WH03 June 19, 2013

Second Moments and Applications 0. Joke 1. 2 nd moment definitions 2. Structure relationships from 2 nd moments vs. rotational constants 3. Number of independent parameters from isotopologs 4. 2 nd moments and scaling 5. -CH 2 -, -CH 3 groups: standard values and applications 6. Isopropyl groups: standard values and applications 7. Phenyl groups: standard values and applications 8. -CF 2 -, -CF 3 groups: standard values and applications

Second Moments J. Kraitchman, Am. J. of Phys. 21 (1953) 17 Moment of inertia: I a =  m i (b i 2 + c i 2 ), etc. Sum of mass times distance from the a axis squared, I a < I b < I c Rotational constant: A(s -1 ) = h / (8  2 I a ), A(MHz) = /I a (uÅ 2 ), etc., for B and C Second moment: P aa = (I b + I c – I a )/2 =  m i a i 2, etc. for P bb and P cc. Sum of mass times distance along the a axis (or from the bc plane) squared Inertial defect:  = I c – I a – I b = -2 P cc (0 for planar molecule)

A B C P aa P bb P cc a b

Table 4.Rotational constants and second moments of Cyclopropyl Benzene and its 13 C Isotopologs. Rot.Const.Parent 13 C 1 13 C 2 13 C 6 13 C 7 13 C 3 13 C 5 13 C 4 13 C 8/9 A/MHz (4)* (4) (2) (11) (3) (3) (2) (4) (3) B/MHz (1) (2) (1) (4) (1) (2) (1) (2) (2) C/MHz (1) (2) (1) (4) (1) (3) (1) (2) (2) P aa /uÅ P bb /uÅ P cc /uÅ c

Second moment: P aa = (I b + I c – I a )/2 =  m i a i 2, etc. Sum of mass times distance along the a axis (or from the bc plane) squared Scaling Multiply each model coordinate, a i, by [P aa (obs)/P aa (calc)] 1/2 and the new set of a i coordinates now will reproduce P aa (obs) Repeat for b i and c i. The scaled set of coordinates reproduce the observed second moments (or rotational constants).

1H-Nonafluorobutane 1 2 CCCC anti/CCCH gauche CCCC anti/CCCH anti (0.0 kcal/mol, ass'd) (0.4 kcal/mol, ass'd) CCCCgauche/CCCHgauche CCCCgauche/CCCHanti CCCCgauche/CCCHgauche (cis, 0.8 kcal/mol, ass’d) (0.8 kcal/mol, ass’d) (trans, 1.1 kcal/mol) a b

Spectroscopic Constants of 1H-nonafluorobutane Conf. 1(Anti/Gauche) Not shown: Conf's 2(AA), 3(GA), 4(GGcis) Parameter Obs'd Calc'd* A/MHz (2) B/MHz (6) C/MHz (6) P aa /uÅ P bb /uÅ P cc /uÅ *PBE0/VTZ

In this example, the a i, b i, and c i coordinates were produced by a PBE0/VTC density functional calculation of the AG conformation of 1H-nonafluorobutane, C 4 HF 9. Scale factors for each principal axis. S a = [P aa (obs)/P aa (model)] 1/2 = [( )/( )] 1/2 = [ ] 1/2 = S b = [P bb (obs)/P bb (model)] 1/2 = [( )/( )] 1/2 = [ ] 1/2 = S c = [P cc (obs)/P cc (model)] 1/2 = [( )/( )] 1/2 = [ )] 1/2 = P aa (model) = m 1 a m 2 a … m 14 a 14 2 = P aa (model)(S a 2 ) = m 1 (a 1 S a ) 2 + m 2 (a 2 S a ) 2 + … m 14 (a 14 S a ) 2 = = [m 1 a m 2 a 2 2 … + m 14 a 14 2 ](S a 2 ) = = P aa (obs) Similarly, repeat for the b and c coordinates of each atom. Note that scaling does not move the center of mass nor the principal axes.

Spectroscopic Constants of 1H-nonafluorobutane Conf. 1(Anti/Gauche) Not shown: Conf's 2(AA), 3(GA), 4(GGcis) Parameter Obs'd Calc'd* (Calc'd) * (Scale Factors) A/MHz (2) B/MHz (6) C/MHz (6) P aa /uÅ P bb /uÅ P cc /uÅ *PBE0/VTZ

-CH 2 -/-CH 3 groups 1.56 uÅ 2 *propane, Pcc = 4.69 (4.69/3 = 1.56) 1-fluorobutane, Pcc = 6.39 (all anti) (6.39/4 = 1.60) 1-chlorobutane, Pcc = 6.32 (all anti) (6.32/4 = 1.58) *5-hexynenitrile, Pcc = (all anti) (4.69/3 = 1.57) butyl cyanide, Pcc = (all anti) (6.29/4 = 1.57) 1-hexyne, Pcc = (all anti) (6.27/4 = 1.57) pentane, Pcc = 7.90 (all anti) (7.90/5 = 1.58) anisole, Pcc = p-anisaldehyde, Pcc = 1.81 (anti), 1.80 (syn) 1.81, hexyne, Pcc = 7.31 (7.31/4 = 1.83) *3-heptyne, Pcc = 8.86 (all anti), (8.86/5 = 1.77) propargyl benzene Pcc = benzyl cyanide, Pcc = a c

Applications of CH 2 /CH 3 2 nd moments S-methyl thiochloroformate 35 ClCOSCH 3 ABC: P aa, P bb, P cc : P cc = 1.55 Heavy-atom-planar Ethyl Cyanoformate NCCOOCH 2 CH 3 ABC of Conf. 1: P aa, P bb, P cc : * ABC of Conf. 2: P aa, P bb, P cc : * Conf. 1: P cc = 3.18 or 1.59 per CH 2 /CH 3, Heavy-atom-planar, C s symmetry a c a c

-CH(CH 3 ) 2 (Isopropyl) Second Moments, 55 uÅ 2 *(CH 3 ) 2 CHF (2-fluoropropane)P aa = 54.9 *(CH 3 ) 2 CF 2 (2,2-difluoropropane)P bb = 55.0 (CH 3 ) 2 CHOH (2-propanol)P aa = 54.7 (CH 3 ) 2 CHSH(2-propanthiol)P bb = 54.8 (CH 3 ) 2 CHCN (2-cyanopropane)P bb = 55.2 (CH 3 ) 2 CHCCH (3-methyl-1-butyne) P bb = 54.9 *(CH 3 ) 2 CHC 6 H 4 CHO (p-Isopropyl benzaldehyde) P cc = 55.5 (syn) P cc = 55.5 (anti) (Isopropyl group straddles phenyl ring) a b c b a c c a

Applications of isopropyl 2 nd moments: 2-methylbutane CH 3 CH 2 CH(CH 3 ) 2 P bb =57.60 [55(isopropyl)+2(1.6)=58.2] 2-methylpentane CH 3 CH 2 CH 2 CH(CH 3 ) 2 P cc =59.27[55(isopropyl)+3(1.6)=59.8] 6-methyl-3-heptyne (isobutyl ethyl acetylene) CH 3 CH 2 C≡CCH 2 CH(CH 3 ) 2 P cc = [55(isopropyl) + 3(1.6) =59.8] Isopropyl Fluoroformate FCOOCH(CH 3 ) 2 P cc = and not 55. C 1 symmetry a b a c a c a c

-C 6 H 5 (phenyl) P bb = 89.2 uÅ 2 Phenylacetylene, P bb = Chlorobenzene, P bb = Cyanobenzene, P bb = Isocyanobenzene, P bb = a a b b

Applications of Phenyl Second moments: Ethyl benzene; P bb = [ (1.6) = 92.4] Benzyl fluoride;P bb = [ = 90.8] (C-F bond orthogonal to phenyl) Propargyl benzene; P bb = C 6 H 5 CH 2 C≡CH P cc = Benzyl Alcohol P bb = [90.8 if C-O bond orthogonal] P cc = [1.6 if heavy-atom-planar] (C-O bond IS NEITHER orthogonal to phenyl nor heavy-atom-planar) Isobutyl benzene P bb = [ = 145.8] b b a a b a b c b c

Perfluoromethylene/methyl (-CF 2 -/-CF 3 ), 45 uÅ 2 C 3 F 8 (C 2v ) P cc = perfluoropropane (134.34/3 = 44.78) HCF 2 CF 2 CF 3 (C s ) P cc = H-perfluoropropane ( /3 = 45.10) C 5 F 12 (C 2 ) P cc = perfluoropentane ( /5 = 45.92) helical C 6 F 14 (C 2 ) P cc = perfluorohexane ( /6 = 46.98) helical CF 3 (CF 2 ) 6 CN (C 1 ) P cc = ( /7 = 48.76) Perfluoroheptyl cyanide (helical) c b b c

Acknowledgments David Lide (NBS, NIST) Joseph Fournier (UConn, Yale) Stewart Novick (Wesleyan) Pete Pringle " Herb Pickett " Steve Cooke" and SUNY at Purchase)