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.

SECOND (PLANAR) MOMENTS AND THEIR APPLICATIONS IN SPECTROSCOPY

Robert K. Bohn1, John A. Montgomery, Jr.2, H. Harvey Michels2, Jason Byrd2

1. Univ. of Connecticut, Dept. of Chemistry2. Univ. of Connecticut, Dept. of Physics.

WH03 June 19, 2013

Second Moments and Applications 0. Joke

1. 2nd moment definitions

2. Structure relationships from 2nd moments vs. rotational constants

3. Number of independent parameters from isotopologs

4. 2nd moments and scaling 5. -CH2-, -CH3 groups: standard values and applications

6. Isopropyl groups: standard values and applications

7. Phenyl groups: standard values and applications

8. -CF2-, -CF3 groups: standard values and applications

Second MomentsJ. Kraitchman, Am. J. of Phys. 21 (1953) 17

Moment of inertia: Ia = mi (bi2 + ci

2), etc. Sum of mass times distance from the a axis squared, Ia < Ib < Ic

Rotational constant: A(s-1) = h / (82Ia),

A(MHz) = 505379.05/Ia(uÅ2), etc., for B and C

Second moment: Paa = (Ib + Ic – Ia)/2 = mi ai2, etc. for Pbb and Pcc.

Sum of mass times distance along the a axis (or from the bc plane) squared

Inertial defect: = Ic – Ia – Ib = -2 Pcc (0 for planar molecule)

N NN

O

N

O

NN

PiperidinesPyrrolidines

Morpholines

PyrCHO PyrNO PipCHO PipNO MorCHO MorNO

CO H C

OH

CO

H

NO N

ON

O

A 6097.201 6061.41 3876.798 3885.0 4226.363 4265.363

B 1957.506 2077.557 1557.793 1623.354 1551.864 1610.575

C 1570.705 1650.531 1237.498 1276.971 1244.250 1277.806

Paa 248.52 233.04 301.22 288.50 306.13 295.41

Pbb 73.23 73.16 107.16 107.26 100.05 100.10

Pcc 9.65 10.22 23.20 22.82 19.53 18.38

a

b

Bisected form = 0o

Perpendicular form = 90o

1

6 5

4

32

7

H

9

8

7

H

9

8

H

89

5,6

3,2

89

413,25,6

2 3

56

Table 4. Rotational constants and second moments of Cyclopropyl Benzene and its 13C Isotopologs.Rot.Const. Parent 13C1

13C213C6

13C713C3

13C513C4

13C8/9

A/MHz 4228.7369(4)* 4226.15(4) 4190.07(2) 4170.11(11) 4215.10(3) 4166.43(3) 4193.80(2) 4225.39(4) 4207.57(3)B/MHz 1108.1111(1) 1108.0905(2) 1107.9552(1) 1106.6538(4) 1101.8516(1) 1101.6445(2) 1097.0567(1) 1092.2242(2) 1090.4263(2)C/MHz 943.9661(1) 943.8275(2) 941.9146(1) 939.9710(4) 938.7546(1) 936.1569(3) 934.2059(1) 932.2520(2) 931.9663(2)

Paa/uÅ2 435.97 435.98 436.03 436.57 438.56 438.65 440.57 442.60 442.82Pbb/uÅ2 99.41 99.48 100.51 101.09 99.79 101.20 100.40 99.50 99.46 Pcc/uÅ2 20.10 20.10 20.10 20.10 20.11 20.10 20.10 20.10 20.66

c

Second moment: Paa = (Ib + Ic – Ia)/2 = mi ai2, etc.

Sum of mass times distance along the a axis (or from the bc plane) squared

Scaling Multiply each model coordinate, ai , by [Paa(obs)/Paa(calc)]1/2 and the new set of ai coordinates now will reproduce Paa(obs)

Repeat for bi and ci. 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)

3 4 5 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 1428.9502(2) 1435.626B/MHz 593.32878(6) 593.583C/MHz 546.43577(6) 547.162

Paa/uÅ2 711.4812 711.507 Pbb/uÅ2 213.3838 212.130 Pcc/uÅ2 140.2878 139.897

*PBE0/VTZ

In this example, the ai, bi, and ci coordinates were produced by a PBE0/VTC density functional calculation of the AG conformation of 1H-nonafluorobutane, C4HF9. Scale factors for each principal axis.  Sa = [Paa(obs)/Paa(model)]1/2 = [(711.4812)/(711.507)]1/2

= [0.99996374] 1/2 = 0.9999818 Sb = [Pbb(obs)/Pbb(model)]1/2 = [(213.3838)/(212.130)]1/2

= [1.0059105] 1/2 = 1.0029510 Sc = [Pcc(obs)/Pcc(model)]1/2 = [(140.2878)/(139.897)]1/2

= [1.002793)] 1/2 = 1.0013958 Paa(model) = m1 a1

2 + m2 a22 + … m14 a14

2 = 711.507 Paa(model)(Sa

2) = m1 (a1Sa)2 + m2 (a2Sa)2 + … m14 (a14Sa)2 = = [m1 a1

2 + m2 a22… + m14 a14

2](Sa2) = 711.4812

= Paa(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 1428.9502(2) 1435.626 1428.962B/MHz 593.32878(6) 593.583 593.328C/MHz 546.43577(6) 547.162 546.436

Paa/uÅ2 711.4812 711.507 711.483Pbb/uÅ2 213.3838 212.130 213.381Pcc/uÅ2 140.2878 139.897 140.287

*PBE0/VTZ

-CH2-/-CH3 groups 1.56 uÅ2

*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 = 4.692 (all anti) (4.69/3 = 1.57)butyl cyanide, Pcc = 6.286 (all anti) (6.29/4 = 1.57) 1-hexyne, Pcc = 6.2689 (all anti) (6.27/4 = 1.57)pentane, Pcc = 7.90 (all anti) (7.90/5 = 1.58)anisole, Pcc = 1.70 1.70p-anisaldehyde, Pcc = 1.81 (anti), 1.80 (syn) 1.81, 1.803-hexyne, Pcc = 7.31 (7.31/4 = 1.83)*3-heptyne, Pcc = 8.86 (all anti), (8.86/5 = 1.77) propargyl benzene Pcc = 2.20 2.20benzyl cyanide, Pcc = 2.13 2.13

a

c

Applications of CH2/CH3 2nd moments S-methyl thiochloroformate 35ClCOSCH3

ABC: 6986.1 2033.35 1590.28 Paa, Pbb, Pcc: 247.00 70.79 1.55

Pcc = 1.55 Heavy-atom-planar 

Ethyl Cyanoformate NCCOOCH2CH3 ABC of Conf. 1: 6453.3 1500.47 1236.36 Paa, Pbb, Pcc: 333.63 75.13 3.18*   ABC of Conf. 2: 6787.8 1549.38 1406.80 Paa, Pbb, Pcc: 305.48 53.76 20.70   * Conf. 1: Pcc = 3.18 or 1.59 per CH2/CH3, Heavy-atom-planar, Cs symmetry 

a

c

a

c

-CH(CH3)2 (Isopropyl) Second Moments, 55 uÅ2

 *(CH3)2CHF (2-fluoropropane) Paa = 54.9*(CH3)2CF2 (2,2-difluoropropane) Pbb = 55.0(CH3)2CHOH (2-propanol) Paa = 54.7(CH3)2CHSH (2-propanthiol) Pbb = 54.8(CH3)2CHCN (2-cyanopropane) Pbb = 55.2(CH3)2CHCCH (3-methyl-1-butyne) Pbb = 54.9*(CH3)2CHC6H4CHO (p-Isopropyl benzaldehyde)

Pcc = 55.5 (syn) Pcc = 55.5 (anti)

(Isopropyl group straddles phenyl ring)a

b

c

b

a

c

c

a

Applications of isopropyl 2nd moments: 2-methylbutane CH3CH2CH(CH3)2

Pbb=57.60 [55(isopropyl)+2(1.6)=58.2]

2-methylpentane CH3CH2CH2CH(CH3)2

Pcc=59.27[55(isopropyl)+3(1.6)=59.8] 

6-methyl-3-heptyne (isobutyl ethyl acetylene) CH3CH2C≡CCH2CH(CH3)2

Pcc = 60.00 [55(isopropyl) + 3(1.6) =59.8] 

Isopropyl Fluoroformate FCOOCH(CH3)2 Pcc = 27.07 and not 55. C1 symmetry

a

b

a

c

a

c

a

c

-C6H5 (phenyl) Pbb = 89.2 uÅ2

 Phenylacetylene, Pbb = 89.01

Chlorobenzene, Pbb = 89.12

Cyanobenzene, Pbb = 89.40

Isocyanobenzene, Pbb = 89.34

a

a

b

b

Applications of Phenyl Second moments: Ethyl benzene; Pbb = 91.46 [89.2 + 2(1.6) = 92.4] Benzyl fluoride; Pbb = 90.57

[89.2 + 1.6 = 90.8](C-F bond orthogonal to phenyl)

Propargyl benzene; Pbb = 114.727 C6H5CH2C≡CH Pcc = 2.196

 Benzyl Alcohol

Pbb = 92.57 [90.8 if C-O bond orthogonal]Pcc = 12.63 [1.6 if heavy-atom-planar](C-O bond IS NEITHER orthogonal to phenyl nor heavy-atom-planar)

 Isobutyl benzene Pbb = 143.7

[89.2 + 55 + 1.6 = 145.8]

b

b

a

a

b

a

b

c

b

c

Perfluoromethylene/methyl (-CF2-/-CF3), 45 uÅ2

 C3F8 (C2v) Pcc = 134.34 perfluoropropane (134.34/3 = 44.78)

HCF2CF2CF3 (Cs) Pcc = 135.312 1H-perfluoropropane (135.312/3 = 45.10) 

C5F12 (C2) Pcc = 229.616 perfluoropentane (229.616/5 = 45.92) helical

C6F14 (C2) Pcc = 198.3355 perfluorohexane (198.3355/6 = 46.98) helical CF3(CF2)6CN (C1) Pcc = 341.3318 (341.3318/7 = 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)