appendices_w2.doc 108KB Jun 05 2011 09:30:46 PM

(1)

[image:1.612.72.546.160.547.2]

Table I. Force Constants and Reference Values in the QMFF for Amides A. Bond length

E = 2K

b

_{(b - b0)2 + 3K}

b

_{(b - b0)}3 + 4K

b

_{(b - b0)}4

b0 2K

b

3K

b

4K

b

bond _(Å) (kcal mol-1 Å-2) (kcal mol-1 Å-3) (kcal mol-1 Å-4) C'-O' 1.19201124.2 -2568.6

C'-N 1.3983 443.4

1415.3

C'-H 1.0934

-780.5 896.3

C-N 1.4416403.9-676.4 650.0

H*-N 1.0015

-1300.8 1908.3

C-C' 1.5103

-522.3 490.0

H-C 1.0845

-851.3 1040.0

C-C 1.5297

-586.1 758.0

B. Bond angle

E = 2K

q

_{(q - q0)}2 + 3K

q

_{(q - q0)}3 + 4K

q

_{(q - q0)}4

q0 2K

q

3K

q

4K

q

(2)

N-C'-O' 124.5 115.2 -41.0 -13.3

H-C'-O' 117.8 54.7 -26.8 0.0

H-C'-N 110.4 62.1 -22.0 0.0

C-N-C' 111.0 38.0 -8.0 -8.1

C'-N-H* 117.0 44.6 -9.7 0.0

C-N-H* 113.9 54.7 -23.9 0.0

C-C-N 114.3 50.8 -12.6 -11.1

H-C-N 108.9 68.3 3.5 0.0

C-C'-O 123.1 66.1 -20.5 0.2

C-C'-N 116.9 46.9 -13.1 -10.4

H*-N-H* 112.9 46.7 -11.3 0.0

C-C-C' 108.5 61.9 -11.3 -13.1

C'-C-H 107.7 48.3 -34.3 0.0

C-N-C 111.6 47.2 -10.2 -10.1

C'-C-N 100.6 62.0 -6.3 -12.7

N-C'-N 122.5 123.9 -43.7 -28.9

C'-N-C' 122.0 90.8 -31.3 -21.1

H-C-H 107.7 51.5 -8.9 -10.8

H-C-C 110.8 52.7 -10.9 -11.3

C. Torsion angle

E = 1K

f

_{(1 - cosf) +}2K

f

_{(1 - cos2f)} + 3K

f

_{(1 - cos3f)}

1K

f

2K

f

3K

f

torsion (kcal mol-1) (kcal mol-1) (kcal mol-1)

O'-C'-N-C 0.830 3.723 -0.050

O'-C'-N-H* -1.882 3.043 -0.373

H-C'-N-C 0.334 2.584 -0.401

(3)

C-C-N-C' 0.020 -0.019 0.013

H-C-N-C' 0.031 -0.037 -0.058

C-C-N-H* -0.069 -0.011 -0.002

H-C-N-H* -0.021 -0.113 -0.175

C-C-C-N 0.108 0.080 -0.287

H-C-C-N -0.025 0.031 -0.207

C-C'-N-H* -0.915 2.385 -0.238

C-C-C'-O' 0.063 0.042 0.080

H-C-C'-O' -0.258 0.002 0.053

C-C-C'-N -0.053 0.056 -0.076

H-C-C'-N 0.241 -0.013 -0.098

C-C-C-C' 0.108 0.080 -0.287

C'-C-C-H -0.025 0.031 -0.207

C-C-N-C -0.002 -0.010 0.001

H-C-N-C 0.058 0.051 -0.236

C'-C-C-C' 0.108 0.080 -0.287

C'-C-C-N 0.108 0.080 -0.287

C'-C-N-C' -0.098 0.109 -0.088

C'-C-N-H* 0.078 0.108 0.104

N-C-C'-O' 0.128 0.174 0.129

N-C-C'-N -0.127 0.180 -0.126

C-C'-N-C -0.753 2.739 0.090

C'-C-N-C -0.005 0.007 0.006

N-C'-N-H* -0.818 0.516 -1.233

O'-C'-N-C' -0.452 1.390 -0.834

H-C'-N-C' 0.212 1.246 0.047

H-C-C-H -1.152 0.012 -0.179

(4)

2K

c

out-of-plane (kcal mol-1 rad-2)

H-C'-N-O' 42.126

C-N-C'-H* 1.250

C-C'-N-O' 44.242

C'-N-H*-H* 0.000

C-N-C-C' 4.247

N-C'-N-O' 49.203

C'-N-C'-H* 0.000

E. Van der Waals interaction

E = e [2(r*/r)9 - 3(r*/r)6] where r* = [(r

i

*6 + r

j

*6) /2] 1/6

and e = (e

i

_{ej) 1/2 2 (r}

i

*r

j

*)3/(r

i

*6 + r

j

*6)

r

i

* e

i

atom (Å) (kcal mol-1)

H* 1.098 0.013

O' 3.535 0.267 C' 3.308 0.120

N 4.070 0.106

H 2.995 0.020

C 4.010 0.054

(5)

E = 332.0 q

i

q

j

/ r

ij

; where q

i

=

d

ik

. Each d

ik

_{donates positive charge to the first atom listed and corresponding negative charge} to the second atom.

d

ik

bond _(electrons)

C'–O' 0.396

C–N 0.211

H*–N 0.440

C'–N 0.000

H–C' 0.046 C'–C 0.000

H–C 0.053

C–C 0.000

G. Bond/bond

E = K

bb'

_{(b - b0)(b' - b'0)}

K

bb'

bond/bond (kcal mol-1 Å-2)

O'-C'/C'-N 200.718

O'-C'/C'-H 61.122 N-C'/C'-H 4.058 C'-N/N-C 17.563 C'-N/N-H* -6.250 C-N/N-H* -5.030 N-C/C-C 5.137

(6)

C-C'/C'-O 66.766

C-C'/C'-N -9.389

N-H*/H*-N -0.820

C'-C/C-C 7.855

C'-C/C-H 1.031

N-C/C-N -2.171

N-C/C-C' -5.558

N-C'/C'-N 37.613

H-C/H-C 11.769

H-C/C-C 11.310

H. Bond/angle

E = K

bq

_{(b - b0)(q - q0)}

K

bq

bond/angle (kcal mol-1Å-1rad-1)

C'-O'/N-C'-O' 75.9

C'-N/N-C'-O' 90.9

C'-O'/H-C'-O' 71.1

C'-H/H-C'-O' 22.1

C'-N/H-C'-N 45.4

C'-H/H-C'-N 32.4

C'-N/C-N-C' 21.5

C-N/C-N-C' 5.5

C'-N/C'-N-H* 42.9

H*-N/C'-N-H* 15.7

C-N/C-N-H* 17.2

H*-N/C-N-H* 8.6

C-N/C-C-N 6.7

C-C/C-C-N -7.9

(7)

C-H/H-C-N 15.5

C'-O'/C-C'-O' 53.8

C-C'/C-C'-O' 50.7

C'-N/C-C'-N 8.8

C-C'/C-C'-N 36.8

H*-N/H*-N-H* 28.7

C-C'/C-C-C' 23.0

C-C/C-C-C' 26.3

C-C'/C'-C-H 18.1

C-H/C'-C-H 13.3

C-N/C-N-C -3.0

C-N/C'-C-N 25.2

C-C'/C'-C-N -7.5

C'-N/N-C'-N 98.7

C'-N/C'-N-C' 29.1

H-C/H-C-H 22.7

H-C/H-C-C 13.9

C-C/H-C-C 34.5

I. Angle/angle

E = K

qq'

_{(q - q0)( q' - q'0)}

K

qq

_’ angle/angle common bond (kcal mol-1rad-2)

C-C-N/H-C-N C-N -1.00

C-C-H/C-C-N C-C -4.88

H-C-N/H-C-N C-N 3.71

C-C-H/H-C-N C-H -1.29

(8)

C-C-C'/C'-C-H C-C' 2.96

C-C-C'/C-C-H C-C -2.64

C'-C-H/C'-C-H C-C' -5.07

C-C-H/C'-C-H C-H 1.57

C'-C-H/H-C-H C-H -4.91

C-C-N/C-C-N C-N -0.72

C-C-C/C-C-N C-C 0.22

C'-C-N/H-C-N C-N 4.39

C'-C-H/C'-C-N C-C' 0.08

C'-C-H/H-C-N C-H -2.39

C-C-C'/C'-C-N C-C' 8.24

C-C-N/C'-C-N C-N 5.76

C-C-C'/C-C-N C-C -1.23

H-C-H/H-C-H H-C 0.93

H-C-H/H-C-C H-C 1.57

H-C-C/H-C-C H-C 3.12

H-C-C/H-C-C C-C -2.18

J. Angle/angle/torsion

E = K

fqq’

_{(q - q0)( q' - q'0) cosf}

K

fqq

_' angle/angle/torsion (kcal mol-1rad-2) N-C'-O'/C-N-C'/O'-C'-N-C -22.5

(9)

H-C-N/C-N-H*/H-C-N-H* -9.7

C-C-C/C-C-N/C-C-C-N -1.5

C-C-H/C-C-N/H-C-C-N -18.5

C-C'-N/C'-N-H*/C-C'-N-H* -1.9 C-C-C'/C-C'-O'/C-C-C'-O' -11.6 C'-C-H/C-C'-O'/H-C-C'-O' -22.2 C-C-C'/C-C'-N/C-C-C'-N -7.9 C'-C-H/C-C'-N/H-C-C'-N -17.7 C-C-C/C-C-C'/C-C-C-C' -0.6 C-C-C'/C-C-H/C'-C-C-H -7.8

C-C-N/C-N-C/C-C-N-C -2.5

H-C-N/C-N-C/H-C-N-C -17.7

C-C-C'/C-C-C'/C'-C-C-C' 0.2

C-C-C'/C-C-N/C'-C-C-N 0.5

C'-C-N/C-N-C'/C'-C-N-C' -13.4 C'-C-N/C-N-H*/C'-C-N-H* -1.4 C'-C-N/C-C'-O'/N-C-C'-O' -9.5 C'-C-N/C-C'-N/N-C-C'-N -2.6 C-C'-N/C-N-C'/C-C'-N-C -9.5

C'-C-N/C-N-C/C'-C-N-C 0.2

N-C'-N/C'-N-H*/N-C'-N-H* -2.2 N-C'-O'/C'-N-C'/O'-C'-N-C' -4.9 H-C'-N/C'-N-C'/H-C'-N-C' -1.1

H-C-C/H-C-C/H-C-C-H -14.8

K. Bond/torsion(Type 1)

E = (b - b0) [1K

fb

cosf + 2K

fb

cos2f + 3K

fb

cos3f]

1K

fb

2K

fb

3K

fb

bond/torsion (kcal mol-1Å-1) (kcal mol-1Å-1) (kcal mol-1Å-1)

C'-N/O'-C'-N-C -12.797 20.736 -2.568

(10)

C'-N/H-C'-N-C -16.993 4.645 -4.365

C'-N/H-C'-N-H* -1.399 7.542 -3.346

C-N/C-C-N-C' -5.725 -0.580 -0.985

C-N/H-C-N-C' -0.100 -3.282 1.678

C-N/C-C-N-H* -5.131 -4.908 0.051

C-N/H-C-N-H* -1.703 4.066 1.171

C-C/C-C-C-N -6.134 -4.786 -1.919

C-C/H-C-C-N -5.946 -0.861 -0.068

C'-N/C-C'-N-H* -0.768 6.863 -1.542

C-C'/C-C-C'-O' 0.491 -0.159 0.177

C-C'/H-C-C'-O' 0.342 1.324 1.390

C-C'/C-C-C'-N -2.907 -2.236 2.767

C-C'/H-C-C'-N 0.333 -0.601 1.160

C-C/C-C-C-C' -2.311 0.328 -1.002

C-C/C'-C-C-H -5.078 1.806 -1.103

C-N/C-C-N-C -6.822 -1.530 -4.325

C-N/H-C-N-C -3.323 0.472 1.400

C-C/C'-C-C-C' 2.139 0.848 -0.270

C-C/C'-C-C-N -1.770 -5.899 -4.924

C-N/C'-C-N-C' -6.875 -7.398 -7.869

C-N/C'-C-N-H* -2.104 5.859 -0.765

C-C'/N-C-C'-O' -6.527 7.099 0.619

C-C'/N-C-C'-N -6.327 -3.236 -7.968

C'-N/C-C'-N-C -13.408 4.941 -4.111

C-N/C'-C-N-C 1.828 -5.164 -4.479

C'-N/N-C'-N-H* -1.803 -6.429 3.201

C'-N/O'-C'-N-C' -0.162 -1.738 0.983

C'-N/H-C'-N-C' -0.699 -0.856 -1.197

C-C/H-C-C-H -16.582 -0.784 -0.901

L. Bond/torsion(type 2)

(11)

1K

fb'

2K

fb'

3K

fb'

bond/torsion _{(kcal mol}-1Å-1) (kcal mol-1Å-1) (kcal mol-1Å-1)

C'-O'/O'-C'-N-C 0.178 -3.091 0.809

C-N/O'-C'-N-C 0.232 1.051 -0.146

C'-O'/O'-C'-N-H* -1.102 -3.831 1.807

H*-N/O'-C'-N-H 0.176 0.281 0.118

C'-H/H-C'-N-C -0.859 -0.007 0.215

C-N/H-C'-N-C -0.773 0.830 -0.094

C'-H/H-C'-N-H* -0.372 0.693 0.517

H*-N/H-C'-N-H* 0.143 0.808 0.170

C'-N/C-C-N-C' -0.180 -1.358 1.128

C-C/C-C-N-C' -0.295 0.005 0.081

C'-N/H-C-N-C' 0.332 1.700 -0.084

C-H/H-C-N-C' -0.531 1.188 0.194

H*-N/C-C-N-H* -0.144 -0.105 -0.600

C-C/C-C-N-H* 0.191 0.002 0.192

H*-N/H-C-N-H* -0.709 0.238 0.450

C-H/H-C-N-H* -1.302 0.410 0.128

C-N/C-C-C-N -0.115 -0.059 0.037

C-C/C-C-C-N 0.108 0.015 0.075

C-N/H-C-C-N 0.438 0.364 0.673

C-H/H-C-C-N -0.087 -0.545 -0.272

C-C'/C-C'-N-H* -1.011 0.814 0.610

H*-N/C-C'-N-H* 0.929 0.243 0.209

C'-O'/C-C-C'-O' -0.407 0.118 -0.221

C-C/C-C-C'-O' 0.385 0.073 0.152

C'-O'/H-C-C'-O' -0.333 0.051 0.558

C-H/H-C-C'-O' 1.760 0.410 0.568

C'-N/C-C-C'-N -0.399 -0.443 -0.256

C-C/C-C-C'-N -0.381 -0.011 -0.166

(12)

C-H/H-C-C'-N -0.039 1.136 0.005

C-C'/C-C-C-C' 0.008 0.009 -0.001

C-C/C-C-C-C' 0.009 0.000 0.005

C-C'/C'-C-C-H -0.030 0.526 -0.642

C-H/C'-C-C-H -0.014 -0.046 -0.109

C-N/C-C-N-C -0.119 -0.011 -0.135

C-C/C-C-N-C -0.181 -0.164 -0.112

C-N/H-C-N-C 0.181 0.470 -0.108

C-H/H-C-N-C -1.954 1.159 0.979

C-C'/C'-C-C-C' 0.008 -0.001 -0.006

C-N/C'-C-C-N -0.244 -0.214 -0.214

C-C'/C'-C-C-N -0.191 -0.161 -0.168

C'-N/C'-C-N-C' -0.645 0.617 -0.631

C-C'/C'-C-N-C' -0.259 0.311 -0.406

H*-N/C'-C-N-H* 1.305 0.430 0.085

C-C'/C'-C-N-H* 0.158 0.487 0.134

C-N/N-C-C'-O' -0.110 0.379 0.234

C'-O'/N-C-C'-O' 1.456 -0.479 0.945

C-N/N-C-C'-N -0.252 0.104 -0.865

C'-N/N-C-C'-N -0.018 0.028 -1.389

C-C'/C-C'-N-C 0.135 -0.671 0.418

C-N/C-C'-N-C 0.333 -0.165 -0.206

C-N/C'-C-N-C 0.026 -0.131 -0.117

C-C'/C'-C-N-C 0.097 -0.115 -0.134

H*-N/N-C'-N-H* -0.707 -1.033 0.191

C'-N/N-C'-N-H* 0.112 -0.767 -0.006

C'-O'/O'-C'-N-C' -1.017 1.204 -0.996

C'-N/O'-C'-N-C' 0.250 -0.699 0.386

C'-N/H-C'-N-C' -0.306 -0.609 -0.330

(13)

M. Angle/torsion

E = (q - q0) [1K

fq

cosf + 2K

fq

cos2f + 3K

fq

cos3f]

1K

fq

2K

fq

3K

fq

angle/torsion (kcal mol-1rad-1) (kcal mol-1rad-1) (kcal mol-1rad-1)

N-C'-O'/O'-C'-N-C 6.444 5.843 2.482

C-N-C'/O'-C'-N-C 10.787 3.117 -0.320

N-C'-O'/O'-C'-N-H* -3.803 0.523 0.793

C'-N-H*/O'-C'-N-H* 6.115 1.803 0.359

H-C'-N/H-C'-N-C 0.197 4.539 0.310

C-N-C'/H-C'-N-C 8.960 -0.511 -0.311

H-C'-N/H-C'-N-H* -3.163 2.963 -0.211

C'-N-H*/H-C'-N-H* 5.694 1.463 -0.046

C-N-C'/C-C-N-C' -2.207 1.637 1.039

C-C-N/C-C-N-C' -1.095 0.082 1.765

C-N-C'/H-C-N-C' 0.054 -0.495 -0.112

H-C-N/H-C-N-C' -2.197 3.012 0.777

C-N-H*/C-C-N-H* -1.489 0.523 -0.355

C-C-N/C-C-N-H* -4.198 3.925 -0.054

C-N-H*/H-C-N-H* -0.992 0.523 0.114

H-C-N/H-C-N-H* -5.365 2.011 0.347

C-C-N/C-C-C-N 0.295 0.232 -1.152

C-C-C/C-C-C-N -0.797 -2.461 0.360

C-C-N/H-C-C-N -2.872 0.337 -0.569

C-C-H/H-C-C-N -1.807 2.454 -1.751

C-C'-N/C-C'-N-H* -3.208 1.871 1.410

C'-N-H*/C-C'-N-H* 4.950 0.540 0.143

C-C'-O'/C-C-C'-O' 0.978 0.864 0.975

C-C-C'/C-C-C'-O' 0.128 -1.986 -0.790

C-C'-O'/H-C-C'-O' -2.166 1.059 -0.302

(14)

C-C'-N/C-C-C'-N 3.076 0.729 -0.111

C-C-C'/C-C-C'-N 3.160 -0.049 -2.002

C-C'-N/H-C-C'-N 2.900 0.735 1.218

C'-C-H/H-C-C'-N 10.283 0.011 1.001

C-C-C'/C-C-C-C' 0.075 -0.098 -0.069

C-C-C/C-C-C-C' -0.378 0.464 -0.331

C-C-C'/C'-C-C-H -1.082 -1.369 -0.916

C-C-H/C'-C-C-H 0.023 2.060 -2.042

C-N-C/C-C-N-C 1.874 2.990 -0.223

C-C-N/C-C-N-C -0.417 2.571 0.397

C-N-C/H-C-N-C 0.513 -0.577 -0.283

H-C-N/H-C-N-C -2.541 1.884 0.733

C-C-C'/C'-C-C-C' 5.002 1.813 -0.065

C-C-N/C'-C-C-N -2.292 -1.202 -2.330

C-C-C'/C'-C-C-N -1.959 -3.449 -0.383

C-N-C'/C'-C-N-C' -3.491 1.270 -1.604

C'-C-N/C'-C-N-C' 6.929 2.668 1.883

C-N-H*/C'-C-N-H* 0.159 -0.812 -3.753

C'-C-N/C'-C-N-H* -5.324 2.945 0.548

C'-C-N/N-C-C'-O' -2.636 -4.079 3.410

C-C'-O'/N-C-C'-O' 1.425 5.477 7.985

C'-C-N/N-C-C'-N -1.188 -1.194 3.564

C-C'-N/N-C-C'-N -0.065 0.924 -9.223

C-C'-N/C-C'-N-C 6.106 4.247 4.769

C-N-C'/C-C'-N-C 8.574 2.588 0.587

C-N-C/C'-C-N-C -0.650 3.641 3.724

C'-C-N/C'-C-N-C 5.071 -5.186 -3.202

C'-N-H*/N-C'-N-H* 1.178 -1.183 0.899

N-C'-N/N-C'-N-H* -3.877 2.284 0.106

N-C'-O'/O'-C'-N-C' -2.282 3.478 -0.413

C'-N-C'/O'-C'-N-C' -0.440 -0.079 -0.462

(15)

C'-N-C'/H-C'-N-C' 2.356 -1.832 0.859

[image:15.612.69.542.192.721.2]

H-C-C/H-C-C-H -1.622 0.739 -0.449

Table II.A. Comparison of Formamide Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

Coordinate HF/6-31G* HDFF QMFF

Bonds (Å)

C'1 - O'2 1.193 1.187 (-0.006) 1.193

(0.000)

C'1 - N3 1.348 1.377 (0.029) 1.347

(-0.001)

C'1 - H6 1.091 1.095 (0.004) 1.089

(-0.002)

N3

-H*4 0.996

0.999 (0.003)

0.995

(-0.001)

N3 - H*5 0.993 0.998 (0.005) 0.992

(-0.001)

Angles (degrees)

O'2 -C'1 - _N3 124.9 123.2 (-1.8)

124.2(-0.7)

O'2 -C'1 - _H6 122.3 120.4 (-1.9)

122.2(-0.2)

N3 -C'1 - _H6 112.7 116.4 (3.7)

113.6(0.9)

C'1 - N3

-H*4 119.3 118.8(-0.5) 116.8(-2.4)

C'1 -N3 - _H*5 121.8 123.0 (1.2)

123.4 (1.5)

H*4 -N3 - _H*5 118.9 118.2 (-0.7)

(16)

Torsions (degrees)

O'2 - C'1 - N3 - _H*4 0.0 0.0 (0.0) 0.0

(0.0)

O'2 - C'1 - N3 - _H*5 180.0 180.0 (0.0)

180.0 (0.0)

H6

-C'1

-N3

-H*4 180.0 180.0 (0.0) 180.0 (0.0)

H6 - C'1 - N3 - _H*5 0.0 0.0 (0.0) 0.0

(0.0)

Out-of-Planes (degrees)

O'2 - C'1 - N3 - _H6 0.0 0.0 (0.0) 0.0

(0.0)

C'1 - N3 - H*4 - _H*5 0.0 0.0 (0.0) 0.0

(0.0)

Table II.B. Comparison of Planar Acetamide Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

Bonds (Å)

O'1 - _C'2

1.198 1.187

(-0.011) 1.196

(-0.002)

C'2 - _N3

1.356 1.369

[image:16.612.70.542.84.442.2]

(17)

(-0.004)

C'2 - _C4

1.514 1.509

(-0.005) 1.503

(-0.011)

N3

-H*5 0.995

0.998 (0.003)

0.995 (0.000)

N3

-H*6 0.993

0.996 (0.003)

0.990

(-0.002)

C4 - _H7

1.085 1.085

(0.000) 1.084

(-0.001)

C4 - _H8

1.085 1.085

(0.000) 1.084

(-0.001)

C4 - _H9

1.080 1.085

(0.005) 1.079

(-0.001) Angles (degrees)

O'1 - C'2

-N3 122.2 121.3 (-0.9) 121.4 (-0.8)

O'1 - C'2

-C4 122.9 123.4 (0.5) 123.0 (0.1)

N3 - C'2

-C4 114.9 115.3(0.4) 115.7(0.7)

C'2 - N3

(18)

118.8(0.3) 116.5(-2.1)

C'2 - N3

-H*6 122.7

122.6 (-0.1) 123.5 (0.8)

H*5 - N3

-H*6 118.7 118.6(-0.1) 120.1 (1.3)

C'2 - C4

-H7 110.6 109.4 (-1.2) 110.7(0.1)

C'2 - C4

-H8 110.6 109.4 (-1.2) 110.7(0.1)

C'2 - C4

-H9 108.9 111.2(2.3) 109.3 (0.4)

H7 - C4

-H8 108.0 106.9 (-1.1) 108.9 (0.9)

H7 - C4

-H9 109.4 109.9 (0.5) 108.6 (-0.8)

H8 - C4

-H9 109.4 109.9 (0.5) 108.6 (-0.8) Torsions (degrees)

O'1

-C'2

-N3

(19)

0.0

(0.0) 0.0

(0.0)

O'1

-C'2

-N3

-H*6 180.0 180.0 (0.0) 180.0 (0.0)

C4

-C'2

-N3

-H*5 180.0 180.0 (0.0) 180.0 (0.0)

C4

-C'2

-N3

-H*6 0.0

0.0

(0.0) 0.0

(0.0)

O'1

-C'2

-C4

-H7 120.2 121.6 (1.4)

119.6

(-0.6)

O'1

-C'2

-C4

(20)

238.4 (-1.4) 240.4

(0.6)

O'1

-C'2

-C4

-H9 0.0

0.0

(0.0) 0.0

(0.0)

N3

-C'2

-C4

-H7 300.2 301.6 (1.4)

299.6

(-0.6)

N3

-C'2

-C4

-H8 59.8

58.4

(-1.4) 60.4 (0.6)

N3

-C'2

-C4

-H9 180.0 180.0 (0.0) 180.0 (0.0) Out-of-Planes (degrees)

O'1

-C'2

-C4

(21)

0.0

(0.0) 0.0

(0.0)

C'2

-N3

-H*6

-H*5 0.0

0.0

(0.0) 0.0

(0.0)

Appendix II.C. Comparison of Planar N-Methylformamide Trans and Cis Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

trans cis Coordinate HF/6-31G* HDFF QMFF HF/6-31G* HDFF QMFF

Bonds (Å)

O'1 -C'2 1.196 1.190 (-0.006) 1.196 (0.001) 1.195 1.189 (-0.006) 1.194 (-0.001) C'2 -N3 1.345 1.401 (0.056) 1.348 (0.003) 1.347 1.389 (0.041) 1.349 (0.002) C'2 -H5 1.091 1.094 (0.003) 1.088 (-0.003) 1.091 1.095 (0.004) 1.092 (0.000) N3 -C4 1.448 1.452 (0.004) 1.445 (-0.003) 1.442 1.450 (0.007) 1.440 (-0.002) N3 -H*6 0.993 0.999 (0.006) 0.995 (0.002) 0.997 1.001 (0.004) 1.000 (0.003) C4 -H7 1.081 1.085 (0.004) 1.083 (0.002) 1.082 1.086 (0.003) 1.082 (0.000) C4 -H8 1.083 1.086 (0.003) 1.085 (0.002) 1.084 1.086 (0.001) 1.085 (0.001) C4 -H9 1.083 1.086 (0.003) 1.085 (0.002) 1.084 1.086 (0.001) 1.085 (0.001)

Angles (degrees)

O'1 -C'2 -N3 124.8 125.8 (1.0) 124.6 (-0.2) 124.9 123.4 (-1.5) 125.1 (0.2) O'1 -C'2 -H5 122.2 119.6 (-2.7) 121.8 (-0.4) 122.1 120.0 (-2.2) 121.9 (-0.2) N3 -C'2 -H5 113.0 114.6 (1.6) 113.6 (0.6) 112.9 116.6 (3.7) 113.0 (0.0) C'2 -N3 -C4 121.8 122.5 (0.7) 120.8 (-0.9) 125.4 124.5 (-0.9) 124.5 (-0.9) C'2 -N3 -H*6 118.7 120.0 (1.3) 120.7 (2.0) 115.5 117.1 (1.6) 115.4 (-0.1) C4 -N3 -H*6 119.6 117.5 (-2.0) 118.5 (-1.1) 119.1 118.4 (-0.7) 120.1 (1.0) N3 -C4 -H7 108.7 110.2 (1.5) 109.0 (0.3) 109.3 110.7 (1.5) 108.3 (-1.0) N3 -C4 -H8 110.9 110.7 (-0.2) 111.1 (0.2) 111.4 110.5 (-0.8) 111.4 (0.0) N3 -C4 -H9 110.9 110.7 (-0.2) 111.1 (0.2) 111.3 110.5 (-0.8) 111.4 (0.1) H7 -C4 -H8 109.0 107.9 (-1.1) 108.4 (-0.5) 108.1 107.9 (-0.2) 108.5 (0.4) H7 -C4 -H9 109.0 107.9 (-1.1) 108.4 (-0.5) 108.1 107.9 (-0.1) 108.5 (0.4) H8 -C4 -H9 108.4 109.3 (1.0) 108.7 (0.3) 108.7 109.1 (0.5) 108.7 (0.0)

Torsions (degrees)

(22)

H*6 -N3 -C4 -H7 0.0 0.0 (0.0) 0.0 (0.0) 179.9 180.0 (0.1) 180.0 (0.1) H*6 -N3 -C4 -H8 119.8119.3 (-0.5) 119.4 (-0.3) 299.2 299.5 (0.4) 299.2 (0.1) H*6 -N3 -C4 -H9 240.2240.7 (0.5) 240.6 (0.3) 60.6 60.5 (-0.2) 60.8 (0.1)

Out-of-Planes (degrees) O’ '1-C'2 -N3 -H5 0.0 0.0

0.0 (0.0)

0.0 (0.0 )0.0 (0.0) C'2 -N3 -H*6 -C4 0.0 0.0

0.0 (0.0)

0.0 (0.0 )0.0 (0.0)

Appendix II.D. Comparison of Planar N-Methylacetamide Trans and Cis Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

trans cis Coordinate HF/6-31G* HDFF QMFF HF/6-31G* HDFF QMFF Bonds (Å)

C1 - C'2 1.514 1.514 (0.000) (-0.001) 1.514 1.515 (0.001) 1.512 (-0.001)

C1 - H7 1.083 1.085 (0.002) 1.084 (0.001) 1.085 1.084 0.001) 1.084 (-0.001)

C1 - H8 1.084 1.085 (0.001) (-0.002) 1.080 1.085 (0.005) 1.079 (-0.001)

C1 - H9 1.083 1.085 (0.002) (0.001) 1.085 1.084 (-0.001) 1.084 (-0.001)

C'2 -N3 1.350 1.398 (0.048) 1.351 (0.001) 1.357 1.389 (0.032) 1.358 (0.001) C'2 -O'5 1.201 1.190 (-0.011) 1.202 (0.001) 1.200 1.189(-0.011) 1.197 (-0.003) N3 - C4 1.447 1.452 (0.005) 1.449 (0.002) 1.445 1.450 (0.005) 1.444 (-0.001)

N3 - H*6 0.992 0.998 (0.006) (0.002) 0.995 1.000 (0.005) 0.999 (0.004)

C4 - H10 1.083 1.086 (0.003) (0.002) 1.085 1.086 (0.001) 1.085 (0.000)

C4 - H11 1.082 1.085 (0.003) 1.083 (0.001) 1.081 1.085 (0.004) 1.084 (0.003)

C4 - H12 1.083 1.086 (0.003) (0.002) 1.085 1.086 (0.001) 1.085 (0.000) Angles (degrees)

(23)

N3 - C4 - H12 111.0 110.7 (-0.3) 111.1 (0.1) 112.2 110.9 (-1.3) 111.5 (-0.7) H10 - C4 - H11 109.0 107.9 (-1.1) 108.4 (-0.6) 107.8 107.7 (-0.1) 108.2 (0.4)

H10 - C4 - H12 108.3 109.3 (1.0) 108.8 (0.5) 108.5 109.6 (1.1) 109.0 (0.5)

H11- C4 - H12 109.0 107.9 (-1.1) 108.4 (-0.6) 107.8 107.7 (-0.1) 108.2 (0.4) Torsions (degrees)

H7 - C1 - C'2 - _{N3 238.4} 238.5 (0.1) 238.7 (0.3) 300.0 301.6 299.2 (-0.8)

H7 - C1 - C'2 - _{O'5 58.4} 58.5 (0.1) 58.7 (0.3) 120.0 121.6 119.2 (-0.8)

H8 - C1 - C'2 - _{N3 0.0} 0.0 (0.0) 0.0 (0.0) 180.0 180.0 180.0 (0.0)

H8 - C1 - C'2 - _{O'5 180.0} 180.0 (0.0) 180.0 (0.0) 0.0 0.0(0.0) 0.0 (0.0)

H9 - C1 - C'2 - _{N3 121.6} 121.5 (-0.1) 121.3 (-0.3) 60.0 58.4(-1.6)60.8 (0.8)

H9 - C1 - C'2 - _{O'5 301.6} 301.5 (-0.1) 301.3 (-0.3) 240.0 238.4 240.8 (0.8)

C1 - C'2- N3 - C4 180.0 180.0 (0.0) 180.0 (0.0) 0.0 0.0 (0.0)0.0 (0.0) C1 - C' - N3 - H*6 0.0 0.0 (0.0) 0.0 (0.0) 180.0 180.0 (0.0)180.0(0.0) O'5- C'2 - N3 - C4 0.0 0.0 (0.0) 0.0 (0.0) 180.0 180.0 (0.0) 180.0 O'5- C'2 - N3 - H*6 180.0 180.0 (0.0) 180.0 (0.0) 0.0 0.0 (0.0) 0.0 (0.0) C'2 - N3 - C4 - _{H10 299.8} 299.3 (-0.5) 299.4 (-0.4) 298.8 299.0 290.0 (0.2)

C'2 - N3 - C4 - _{H11 180.0} 180.0 (0.0) 180.0 (0.0) 180.0 180.0 180.0 (0.0)

C'2 - N3 - C4 - _{H12 60.2} 60.7 (0.5) 60.6 (0.4) 61.2 61.0(-0.2)61.0 (0.2)

H*6 - N3 - C4 - _{H11 0.0} 0.0 (0.0) 0.0 (0.0) 0.0 0.0(0.0) 0.0 0.0)

H*6 - N3 - C4 - _{H12 240.2} 240.7 (0.5) 240.6 (0.4) 241.2 241.0 241.0 (-0.2)

Out-of-Planes

[image:23.612.94.542.516.712.2]

C1 - C'2-N3 - O'5 0.0 0.0 (0.0) 0.0 (0.0) 0.0 0.0 (0.0)0.0 (0.0) C'2 - N3 - H*6 -C4 0.0 0.0 (0.0) 0.0 (0.0) 0.0 0.0 (0.0)0.0 (0.0) ______________________________________________________________________________________________________________

Table II.E. Comparison of N,N-Dimethylformamide Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

Bonds (Å)

O'1 - _{C'2 1.196}

1.192 (-0.004) 1.197 (0.001)

C'2 - _{N3 1.349}

1.415 (0.067) 1.350 (0.002)

C'2 - _H6

1.091 1.094 (0.004)1.091

(24)

N3 - _{C4 1.442}

1.454 (0.012) 1.447 (0.005)

N3 - _{C5 1.446}

1.457 (0.011) 1.448 (0.002)

C4 - _{H7 1.082}

1.085 (0.003) 1.080

(-0.002)

C4 - _{H8 1.086}

1.086 (0.000) 1.087 (0.001)

C4 - _{H9 1.086}

1.086 (0.000) 1.087 (0.001)

C5 - _{H10 1.077}

1.085 (0.008) 1.080 (0.003)

C5 - _{H11 1.086}

1.085 (-0.001) 1.087 (0.001)

C5 - _{H12 1.086}

1.085 (-0.001) 1.087 (0.001)

Angles (degrees)

O'1 - _{C'2 - N3}

125.9 126.1 (0.2)

126.2 (0.3)

O'1 - _{C'2 - H6}

121.5 118.8 (-2.7)

120.9 (-0.6)

N3 - _{C'2 - H6}

112.6 115.0 (2.5)

112.9 (0.3)

C'2 - _{N3 - C4}

122.0 121.3 (-0.7)

121.4 (-0.6)

C'2 - _{N3 - C5}

120.6 122.9 (2.3)

122.1 (1.5)

C4 - _{N3 - C5}

117.4 115.8 (-1.6)

116.6 (-0.9)

N3 - _{C4 - H7}

110.2 111.4 (1.3)

109.3 (-0.9)

N3 - _{C4 - H8}

110.9 110.4 (-0.5)

(25)

N3 - _{C4 - H9}

110.9 110.4 (-0.5)

111.1 (0.2)

H7 - _{C4 - H8}

108.3 108.4 (0.1)

108.3 (0.1)

H7 - _{C4 - H9}

108.3 108.4 (0.1)

108.3 (0.1)

H8 - _{C4 - H9}

108.2 107.6 (-0.6)

108.6 (0.3)

N3 - _C5

-H10 109.0 111.7

(2.8) 109.9 (0.9)

N3 - _C5

-H11 110.5 110.4

(-0.1) 111.0 (0.6)

N3 - _C5

-H12 110.5 110.4

(-0.1) 111.0 (0.6)

H10 - _C5

-H11 109.3 108.3

(-1.0) 108.1 (-1.1)

H10 - _C5

-H12 109.3 108.3

(-1.0) 108.1 (-1.1)

H11 - _C5

-H12 108.4 107.7

(-0.7) 108.5 (0.1)

Torsions (degrees)

O'1 - _{C'2 - N3}

- _C4 180.0

180.0 (0.0) 180.0

(0.0)

O'1 - _{C'2 - N3}

- _C5 0.0

0.0 (0.0) 0.0

(0.0)

(26)

- _C4 0.0

0.0 (0.0) 0.0

(0.0)

H6 - _{C'2 - N3}

- C5 180.0

180.0 (0.0) 180.0

(0.0)

C'2 - _{N3 - C4}

- _H7 0.0

0.0 (0.0) 0.0

(0.0)

C'2 - _{N3 - C4}

- _H8 240.1

239.4 (-0.7) 240.5

(0.4)

C'2 - _{N3 - C4}

- _H9 119.9

120.6 (0.7) 119.5

(-0.4)

C5 - _{N3 - C4}

- _H7 180.0

180.0 (0.0) 180.0

(0.0)

C5 - _{N3 - C4}

- _H8 60.1

59.4 (-0.7) 60.5

(0.4)

C5 - _{N3 - C4}

- _H9 299.9

300.6 (0.7) 299.5

(-0.4)

C'2 - _{N3 - C5}

- _H10 0.0

0.0 (0.0) 0.0

(0.0)

C'2 - _{N3 - C5}

- _H11 120.0

120.5 (0.5) 119.6

(-0.5)

C'2 - _{N3 - C5}

- _H12 240.0

(27)

(0.5)

C4 - _{N3 - C5}

- _H10 180.0

180.0 (0.0) 180.0

(0.0)

C4 - _{N3 - C5}

- _H11 300.0

300.5 (0.5) 299.6

(-0.5)

C4 - _{N3 - C5}

- _H12 60.0

59.5 (-0.5) 60.4

(0.5) Out-of-Planes (degrees)

O'1 - _{C'2 - N3}

- _H6 0.0

0.0 (0.0) 0.0

(0.0)

C'2 - _{N3 - C4}

- _C5 0.0

0.0 (0.0) 0.0

[image:27.612.72.540.69.436.2] [image:27.612.70.540.536.718.2]

(0.0)

Table II.F. Comparison of Planar N,N-Dimethylacetamide Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

Bonds (Å)

C1 - _{C'2 1.518}

1.520 (0.002) 1.521

(0.004)

C1 - _{H7 1.079}

1.085 (0.006) 1.080

(0.001)

(28)

1.084 (0.000) 1.084 (-0.001)

C1 - _{H9 1.085}

1.084 (0.000) 1.084

(-0.001)

C'2 - _{O'3 1.203}

1.192 (-0.010) 1.201

(-0.001)

C'2 - _N4

1.361 1.430 (0.069)

1.366 (0.006)

N4 - _C5

1.449 1.461 (0.012)

1.455 (0.006)

N4 - _{C6 1.445}

1.459 (0.014) 1.450

(0.005)

C5 - _H10

1.076 1.085 (0.009)

1.079 (0.004)

C5 - _{H11 1.087}

1.085 (-0.001) 1.087

(0.001)

C5 - _{H12 1.087}

1.085 (-0.001) 1.087

(0.001)

C6 - _{H13 1.077}

1.083 (0.006) 1.078

(0.001)

C6 - _{H14 1.087}

1.086 (-0.001) 1.088

(0.001)

C6 - _{H15 1.087}

1.086 (-0.001) 1.088

(0.001) Angles (degrees)

C'2 - _{C1 - H7}

107.2 111.4 (4.2)

108.1 (0.9)

C'2 - _{C1 - H8}

111.6 109.5 (-2.1)

111.4 (-0.3)

(29)

111.6 109.5 (-2.1)

111.4 (-0.3)

H7 - _{C1 - H8}

109.1 109.5 (0.5)

108.3 (-0.8)

H7 - _{C1 - H9}

109.1 109.5 (0.5)

108.3 (-0.8)

H8 - _{C1 - H9}

108.1 107.3 (-0.9)

109.3 (1.1)

C1 - _{C'2 - O'3}

119.9 119.0 (-0.9)

119.0 (-0.8)

C1 - _{C'2 - N4}

118.0 118.3 (0.3)

118.8 (0.8)

O'3 - _{C'2 - N4}

122.1 122.1 (0.6)

122.2 (0.1)

C'2 - _{N4 - C5}

119.5 121.4 (1.8)

120.9 (1.4)

C'2 - _{N4 - C6}

125.6 124.8 (-0.8)

124.9 (-0.7)

C5 - _{N4 - C6}

114.9 113.9 (-1.0)

114.2 (-0.6)

N4 - _C5

-H10 109.5 112.4

(3.0) 110.8 (1.4)

N4 - _C5

-H11 110.3 110.3

(0.0) 110.8 (0.4)

N4 - _C5

-H12 110.3 110.3

(0.0) 110.8 (0.4)

H10 - _C5

-H11 109.3 108.0

(-1.2) 107.9 (-1.3)

(30)

-H12 109.3 108.0

(-1.2) 107.9 (-1.3)

H11 - _C5

-H12 108.2 107.5

(-0.6) 108.5 (0.3)

N4 - _C6

-H13 111.8 113.0

(1.1) 111.1 (-0.7)

N4 - _C6

-H14 110.4 110.2

(-0.2) 110.6 (0.3)

N4 - _C6

-H15 110.4 110.2

(-0.2) 110.6 (0.3)

H13 - _C6

-H14 108.1 108.0

(-0.1) 108.0 (-0.1)

H13 - _C6

-H15 108.1 108.0

(-0.1) 108.0 (-0.1)

H14 - _C6

-H15 107.9 107.4

(-0.6) 108.4 (0.5)

Torsions (degrees)

H7 - _{C1 - C'2}

- _O'3 0.0

0.0 (0.0) 0.0

(0.0)

H7 - _{C1 - C'2}

- _N4 180.0

180.0 (0.0) 180.0

(0.0)

H8 - _{C1 - C'2}

- _O'3 119.4

121.3 (1.9) 118.9

(-0.6)

H8 - _{C1 - C'2}

- _N4 299.4

301.3 (1.9) 298.9

(31)

H9 - _{C1 - C'2}

- _O'3 240.6

238.7 (-1.9) 241.1

(0.6)

H9 - _{C1 - C'2}

- _N4 60.6

58.7 (-1.9) 61.1

(0.6)

C1 - _{C'2 - N4}

- _C5 180.0

180.0 (0.0) 180.0

(0.0)

C1 - _{C'2 - N4}

- _C6 0.0

0.0 (0.0) 0.0

(0.0)

O'3 - _{C'2 - N4}

- _C5 0.0

0.0 (0.0) 0.0

(0.0)

O'3 - _{C'2 - N4}

- _C6 180.0

180.0 (0.0) 180.0

(0.0)

C'2 - _{N4 - C5}

- _H10 0.0

0.0 (0.0) 0.0

(0.0)

C'2 - _{N4 - C5}

- _H11 120.3

120.7 (0.4) 119.8

(-0.5)

C'2 - _{N4 - C5}

- _H12 239.7

239.3 (-0.4) 240.2

(0.5)

C6 - _{N4 - C5}

- _H10 180.0

180.0 (0.0) 180.0

(0.0)

(32)

- _H11 300.3

300.7 (0.4) 299.8

(-0.5)

C6 - _{N4 - C5}

- _H12 59.7

59.3 (-0.4) 60.2

(0.5)

C'2 - _{N4 - C6}

- _H13 0.0

0.0 (0.0) 0.0

(0.0)

C'2 - _{N4 - C6}

- _H14 120.4

120.9 (0.5) 119.9

(-0.5)

C'2 - _{N4 - C6}

- _H15 239.6

239.1 (-0.5) 240.1

(0.5)

C5 - _{N4 - C6}

- _H13 180.0

180.0 (0.0) 180.0

(0.0)

C5 - _{N4 - C6}

- _H14 300.4

300.9 (0.5) 299.9

(-0.5)

C5 - _{N4 - C6}

- _H15 59.6

59.1 (-0.5) 60.1

(0.5) Out-of-Planes (degrees)

C1 - _{C'2 - O'3}

- _N4 0.0 0.0

(0.0) 0.0 (0.0)

C'2 - _{N4 - C5}

- _C6 0.0 0.0

(33)

[image:33.612.73.542.156.725.2]

Table II.G. Comparison of Urea Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

Bonds (Å)

N1 - C'2

1.373 1.308

(-0.065) 1.372

(-0.001)

N1 - H*5

0.996 0.996

(0.000) 0.996

(0.000)

N1 - H*6

0.996 0.994

(-0.003) 0.993

(-0.003)

C'2 - O'3

1.197 1.180

(-0.017) 1.192

(-0.005)

C'2 - N4

1.373 1.308

(-0.065) 1.372

(-0.001)

N4 - H*7

0.996 0.996

(0.000) 0.996

(0.000)

N4 - H*8

0.996 0.994

(-0.003) 0.993

(-0.003) Angles (degrees)

C'2 - _N1

- _H*5

113.4 112.3

(34)

C'2 - _N1

- _H*6

117.7 114.5

(-3.3) 117.3 (-0.4)

H*5 - N1

- _H*6

114.4 116.2

(1.7) 116.2

(1.8)

N1 - _C'2

- _O'3

123.0 122.5

(-0.5) 121.9 (-1.1)

N1 - _C'2

- _N4

114.0 115.0

(1.1) 116.2

(2.2)

O'3 - _C'2

- _N4

123.0 122.5

(-0.5) 121.9 (-1.1)

C'2 - _N4

- _H*7

113.4 112.3

(-1.0) 109.3 (-4.1)

C'2 - _N4

- _H*8

117.7 114.5

(-3.3) 117.3 (-0.4)

H*7 - _N4

- _H*8

114.4 116.2

(1.7) 116.2

(1.8) Torsions (degrees)

H*5 - _N1

- _C'2

-O'3 12.6

13.9 (1.3) 9.2

(35)

H*5 - _N1

- _C'2

-N4 192.6

193.9 (1.3)

189.2 (-3.4)

H*6 - _N1

- _C'2

-O'3 150.0

149.2 (-0.8)

144.2 (-5.8)

H*6 - _N1

- _C'2

-N4 330.0

329.2 (-0.8)

324.2 (-5.8)

N1 - _C'2

- _N4

-H*7 192.6

193.9 (1.3)

189.2 (-3.4)

N1 - _C'2

- _N4

-H*8 330.0

329.2 (-0.8)

324.2 (-5.8)

O'3 - _C'2

- _N4

-H*7 12.6

13.9 (1.3) 9.2

(-3.4)

O'3 - _C'2

- _N4

-H*8 150.0

149.2 (-0.8)

144.2 (-5.8)

Out-of Planes (degrees)

C'2 - _N1

- _H*6

-H*5 37.4

(36)

(-3.3)

N1 - _C'2

- _O'3

-N4 0.0 0.0

(0.0) 0.0

(0.0)

C'2 - _N4

- _H*7

-H*8 37.4

40.6 (3.2)

[image:36.612.66.541.359.716.2]

40.8 (3.3)

Table II.H. Comparison of N-Formylformamide Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

Bonds (Å)

O'1 -C'2 1.185 1.188 (0.003)

(0.004)

C'2 -N3 1.373 1.379 (0.006)

1.373(0.000)

C'2 -H6 1.088 1.095 (0.007)

1.089(0.001)

N3 - _C'4 1.373 1.379(0.006)

1.373 (0.000)

N3 - _H*8 1.000 0.996(-0.004)

0.994 (-0.006)

C'4 -O'5 1.185 1.188 (0.003)

1.189(0.004)

C'4 -H7 1.088 1.095 (0.007)

1.089(0.001) Angles (degrees)

(37)

N3 -C'2 - H6 113.3 116.2 (2.9) 112.9 (-0.4)

C'2 - N3 - _C'4 125.0 125.7 (0.7) 125.4

(0.4)

C'2 - N3 - _H*8 117.5 117.2 (-0.3) 117.3

(-0.2)

C'4 - N3 - _H*8 117.5 117.2 (-0.3) 117.3

(-0.2)

N3 -C'4 - O'5 123.7 123.6 (-0.1) 124.2 (0.5) N3 -C'4 - H7 113.3 116.2 (2.9) 112.9 (-0.4) O'5 - C'4 - H7 122.9 120.2 (-2.7) 122.9 (0.0) Torsions (degrees)

O'1 - C'2 - N3 - C'4 180.0 180.0 (0.0) 180.0 (0.0) O'1 - C'2 - N3 - H*8 0.0 0.0 (0.0) 0.0 (0.0) H6 -C'2 - N3 - C'4 0.0 0.0 (0.0) 0.0 (0.0) H6 -C'2 - N3 - H*8 180.0 180.0 (0.0) 180.0 (0.0)

C'2 - N3 - _C'4 - _{O'5 180.0} 180.0 (0.0)

180.0 (0.0)

C'2 - N3 - _C'4 - _{H7 0.0} 0.0 (0.0)

0.0 (0.0)

H*8 - N3 - _C'4 - _O'5 0.0 0.0 (0.0)

0.0 (0.0)

H*8 - N3 - _C'4 - _{H7 180.0} 180.0 (0.0)

180.0 (0.0) Out-of-Planes (degrees)

O'1 - C'2 - N3 - H6 0.0 0.0 (0.0) 0.0 (0.0)

C'2 - N3 - _H*8 - _C'4 0.0 0.0 (0.0)

0.0 (0.0)

[image:37.612.72.535.65.557.2]

O'5 - C'4 - N3 - H7 0.0 0.0 (0.0) 0.0 (0.0)

Table II.I. Comparison of Butyrolactam Structures Optimized by Ab Initio Calculation (HF/6-31G*) and by the HDFF and QMFF Force Fields.

Structures

(38)

Bonds (Å)

C'1 - C2 1.533 1.527 (-0.006) 1.527 C'1 - N4 1.358 1.384 (0.027) 1.354 C'1 - O'5 1.186 1.189 (0.002) 1.186 C2 -C3 1.549 1.533 (-0.016) 1.542 C2 -H6 1.082 1.085 (0.003) 1.080 C2 -H7 1.082 1.085 (0.003) 1.080 C3 -N4 1.455 1.429 (-0.026) 1.450 C3 -H8 1.083 1.086 (0.003) 1.082 C3 -H9 1.083 1.086 (0.003) 1.082 N4 - H*10 0.996 0.999 (0.003) 0.994 Angles (degrees)

C2 - C'1 - N4 91.2 93.9 (2.8) 91.2 (0.0) C2 - C'1 - O'5 135.9 134.3 (-1.6) 136.2 (0.3) N4 - C'1 - O'5 133.0 131.8 (-1.2) 132.7 (-0.3) C'1 - C2 - C3 85.7 82.5 (-3.1) 85.7 (0.0) C'1 - C2 - H6 114.1 116.0 (1.9) 113.5 (-0.6) C'1 - C2 - H7 114.1 116.0 (1.9) 113.5 (-0.6) C3 - C2 - H6 115.7 115.0 (-0.7) 116.2 (0.4) C3 - C2 - H7 115.7 115.0 (-0.7) 116.2 (0.4) H6 - C2 - H7 109.9 110.1 (0.2) 110.1 (0.2) C2 - C3 - N4 86.9 91.9 (4.9) 87.1 (0.1) C2 -C3 - H8 115.3 115.2 (-0.1) 115.5 (0.2) C2 - C3 - H9 115.3 115.2 (-0.1) 115.5 (0.2) N4 - C3 - H8 114.1 109.3 (-4.8) 113.1 (-1.0) N4 - C3 - H9 114.1 109.3 (-4.8) 113.1 (-1.0) H8 - C3 - H9 109.7 113.6 (3.9) 110.8 (1.1) C'1 - N4 - C3 96.2 91.7 (-4.6) 96.1 (-0.1) C'1 - N4 - H*10 131.0 137.5 (6.5) 130.5 (-0.4) C3 - N4 - H*10 132.8 130.8 (-2.0) 133.4 (0.6) Torsions (degrees)

(39)

C2 - C'1 - N4 - C3 0.0 0.0 (0.0) 0.0 (0.0) C2 - C'1 - N4 - H*10 180.0 180.0 (0.0) 180.0 (0.0) O'5- C'1 - N4 - C3 180.0 180.0 (0.0) 180.0 (0.0) O'5- C'1 - N4 - H*10 0.0 0.0 (0.0) 0.0 (0.0) C'1 - C2 - C3 - N4 0.0 0.0 (0.0) 0.0 (0.0) C'1 - C2 - C3 - H8 244.7 247.6 (2.9) 245.8 (1.1) C'1 - C2 - C3 - H9 115.3 112.4 (-2.9) 114.2 (-1.1) H6 - C2 - C3 - N4 245.3 244.7 (-0.6) 245.9 (0.6) H6 - C2 - C3 - H8 130.0 132.3 (2.3) 131.7 (1.7) H6 - C2 - C3 - H9 0.6 357.1 (-3.5) 0.2 (-0.4) H7 - C2 - C3 - N4 114.7 115.3 (0.6) 114.1 (-0.6) H7 - C2 - C3 - H8 359.4 2.9 (3.5) 359.8 (0.4) H7 - C2 - C3 - H9 230.0 227.7 (-2.3) 228.3 (-1.7) C2 - C3 - N4 - C'1 0.0 0.0 (0.0) 0.0 (0.0) C2 - C3 - N4 - H*10 180.0 180.0 (0.0) 180.0 (0.0) H8 - C3 - N4 - C'1 116.4 117.6 (1.1) 116.5 (0.1) H8 - C3 - N4 - H*10 296.4 297.6 (1.1) 296.5 (0.1) H9 - C3 - N4 - C'1 243.6 242.4 (-1.1) 243.5 (-0.1) H9 - C3 - N4 - H*10 63.6 62.4 (-1.1) 63.5 (-0.1) Out-of-Planes (degrees)

[image:39.612.74.522.70.472.2]

C2 - C'1 - N4 - O'5 0.0 0.0 (0.0) 0.0 (0.0) C'1 - N4 - C3 - H*10 0.0 0.0 (0.0) 0.0 (0.0)

Table III.A. Comparison of Formamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

(40)

1788.7 2055.6 (266.9) 1806.0 (17.2) _{NH2 bend} 1563.0 1498.2 (-64.8) 1529.0 (-34.0) C'H rock 1378.6 1168.6 (-210.0) 1333.7 (-44.8) C'N stretch

1182.5 1276.8 (94.3) 1230.5 (48.0) C'O' oop deformation 1159.9 933.4 (-226.5) 1116.8 (-43.1) _{NH2 rock}

[image:40.612.83.538.72.188.2] [image:40.612.73.535.282.712.2]

673.4 679.5 (6.1) 697.2 (23.8) C'N torsion 617.6 578.3 (-39.3) 627.3 (9.7) C'O' rock 109.1 353.6 (244.5) 402.5 (293.3) amino inversion

Table III.B. Comparison of Planar Acetamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3975.1 3997.6 (22.5) 3970.0 (-5.1)NH asym stretch 3843.4

3873.9 (30.6) 3829.1 (-14.3) NH sym stretch 3337.2

3268.7 (-68.5) 3308.6 (-28.7) _{CH3 asym stretch} 3272.1

3259.2 (-12.9) 3265.5 (-6.5) _{CH3 asym stretch} 3214.4

3140.7 (-73.7) 3226.7 (12.3) _{CH3 sym stretch} 1985.2

1974.8 (-10.4) 2004.3 (19.0) C'O' stretch 1795.0

2049.8 (254.8) 1799.8 (4.9) _{NH2 bend} 1627.2

1624.8 (-2.4) 1692.9 (65.7) _{CH3 asym deformation} 1617.2

1623.3 (6.1) 1681.7 (64.5) _{CH3 asym deformation} 1562.3

1543.3 (-19.0) 1619.7 (57.5) _{CH3 sym deformation} 1463.6

1324.0 (-139.6) 1485.5 (21.9) C'N stretch 1234.2

(41)

1168.9

1042.5 (-126.4) 1143.8 (-25.1) _{CH3 rock} 1076.6

1001.5 (-75.1) 1060.5 (-16.1) _{CH3 rock} 913.0

733.5 (-179.5) 886.4 (-26.6) C'C stretch 696.4

783.9 (87.5) 715.0 (18.5) C'O' oop deformation 598.1

558.2 (-39.9) 605.7 (7.6) C'O' rock 562.6

641.6 (79.0) 614.1 (51.5) C'N torsion 446.6

356.5 (-90.1) 403.7 (-42.9) C'C rock 11.7

-6.5a,b (-18.2) 118.0 (106.3) _{CH3 torsion} -144.5a

175.9 (320.4) 380.8 (525.3) amino inversion

[image:41.612.80.522.507.723.2]

a The minus sign indicates that the frequency was calculated from the absolute value of a negative eigenvalue. bThis imaginary frequency arises from selecting the force field stationary state with the geometry closest to the corresponding ab initio structure for comparison. In this case the configuration computed with the force field corresponds to a transition state.

Table III.C. Comparison of Planar Trans N-Methylformamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3900.8 3934.0 (33.2) 3867.0 (-38.3) NH stretch 3312.3 3259.5 (-52.8) 3268.3 (-44.0) _{CH3 asym stretch} 3296.9 3262.8 (-34.1) 3255.2 (-41.7) _{CH3 asym stretch} 3230.5 3142.0 (-88.6) 3207.0 (-23.5) _{CH3 sym stretch} 3206.7 3149.2 (-57.5) 3235.7 (28.9) C'H stretch 1977.2 1994.6 (17.4) 1978.5 (1.3) C'O' Stretch 1694.9 1792.2 (97.3) 1699.2 (4.2) NH rock

(42)

1609.3 1586.9 (-22.4) 1601.2 (-8.2) _{CH3 sym deformation} 1559.9 1487.6 (-72.3) 1529.4 (-30.5) C'H rock

1348.6 1113.1 (-235.4) 1304.3 (-44.2) C'N stretch 1283.7 1039.3 (-244.4) 1239.1 (-44.6) _{CH3 rock} 1266.0 1034.3 (-231.7) 1269.5 (3.5) _{CH3 rock}

1170.7 1283.5 (112.8) 1242.8 (72.1) C'O' oop deformation 1035.4 823.9 (-211.5) 1000.1 (-35.3) NC stretch

837.8 692.0 (-145.9) 812.8 (-25.0) C'O' rock 486.9 560.8 (73.9) 574.4 (87.5) C'N torsion 291.8 301.2 (9.4) 317.4 (25.6) NC rock

228.5 323.4 (94.9) 328.1 (99.6) amino inversion -60.6a -62.5a (-1.9) -136.5a (-75.9) _{CH3 torsion}

a The minus sign indicates that the frequency was calculated from the absolute value of a negative eigenvalue.

Table III.D. Comparison of Cis N-Methylformamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3855.6 3941.0 (85.4) 3810.5 (-45.1) NH stretch 3299.0 3259.9 (-39.0) 3278.2 (-20.8) _{CH3 asym stretch} 3268.8 3261.4 (-7.4) 3252.0 (-16.8) _{CH3 asym stretch} 3215.4 3141.7 (-73.6) 3206.4 (-8.9) _{CH3 sym stretch} 3201.4 3149.8 (-51.6) 3205.7 (4.3) C'H stretch 1988.8 2012.1 (23.3) 1988.0 (-0.8) C'O' stretch

1681.4 1616.1 (-65.3) 1690.8 (9.4) _{CH3 asym deformation} 1643.2 1748.2 (105.0) 1626.3 (-16.9) NH rock

1631.5 1602.2 (-29.3) 1641.2 (9.7) _{CH3 asym deformation} 1623.1 1595.2 (-27.9) 1638.1 (15.0) _{CH3 sym deformation} 1542.4 1515.9 (-26.5) 1562.4 (20.1) C'H rock

1412.8 1049.9 (-362.9) 1386.1 (-26.7) C'N stretch 1270.2 1105.5 (-164.7) 1241.8 (-28.3) _{CH3 rock} 1258.9 1024.2 (-234.7) 1241.0 (-18.0) _{CH3 rock}

1179.5 1254.5 (75.1) 1180.0 (0.5) C'O' oop deformation 1096.1 953.9 (-142.1) 1068.9 (-27.1) NC stretch

[image:42.612.77.530.396.720.2]

(43)

193.0 179.5 (-13.5) 215.3 (22.3) _{CH3 torsion} 66.3 -50.8a (-117.1) -74.9a (-141.2) amino inversion

Table III.E. Comparison of Trans N-Methylacetamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3914.8 3934.0 (19.2) 3886.2 (-28.6) NH stretch

3307.6 3259.5 (-48.1) 3269.1 (-38.4) _{N-CH3 asym stretch} 3301.9 3261.6 (-40.3) 3267.1 (-34.9) _{C'-CH3 asym stretch} 3296.4 3265.0 (-31.4) 3280.5 (-15.9) _{C'-CH3 asym stretch} 3295.9 3262.9 (-33.0) 3256.2 (-39.7) _{N-CH3 asym stretch} 3229.0 3142.0 (-87.0) 3207.7 (-21.3) _{N-CH3 sym stretch} 3223.7 3140.9 (-82.8) 3222.0 (-1.6) _{C'-CH3 sym stretch} 1956.5 1974.9 (18.4) 1973.3 (16.7) C'O' stretch

1711.0 1792.0 (81.0) 1707.0 (-4.0) NH rock

1658.9 1617.7 (-41.2) 1675.2 (16.2) _{N-CH3 asym deformation} 1630.8 1627.0 (-3.8) 1650.4 (19.6) _{C'-CH3 asym deformation} 1628.8 1605.9 (-22.9) 1639.8 (11.0) _{N-CH3 asym deformation} 1617.3 1626.3 (9.0) 1693.2 (75.9) _{C'-CH3 asym deformation} 1609.1 1586.3 (-22.8) 1603.4 (-5.7) _{N-CH3 sym deformation} 1555.2 1542.0 (-13.2) 1594.6 (39.4) _{C'-CH3 sym deformation} 1408.2 1289.9 (-118.3) 1416.8 (8.6) C'-N stretch

1311.3 1044.3 (-267.0) 1249.8 (-61.4) _{N-CH3 rock} 1265.7 1030.5 (-235.2) 1268.7 (3.0) _{N-CH3 rock} 1191.5 1007.8 (-183.7) 1116.5 (-75.0) N-C stretch 1172.2 1058.3 (-113.9) 1151.6 (-20.6) _{C'-CH3 rock} 1094.9 1034.8 (-60.1) 1033.7 (-61.2) _{C'-CH3 rock} 950.6 731.2 (-219.4) 932.8 (-17.8) C'-C stretch

686.0 793.6 (107.6) 714.4 (28.4) C'O' oop deformation 673.6 605.8 (-67.8) 653.6 (-20.0) C'O' rock

[image:43.612.77.530.277.706.2]

(44)

365.9 373.4 (7.5) 506.5 (140.6) C'N torsion 284.0 266.6 (-17.4) 290.8 (6.8) NC rock

168.1 206.6 (38.5) 190.2 (22.1) amino inversion 19.8 _{-55.5a,b (-75.3) -110.4a,b(-130.2) C'-CH3 torsion} -41.4a -78.5a (-37.1) -127.0a (-85.6) _{N-CH3 torsion}

[image:44.612.78.530.409.706.2]

Table III.F. Comparison of Cis Planar N-Methylacetamide Frequencies Obtained byAb Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3872.7 3940.6 (67.9) 3831.3 (-41.4) NH stretch

3337.8 3268.6 (-69.2) 3305.8 (-32.0) _{C'-CH3 asym stretch} 3306.7 3258.8 (-47.9) 3263.7 (-43.1) _{N-CH3 asym stretch} 3276.5 3258.6 (-17.9) 3267.2 (-9.3) _{C'-CH3 asym stretch} 3260.8 3262.6 (1.8) 3259.1 (-1.8) _{N-CH3 asym stretch} 3218.9 3140.4 (-78.5) 3227.3 (8.4) _{C'-CH3 sym stretch} 3208.6 3141.8 (-66.8) 3208.0 (-0.6) _{N-CH3 sym stretch} 1969.9 1985.1 (15.2) 1999.5 (29.6) C'O' stretch

1670.8 1620.2 (-50.6) 1694.5 (23.7) _{N-CH3 asym deformation} 1644.2 1608.4 (-35.8) 1643.0 (-1.2) _{N-CH3 asym deformation} 1633.9 1583.5 (-50.4) 1634.7 (0.8) _{N-CH3 sym deformation} 1626.7 1742.4 (115.7) 1589.0 (-37.7) NH rock

1625.2 1627.7 (2.5) 1701.9 (76.7) _{C'-CH3 asym deformation} 1611.2 1628.6 (17.4) 1686.0 (74.8) _{C'-CH3 asym deformation} 1562.4 1543.6 (-18.8) 1617.5 (55.1) _{C'-CH3 deformation} 1469.5 1314.4 (-155.1) 1492.6 (23.1) C'-N stretch

(45)

1193.1 1029.5 (-163.6) 1131.4 (-61.7) NC stretch 1166.8 1042.9 (-123.9) 1137.5 (-29.3) _{C'-CH3 rock} 1093.9 1003.4 (-90.5) 1077.4 (-16.4) _{C'-CH3 rock} 867.3 708.5 (-158.8) 838.7 (-28.6) C'C stretch

529.0 507.0 (-22.0) 495.1 (-33.9) C'C rock 508.3 594.3 (86.0) 477.9 (-30.4) C'N torsion 297.8 268.3 (-29.5) 295.0 (-2.7) NC rock 183.4 142.1 (-41.3) 195.1 (11.7) _{N-CH3 torsion} 115.2 98.5 (-16.7) 166.1 (50.9) _{C'-CH3 torsion} -58.6a -66.9a (-8.3) -135.5a (-77.0) amino inversion

Table III.G. Comparison of N,N-Dimethylformamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3361.4 3261.1 (-100.3) 3293.8 (-67.7) _{CH3 asym stretch} 3300.4 3264.4 (-36.0) 3290.6 (-9.8) _{CH3 asym stretch} 3249.6 3259.4 (9.8) 3233.1 (-16.5) _{CH3 asym stretch} 3248.6 3259.0 (10.4) 3234.2 (-14.4) _{CH3 asym stretch} 3214.5 3148.5 (-66.0) 3208.6 (-5.8) C'H stretch 3201.1 3142.7 (-58.4) 3194.5 (-6.6) _{CH3 sym stretch} 3196.2 3143.5 (-52.7) 3193.1 (-3.1) _{CH3 sym stretch} 1961.1 2001.1 (40.0) 1974.2 (13.1) C'O' stretch

[image:45.612.76.529.452.717.2]

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1557.1 1525.0 (-32.1) 1553.1 (-4.0) C'H rock

1404.6 1231.3 (-173.3) 1406.0 (1.4) NC asym stretch 1287.8 1042.6 (-245.2) 1273.9 (-13.9) _{CH3 rock} 1239.0 1001.6 (-237.4) 1225.2 (-13.8) _{CH3 rock} 1199.3 988.7 (-210.6) 1160.2 (-39.2) _{CH3 rock} 1185.5 1028.8 (-156.7) 1180.7 (-4.8) _{CH3 rock}

1165.1 1262.6 (97.5) 1187.1 (22.0) C'O' oop deformation 941.5 821.0 (-120.5) 909.7 (-31.8) NC sym stretch 711.9 586.9 (-125.0) 695.7 (- 16.2) C'O' rock 426.3 419.6 (-6.7) 402.1 (-24.2) CNC bend 351.2 307.3 (-43.9) 356.3 (5.1) CNC rock 346.1 394.9 (48.8) 352.0 (6.0) C'N torsion 242.7 258.8 (16.1) 243.1 (0.4) amino inversion 161.7 143.3 (-18.4) 83.4 (-78.2) _{CH3 sym torsion} 83.9 87.8 _{(3.9) -127.2a,b (-211.1) CH3 asym torsion}

[image:46.612.79.537.68.302.2]

Table III.H. Comparison of Planar N,N-Dimethylacetamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

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1935.2 1968.4 (33.3) 1974.6 (39.4) C'O' stretch

1690.9 1592.8 (-98.1) 1675.7 (-15.3) _{N-CH3 asym deformation} 1657.5 1605.0 (-52.5) 1679.5 (22.0) _{N-CH3 asym deformation} 1655.2 1619.7 (-35.5) 1647.8 (-7.4) _{N-CH3 asym deformation} 1645.4 1633.5 (-11.9) 1640.0 (-5.5) _{N-CH3 asym deformation} 1637.8 1669.2 (31.4) 1710.1 (72.3) _{N-CH3 sym deformation} 1627.7 1610.9 (-16.8) 1703.5 (75.9) _{C'-CH3 asym deformation} 1616.3 1633.6 (17.3) 1703.3 (87.0) _{C'-CH3 asym deformation} 1593.0 1371.7 (-221.3) 1621.9 (28.9) _{N-CH3 sym deformation} 1581.6 1675.5 (93.9) 1690.5 (108.9) C'-N stretch

1538.5 1549.1 (10.6) 1569.1 (30.6) _{C'-CH3 sym deformation} 1408.1 1242.1 (-166.0) 1423.2 (15.1) NC asym stretch

1313.6 1156.7 (-156.9) 1302.0 (-11.6) _{N-CH3 rock} 1286.7 1034.1 (-252.6) 1269.5 (-17.1) _{N-CH3 rock} 1237.5 997.6 (-239.8) 1219.5 (-18.0) _{N-CH3 rock} 1182.2 1040.0 (-142.2) 1184.7 (2.5) _{N-CH3 rock} 1164.0 1053.9 (-110.1) 1129.3 (-34.7) _{C'-CH3 rock} 1126.8 1028.2 (-98.6) 1109.2 (-17.7) _{C'-CH3 rock} 1053.6 966.5 (-87.1) 1021.5 (-32.2) NC sym stretch 789.1 678.5 (-110.7) 767.4 (-21.7) C'C stretch

500.7 390.0 (-110.8) 470.9 (-29.8) C'C rock 435.6 439.9 (4.3) 435.7 (0.2) CNC bend 348.3 321.6 (-26.7) 361.0 (12.8) CNC rock 274.7 322.3 (47.6) 284.7 (10.0) amino inversion 212.5 208.1 (-4.4) 230.0 (17.5) _{C'-CH3 torsion} 143.1 145.8 (2.7) 128.7 (-14.5) C'N torsion 78.3 85.0 (6.7) _{-84.1a,b (-162.5) N-CH3 torsion} -62.8a 10.9 (73.7) -171.2a (-108.4) _{N-CH3 torsion}

[image:47.612.90.535.75.547.2]

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Frequencies

HF/6-31G* HDFF QMFF

Mode

3926.2 3989.0 (62.8) 3927.2 (1.0) NH asym stretch 3925.9 3996.5 (70.6) 3932.8 (6.9) NH asym stretch 3814.9 3884.8 (69.9) 3813.5 (-1.4) NH sym stretch 3810.8 3870.7 (59.9) 3801.9 (-8.9) NH sym stretch 2000.3 2037.0 (36.7) 1996.5 (-3.7) C'O' stretch 1811.9 1929.0 (117.1) 1726.5 (-85.4) _{NH2 asym bend} 1805.5 1953.0 (147.5) 1755.0 (-50.5) _{NH2 sym bend} 1550.2 1404.7 (-145.5) 1552.1 (1.8) C'N asym stretch 1303.6 1118.7 (-184.9) 1168.4 (-135.2) _{NH2 sym rock} 1166.1 990.0 (-176.1) 1064.0 (-102.1) _{NH2 asym rock} 1034.8 640.8 (-394.0) 947.2 (-87.6) C'N sym stretch 882.1 919.3 (37.2) 970.8 (88.7) C'O' oop deformation 648.8 770.6 (121.8) 720.7 (71.9) asym amino inversion 629.9 541.3 (-88.6) 666.3 (36.4) C'O' rock

598.8 675.5 (76.7) 607.6 (8.8) sym amino inversion 514.2 498.3 (-15.9) 567.5 (53.3) NC'N bend

[image:48.612.73.537.148.409.2]

483.2 415.1 (-68.1) 435.5 (-47.6) asym C'N torsion 417.2 416.5 (-0.7) 452.3 (35.1) sym C'N torsion

Table III.J. Comparison of N-Formylformamide Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3827.6 3944.4 (116.8) 3896.6 (69.0) NH stretch 3256.1 3152.0 (-104.1) 3228.4 (-27.7) C'H sym stretch 3232.7 3148.7 (-84.0) 3224.4 (-8.2) C'H asym stretch 2046.2 1993.8 (-52.4) 2010.4 (-35.8) C'O' sym stretch 2007.6 2017.5 (9.9) 1996.8 (-10.8) C'O asym stretch 1627.9 1534.7 (-93.2) 1570.2 (-57.7) NH rock

1584.9 1518.6 (-66.3) 1575.8 (-9.1) C'H sym rock 1488.2 1493.6 (5.4) 1483.4 (-4.9) C'H asym rock 1370.2 1133.2 (-237.0) 1311.5 (-58.7) C'N sym stretch 1294.4 992.4 (-302.0) 1305.6 (11.2) C'N asym stretch

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[image:49.612.78.540.219.663.2]

777.1 856.5 (79.4) 803.6 (26.5) C'N asym torsion 687.2 680.5 (-6.7) 721.7 (34.5) C'O' asym rock 580.1 430.3 (-149.8) 570.7 (-9.4) C'O' sym rock 303.1 306.7 (3.6) 299.2 (-3.9) C'N sym torsion 275.7 301.4 (25.7) 325.9 (50.2) C'NC' bend 137.3 145.6 (8.3) 142.7 (5.4) amino inversion

Table III.K. Comparison of Butyrolactam Frequencies Obtained by Ab Initio Calculation (HF/6-31G*) and the HDFF and QMFF Force Fields.

Frequencies

HF/6-31G* HDFF QMFF

Mode

3878.3 3937.5 (59.2) 3893.3 (15.0) NH stretch 3324.1 3267.3 (-56.8) 3318.1 (-5.9) CH asym stretch 3282.5 3276.7 (-5.8) 3295.6 (13.1) CH asym stretch 3268.7 3187.2 (-81.5) 3278.1 (9.4) CH sym stretch 3238.4 3175.4 (-62.9) 3247.6 (9.3) CH sym stretch 2057.2 2013.5 (-43.7) 2072.5 (15.3) C'O' stretch 1684.3 1705.0 (20.7) 1709.9 (25.6) _{CH2 scissor} 1609.6 1647.6 (37.9) 1685.9 (76.2) _{CH2 scissor} 1548.7 1203.2 (-345.5) 1449.2 (-99.5) NH rock 1457.9 1345.6 (-112.2) 1431.7 (-26.2) _{CH2 wag} 1353.7 1136.7 (-217.0) 1186.9 (-166.8) _{CH2 wag} 1310.9 1027.4 (-283.5) 1357.4 (46.5) _{CH2 twist} 1304.7 955.5 (-349.1) 1291.6 (-13.0) C'N stretch 1264.2 1088.0 (-176.2) 1270.6 (6.4) _{CH2 twist} 1170.5 1142.2 (-28.3) 1121.1 (-49.4) _{CH2 rock} 1099.4 1783.6 (684.3) 1057.9 (-41.4) NC stretch 1056.5 862.4 (-194.1) 1095.9 (39.4) C'C stretch 965.5 774.6 (-190.9) 913.0 (-52.5) CC stretch

896.7 891.3 (-5.4) 906.5 (9.8) _{CH2 rock}

817.1 519.6 (-297.4) 674.4 (-142.6) ring deformation 611.2 725.9 (114.7) 653.2 (42.0) C'O' oop deformation 518.5 554.4 (35.9) 530.4 (11.9) C'O' rock

407.6 -498.6a (-906.2) 556.5 (148.9) ring puckering 75.3 366.1 (290.7) 199.7 (124.4) amino inversion

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