- Email: [email protected]
Effective bond charges from experimental IR intensities
SpectrochimicaActa, Vol. 51A, No. 5, pp. 739-754, 1995
Pergamon 0584-8539(94)01298-2
Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0584-8539/95 $9.50 + 0.00
Effective bond charges from experimental IR intensities BORIS GALABOV, TODOR D U D E V a n d SONYA ILIEVA Department of Chemistry, University of Sofia, 1126 Sofia, Bulgaria
(Received 15 July 1994; accepted 26 September 1994) Abstract--Experimental gas-phase IR absorption intensities for water, ammonia, methane, ethene, ethyne, propyne, methyl fluoride, methyl chloride, methyl bromide, methyl iodide, formaldehyde, F2CO, CI2CO, F2CS and CI2CS are transformed into quantities termed effective bond charges (6~) following a recently developed formalism. The comparison of 6k values for O--H, N-H, C-H, C-X (X = F, CI, Br, I), C = O and C=S bonds reveals trends of changes that can be associated with the valence state and electronegativities of constituent atoms and also with polarities and electronic polarizabilities of the respective bonds.
INTRODUCTION
IN A recent paper we described a new approach in interpreting vibrational absorption intensities [1]. The formulation employs as initial data vibrational intensities transformed into atomic polar tensors (APTs) [2, 3]. APTs are particularly appropriate representations of the dipole changes inflicted by vibrational distortions since these quantities may be obtained in a simple way from experiments, on the one hand, and are also standard results of ab initio molecular orbital calculations. Thus, direct comparisons between experimental and theoretical dipole moment derivatives are readily available. The physical interpretation of these quantities is, however, hampered by the implicit presence of rotational contributions into the APT elements. Additional difficulties arise from the existence of a considerable number of dependencies between the elements of the APT matrix of a molecule [4-6]. Vibrational absorption intensities in the gas-phase are determined by the fluctuations of the electric charges in molecules accompanying vibrational motion. It is therefore of considerable interest to extract from these experimental quantities molecular parameters characterizing the electric charge properties of molecules. To obtain such information it is necessary to remove from the initial dipole moment derivatives all non-vibrational contributions and also eliminate the redundancies present. Such an approach was proposed recently and the formulation developed lead to the determination of quantities called effective bond charges [1]. Data from 6-31G** ab initio calculations on six molecules were analysed in the previous study. In the present paper bond charges from experimental gas-phase absolute IR intensities on an extended series of molecules are evaluated. The interest is to analyse the trends of changes of these quantities for different types of chemical bonds and, thus, assess the potential of the procedure developed in deriving quantities associated with the intramolecular charge distribution and its dynamics with molecular motion.
EFFECTIVE BOND CHARGES
APTs free from rotational contributions can be obtained from the relation, in matrix notation [1]:
Px(o) = PsUB -- RsUB.
(1)
The elements of Px(v) contain derivatives of the Cartesian components of the molecular dipole moment with respect to atomic Cartesian displacement coordinates that refer to a molecule-fixed system. Ps is a matrix containing dipole moment derivatives with respect to symmetry coordinates and Rs is a matrix containing rotational correction terms that eliminate the contribution arising from the zero angular momentum condition [7-9]. The 739
B. GALABOV et al.
740
elements of Rs can be determined using available methods [7-9]. U and B are the standard matrices used in normal coordinate analysis [10]. The elements of Px(o) are related by nine redundancy conditions [4-6]: N
Z
P"x(V) = 03
(2)
a=I
where P~ is the APT of the ath atom, N is the number of atoms and 03 is a 3 x 3 zero matrix. These redundancies can be removed by representing the dipole derivatives into a bond Cartesian displacement coordinate space [11]. These coordinates are defined in terms of atomic Cartesian displacements by the expression [11]: X~k) - -
( A X ( a k) - -
Ax[~))i + (Ay~0 - Ay ~*))j+
( A z ( a k) -
Az~k))k
(3)
or
Xgk)= Axgk)i+ Ay~k)j+ Az?)k,
(4)
where a and b are indexes of the initial (a) and terminal (b) atoms of the kth bond, and i, j and k are unit vectors along the reference Cartesian frame. The respective dipole derivative tensor for the kth bond has the form
Ok(v)= d x(o)
d z(v)
(5)
d x(O) d Ao) The elements of Dk(V) refer also to a molecule-fixed Cartesian system. Arranged in a row, these form the following matrix: O ( v ) = ( D I ( v ) D z ( v ) . . . D k ( v ) . . . DN-I(V)).
(6)
The elements of D(v) are easily obtained from the respective rotation-free atomic polar tensor matrix Px(V): D(v) = Px(v)C-l.
(7)
The transformation matrix C -1 has a rather simple structure with elements zero or unity appropriately placed [1]. Effective bond charges are the invariants with respect to reorientation of the Cartesian reference system of the tensors Dk(v) 6 2 = Tr(Ok(V). lJk(u)),
(8)
where l)k(u) is the transpose of Dk(V). The quantities 6k are expected to reflect, in a generalized way, electrical properties of the respective bonds. In the following, 6k values for various types of bonds in a series of simple molecules are calculated from experimental gas-phase IR intensity data.
RESULTS H20 a n d NH3 Experimental gas-phase intensities for H20 [12] and NH3 [13] were used to derive 6k quantities for O-H and N-H bonds, respectively. These are given in Table 1. The first step in IR intensity analysis is the transformation of the experimental intensities into dipole moment derivatives with respect to normal coordinates. As is well known, only absolute values of these quantities can be obtained from experiments. Therefore, the signs of Op/OQi derivatives for the molecules treated have been fixed by quantum mechanical calculations [13, 14]. In analysing intensities it is always preferable to further transform the Op/OQi quantities into dipole moment derivatives with respect to symmetry vibrational coordinates. This is of particular importance in the determination of
Effective bond charges from experimental IR intensities Table 1. Observed absolute gas-phase intensities of H 2 0 and NH3 v~ (cm-1)
Molecule H20
NH3
IR
Ai (kin mol -l)
A1
1 2
3657 1597
2.24 53.6
B2
3
3756
44.6
A1
1 2
3337 950
7.6 138
E
3 4
3444 1627
3.8 31.7
band
Ref. 12
13
Table 2. G e o m e t r y data and s y m m e t r y coordinates for H 2 0 and N H 3
Geometry H20 ~ NH3 b
ron =0.9572 A , , / - H O H = 104.5 ° rNn = 1 . 0 1 1 6 / ~ , / _ H N H = 106.67 °
Symmetry coordinates~ H20
NH3
Al
St = (Arl + A r2)/~'2 S2 = A0
B2
$3 = (Arl -- Ar2)/X/2
Al
$1 = (Arl + Ar2+ Ar3)/V3 $2 = (Act1 + Aa2 + Aa3)/%/3
E'
$3~ = (2Arl - Ar2 - Ar3)/V~ S~ = (2Aal - Aa2 -- Aa3)/V6
E ft
S3b = (Ar2 - Ar3)/V~ (Aa2 - Aa3)lVr2
S4b= F r o m ref. [15]. b F r o m ref. [16]. c Internal coordinates are defined in Fig. 1.
zI x
w
×
Fig. 1, Cartesian reference systems, n u m b e r i n g of atoms and definition of internal coordinates for H 2 0 and NH3.
741
B. GALABOVet al.
742
Table 3. Ps matrices for H20 and NH~ (in units D/~ i or D rad -I) H20
(o
o
Si
52
0
-0.234
-/
53
~.992'
0.726
0
/
x Y z
NH3
Si
$2
[~ 0.29
0 0 1.62
S3~
S~
-0.195-0.366 0 0 0 0
S3b
S4b
0 -0.195 0
0 -0.366 0
The symmetry coordinates employed are defined in Table 2.
r o t a t i o n a l c o r r e c t i o n t e r m s a p p e a r i n g as e l e m e n t s o f the Rs m a t r i x [ E q n (1)]. T h e g e o m e t r y d a t a a n d t h e definition o f s y m m e t r y c o o r d i n a t e s e m p l o y e d in the c a l c u l a t i o n s a r e given in T a b l e 2. T h e o r i e n t a t i o n o f m o l e c u l e s in the C a r t e s i a n r e f e r e n c e f r a m e s is s h o w n in Fig. 1. T h e t r a n s f o r m a t i o n o f Op/OQi into Op/OSj d e r i v a t i v e s is c a r r i e d o u t with t h e r e s p e c t i v e n o r m a l c o o r d i n a t e m a t r i c e s Ls. T h e s e a r r a y s a r e o b t a i n e d f r o m n o r m a l c o o r d i n a t e c a l c u l a t i o n s e m p l o y i n g the v a l e n c e force fields o f MILLS [17] for w a t e r a n d DUNCAN a n d MILLS [18] for a m m o n i a . T h e values o f d i p o l e m o m e n t d e r i v a t i v e s with r e s p e c t to s y m m e t r y c o o r d i n a t e s f o r m i n g t h e Ps a r r a y s for the two m o l e c u l e s a r e given in T a b l e 3. T h e e l e m e n t s o f the r e s p e c t i v e Rs m a t r i c e s are e v a l u a t e d by e m p l o y i n g t h e h e a v y i s o t o p e m e t h o d [9], w e i g h t i n g the h e a v y a t o m s by a f a c t o r of 1000. PsBs, RsBs, Px(v) a n d D ( v ) m a t r i c e s for t h e s e m o l e c u l e s a r e given in T a b l e s 4 a n d 5. T h e c a l c u l a t e d 6~ v a l u e s [ E q n (8)] for the O - H a n d N - H b o n d s a r e p r e s e n t e d in T a b l e 6. T h e v a l u e s o b t a i n e d will b e discussed in t h e s u b s e q u e n t sections.
Methane, ethene, ethyne and propyne It was o f i n t e r e s t to f o l l o w t h e c h a n g e s o f effective b o n d c h a r g e s in C - H b o n d s as a f u n c t i o n o f t h e v a r y i n g h y b r i d i z a t i o n o f the c a r b o n a t o m a n d c h a n g e s in e n v i r o n m e n t . E x p e r i m e n t a l g a s - p h a s e I R i n t e n s i t i e s for m e t h a n e [19], e t h e n e [20], e t h y n e [21] a n d p r o p y n e [22] u s e d in e v a l u a t i n g the 6k q u a n t i t i e s for the r e s p e c t i v e C - H b o n d s a r e s u m m a r i z e d in T a b l e 7. T h e g e o m e t r y d a t a a n d the definition o f s y m m e t r y c o o r d i n a t e s for t h e s e m o l e c u l e s a r e given in T a b l e 8. C a r t e s i a n r e f e r e n c e s y s t e m s a n d the definition o f i n t e r n a l c o o r d i n a t e s for t h e series o f f o u r h y d r o c a r b o n s s t u d i e d a r e s h o w n in Fig. 2.
Table 4. Experimental PsBs, RsBs, Px(v) and D(u) matrices for HzO (in units of electrons)a
PsBs =
-0.231 0 0
01 0 0 0
asB $
-0.018 0 0
0 0 0
Px(V) =
-0.213 0 0
0 0 0
0 0 -0.292 0 0 0 0 0 -0.292
H2 0 0 0
0 . 0 8 9 0.115 0 0 0 . 1 4 6 0.069
/43 0 0 0
-0.089 / 0 0.146
0.009 0 0
0 0 0
0 . 0 0 7 0.009 0 0 0 0
0 0 0
-0.007 I 0 0
0.106 0 -0.069
0 0 0
0 . 0 8 2 0.107 0 0 0.146 0.069
0 0 0
-0.082/ 0 0.146 /
r2
t
0
0.146/
0.115 0 -0.069
rt
oO o0O8 oo.lo7 oO
D(v)= ~ -0.069
0
0 . 1 4 6 0.069
a 1 e = 1.602 x 10-19C. The numbering of atoms and bonds and Cartesian reference frame are shown in Fig. 1.
0 -0.028 0
0 -0.132 0
-0.028 0 0
1-0.132 0 0
RsBs =
D(o) =
0 0 -0.547
0 0 0
0 0 -0.547
0 0.080 0
0.009 0 -0.112 0 0.080 0
r~
0 0.009 0
0.009 0 0
0.009 0 -0.112
0 0.089 0
0.018 0 -0.112
H2
0.036 0 0.182
0.036 0 0.182
0.008 0 0
0.044 0 0.182
0.062 0.031 0.056
0.062 0.031 0.056
0.009 0 0
0.071 0.031 0.056
H3
0.031 0.027 -0.097
r2
0.031 0.027 -0.097
0 0.009 0
0.031 0.036 -0.097
a The numbering of atoms and bonds and Cartesian reference system are given in Fig. 1.
Px(v) =
0 -0.160 0
-0.160 0 0
PsBs =
Nl
-0.018 0.031 0.182
-0.018 0.031 0.182
-0.004 0.007 0
-0.022 0.038 0.182
0.062 -0.031 0.056
0.062 -0.031 0.056
0.009 0 0
0.071 -0.031 0.056
Table 5. Experimental PsBs, RsBs, Px(o) and D(v) matrices for NH3 (in units of electrons)a
-0.031 0.027 0.097
r3
-0.031 0.027 0.097
0 0.009 0
-0.031 0.036 0.097
H4
/
-0.018~ -0.031 ] 0.182]
-0.018 -0.031 0.182
-0.004' -0.007 0
-0.022' -0.038 0.182
--,,1 4~
o~
~r O
744
B. GALABOVel al. Table6. Effective bond charges from experimental IR intensities (in units of electrons) Bond
Molecule
O-H N-H C-H
H20 NH 3 CH4 CH2=CH2 CH--CH CHa-=C-CH3b
6,
CH3F CH3CI CH3Br CH3I H2CO
0.210 0.231 0.162 0.179 0.352 0.349 (a) 0.139 (b) 0.163 0.130 0.129 0.139 0.267
C-F
CH3F F2CO F2CS
0.946 1.096 1.064
C-CI
CH3CI C12CO CI2CS
0.470 0.866 0.879
C-Br
CH3Br
0.329
C-I
CH3I
0.135
C=O
H2CO F2CO C12CO
0.789 0.931 1.070
C=S
F2CS CI2CS
0.650 0.781
Table 7. Observed absolute gas-phase IR and band intensities of methane, ethene, ethyne and propyne vi (cm J)
Molecule
Ai (km mol l)
Ref.
CH4
F2
3 4
3019 1311
65.5 31.8
19
CH2=CH2
Bj. B2,,
7 9 10 ll 12
949 3105 826 2989 1443
84.4 26.0 0.03 14.3 10.4
20
3295 730
76.244 194.888
21
43.2 19.5 5.2 1.42 0.65 15.4 17.8 0.25 88.5 15.6
22
B3~ CH-=CH
X~ FI,
3 5
CH3-C---CH
A~
1 2 3 4 5 6 7 8 9 10
E
31335.1 2910 2142 1390.6 930.1 2!)80.8 1450.9 1036 638.6 329.2
Effective bond charges from experimental IR intensities
745
Table 8. Geometry data and symmetry coordinates for methane, ethene, ethyne and propyne
Geometry Methane a Ethene b Ethyne c Propyned
rc, = 1.093 A, a . c , = 109.471 ° rcc = 1.339/~, rcH = 1.085/~, aHcn= 117.83° rcc = 1.203/~, rcn = 1.060 ,~ rc,c = 1.2073 A, rc4: = 1.4596 ,~, rH_c~= 1.060 A rCH(CH3)= 1.096/~, aHCH= 108.28 °
Symmetry coordinates "'f Methane
F2
S3x= (Arl - Ar2 -- Ar3 + A&)/2
S3y = (-Ar~ + Ar 2- Ar3+ Ar4)/2 S3z = (Ar I + Ar 2- Ar 3- A&)/2 S4x-~ (Aa23 -- Aat4)/V~ S4y -~ (Aa13 -- aa24)/V'2 $4~= (Aa34 - Aal2)/V2 Ethene
Blu Bz~
$7 = r0 cos(a/2) (At/I + Ar]E)/V2g' h $9 = (At1 - At2 - Ar 3+ Ar4)/2 S10 ~- r0(Aq~ 1 - A ~ 2 - A ~ 3 + A ~ 4 ) / 2 g
B3~
Sn = (At1 + Ar2 - Ar3 - Ar4)/2 St2 = r0(2Aat - 2Aa2 - ASt - Aq~2+ Aq~3+ A$4)/X/~g
Ethyne
X, n.
S 3=
Propyne
At
St = (Art + Ar2 + Ar3)/V~ S2 = a(Aal + Aa2 + Aa3) - b(Aflt + Aft2+ Aft3) a = 0.41675, b = 0.39956 $3 = AR $4 = AT $5 = Ar'
E'
$6~= (2Arl - Ar2 - Ar3)/X/6 STx= (2Aat - Aa2 - Aa3)/V6
(Aq - Ar2)/V2 $5~ = (a$x + A~')/N/2
&, = (2A#, - A#2 - A~3)/VZ
Sgx= A¢x S1o:¢ = A ~ ) x
E"
S6y= (Ar2 - Ar3)/N/2 STy= (Aa2 -- Aa3)/V2
Sgy= A~y Stay = A~py a From Ref. [18]. b From Ref. [23]. c From Ref. [24]. dFrom Ref. [25]. e Symmetry coordinates describing the IR-active vibrations only are given. f Internal coordinates are defined in Fig. 2. g r0 = 1.085/~. h r/ is an out-of-plane angle.
T h e Op/OQi q u a n t i t i e s a r e t r a n s f o r m e d i n t o d i p o l e m o m e n t d e r i v a t i v e s w i t h r e s p e c t t o s y m m e t r y c o o r d i n a t e s with the aid of t h e r e s p e c t i v e n o r m a l c o o r d i n a t e t r a n s f o r m a t i o n m a t r i c e s . I n t h e i r e v a l u a t i o n , t h e f o r c e f i e l d s o f DUNCAN a n d MILLS f o r m e t h a n e [18], o f DUNCAN et al. f o r e t h a n e [26], o f STREY a n d MILLS f o r e t h y n e [24] a n d o f DUNCAN et al. f o r p r o p y n e [27] w e r e e m p l o y e d . T h e e l e m e n t s o f t h e r e s p e c t i v e Ps m a t r i c e s a r e c o l l e c t e d in T a b l e 9. M e t h a n e , e t h e n e a n d e t h y n e d o n o t p o s s e s s a p e r m a n e n t d i p o l e m o m e n t . Therefore, no rotational terms appear. In the case of propyne, having a dipole moment o f - 0 . 7 5 D [28], a r e f e r e n c e h e a v y i s o t o p e C * H a - C * - = C H w i t h m a s s e s o f t h e r e s p e c t i v e c a r b o n a t o m s m u l t i p l i e d b y 1000 is u s e d t o d e r i v e t h e e l e m e n t s o f Rs f o r t h e v i b r a t i o n s b e l o n g i n g to t h e E s y m m e t r y class. D(v) m a t r i c e s for t h e h y d r o c a r b o n s s t u d i e d are given in T a b l e 10. T h e c a l c u l a t e d 6k v a l u e s f o r t h e C - H b o n d s a r e g i v e n in T a b l e 6.
746
B. GALABOV et al.
zI x ~
01
R
I"1
@ /~,,,
Yl Z
cp~
q>x
%
%
Z
Fig. 2. Cartesian reference systems and definition of internal coordinates for methane, ethene, ethyne and propyne. Table 9. Ps matrices for methane, ethene, ethyne and propyne° (in units D/~-t or D rad -~) Methane S~ ( -i.7502
S3y
$3~
0 -0.7502 0
0 0 -0.7502
$4~
$9
Sl0
SI1
o
o0
S4y
0.38180 0 0.3818 0 0
$4~ 0 ) 0 0.3818
Ethene $7
(:
o
-0.71 0
0.05 0
0.63
S12
ot
0 0.27
y z
Ethyne
$3
( 0
$5~
1.4918
Ssy
0
0 1.3258
0 0
-1.4918 0
S1 0 0 0.618
S2 0 0 0.089
S3 0 0 -0.052
) x y z
Propyne
s,~
s,..
-1.128 0 0
-1.107 0 0
s6y
0 -0.400 0
S4 0 0 - 1.228
Ss 0 0 0.871
sT,
0 0.404 0
S~ -0.400 0 0
S,, 0.404 0 0
ss,
sg,
S.o,
0
0
-0.212 0
° The symmetry coordinates employed are defined in Table 8.
-1.128 0
-0.212 0 0
0
X
-1.107 0
y Z
0.068 -0.020 0.064
r2
0 -0.025 0
R
0 -0.207 0
R
0 0.132 0
-0.011 0.023 -0.013
0 0 0.245
0 0 -0.195
0 0 -0.016
R
0.058 -0.068 -0.037
-0.257 0 0
-0.207 0 0
-0.141 0 0
-0.068 -0.020 -0.064
r3
0 -0.257 0
T
0 0.207 0
rl
0 -0.066 0.081
r2
-0.003 0.066 0.066
0.066 -0.003 -0.066
-0.066 0.066 -0.003
rI
0.066 -0.003 0.066
-0.011 -0.023 -0.013
0 0 -0.437
0 0 0.195
0 0.034 0.008
rl
0.066 -0.066 -0.003
0.211 0 0
-0.059 0 0.074
-0.207 0 0
-0.141 0 0
-0.003 -0.066 -0.066
"Cartesian reference systems and numbering of bonds are shown in Fig. 2.
0.058 0.068 -0.037
-!.025
Propyne
0.207 0 0
Ethyne
- i 516
Ethene
-0.003
Methane
0 0.211 0
r'
0 0.097 0
r~
0 0.207 0
r2
0 -0.066 -0.081
-0.066 -0.003 -0.066
r3
0 0 0.181
0.027 0 -0.013
J
0 1 0 0.195
0 -0.034 0.008
r2
-0.066 -0.066 -0.003
0.141 0 0
-0.003 -0.066 0.066
0 -0.066 0.081
-0.066 -0.003 0.066
F4
0 0.034 0.008
r3
0.066 t 0.066 -0.003
Table 10. Experimental D(v) matrices for methane, ethene, ethyne and propyne (in units of electrons)"
0.141 0 0
0 -0.066 -0.081
0.008 !
034/
r4
¢D
¢D
B
~r O t~
m
B. GALABOV et al.
748
Table 11. Observed absolute gas-phase IR band intensities of methyl halides vi (cm-l)
Molecule
Ai (kin m o V i)
vi (era-i)
Ai (kin tool-l)
Ref.
CH3F
A1
1 2 3
2863.2 1460 1048.6
24.7 0.9 95
E
4 5 6
3005.8 1468 1182.4
61 8.7 2.6
29
CH3CI
Ai
1 2 3
2967.8 1355 732.9
19.15 8.41 23.69
E
4 5 6
3038.9 1452.1 1017.3
10.77 11.38 3.85
30
CH3Br
Aj
1 2 3
2972 1305 611
16.452 15.388 11.186
E
4 5 6
3056 1445 952
5.196 12.591 7.237
31
CH3I
Al
1 2 3
2970 1251 533
11.03 20.66 1.93
E
4 5 6
3061 1440 880
2.15 10.59 8.91
8
xI Z
a2
R
G
2
Fig. 3. Cartesian reference system and definition of internal coordinates for methyl halides.
Table 12. G e o m e t r y data and s y m m e t r y coordinates for methyl halides
Geometry CH3 Fb CH3CI c CH3BI"b CH3 Ib
rcn (A)
rcx (A)
ancn ~°}
Po (D) °
1.095 1.095 1.084 1.083
1.382 1.780 1.935 2.136
110.5 110.83 111.33 111.67
-1.81 -1.87 - 1.80 -1.62
Symmetry coordinates d AI $1 = (Arl + Ar2 + A r 3 ) / ~ 3 $2 = [k(Aa, + Aa2 + Aa3) - (Afll + A~2 + fl3)]/[3(1 + k2)] ~/2 k = - 3 sinfl cos fl/sin a S3= A R
E'
S4,, = (2Arl - Ar2 -- Ar3)/V'6 S5, = (2Aaj - A a 2 - Aa3)/%/6 s~ = (2A#, -
A132-- A133)/X/8
° From Ref. [9]. b From Ref. [34], c From Ref. [35]. a For the definition of the internal coordinates, see Fig. 3.
E"
S4b = ( Ar2 - A r 3 ) / V ~ S5b = ( A a 2 -- ACt3)/V2 s~ = (A~2-
A~3)/X/~
Effective bond charges from experimental IR intensities
749
Table 13. Dipole moment derivatives with respect to symmetry vibrational coordinates for methyl halides (in units of D A -l or D rad 1)a
Si
$2
S3
S~
S~
$6,
S4b
Ssbb
S~
CH3F
0 0.64
0
0 0.20
0 -4.54
0 0 -0.182
0 0 -2.237
07 0 9 0 0
0 0
00 0 0
0
0
0 -0.386 0
0 0.285 0
-0.72 0
0.29 0
i)
.02
CH3CI [~ 0.625
-0.3860.285 0 0 0 0
-0.166 0 0
-0.281
-0.260
0 1 -0.166 0
CHjBr /~
0
0
0
0
0.576-0.317
-1.546
0 0 0.492
0 0 -0.533
0.295
0
0
0
0
0 81
0
0
0
0
0
0 0
0
0
\ 60
)
CH3I 0 0 -0.454
-0.136 0 0
0.347 0 0
-0.380 0 0
0 -0.136 0
0 0.347 0
0 / -0.380 0
)
aThe symmetry coordinates are defined in Table 12.
Methyl halides
Experimental gas-phase IR intensity data of KONDO and SAEKI [29] for methyl fluoride, KONDO et al. [30] for methyl chloride, VAN STRATEN and SMIT [31] for methyl bromide and of DICKSONet al. [8] for methyl iodide were used in the analysis. These data are presented in Table 11. The normal coordinate transformation matrices Ls are calculated from the force fields of BLOM and MULLER ( C H 3 F [32]), of DUNCAN et al. (CH3CI [33]) and of DUNCAN et al. (CH3Br and CH3I [34]). Definitions of internal and symmetry coordinates and molecular geometry data are given in Fig. 3 and Table 12. The Ps matrices containing Op/OSj derivatives for the series of methyl halide molecules are given in Table 13. The determination of the elements of the Rs matrices for vibrations belonging to the non-totally symmetric E class is performed by using hypothetical heavy isotopes with masses of the heavy atoms multiplied by 1000. The D(v) matrices for these molecules are presented in Table 14. The calculated effective bond charges for C-H and C-X (X=F, CI, Br, I) are summarized in Table 6. X2CY molecules Experimental absolute gas-phase IR intensities of HOPPER et al. [36, 37] for F2CO, F2CS, C12CO and CI2CS, and of NAKANAGA et al. [38] for H2CO were used. The respective Ai values are summarized in Table 15. The Op/OQi values obtained from the experimental IR intensities are further reduced to Op/OSj dipole moment derivatives with Ls matrices evaluated from the force fields of OVEREND and HALL [39] for F2CO and C12CO, of HOPPER et al. [37] for F2CS and CI2CS and of DUNCAN and MALUNSON[40] for H2CO. Internal and symmetry coordinates and geometry data are defined in Fig. 4 and Table 16. The Ps arrays employed in the calculations are given in Table 17. The D(u) matrices evaluated for the X2CY molecules studied are presented in Table 18. The C-X and C-Y effective bond charges obtained are shown in Table 6.
DISCUSSION OF THE EFFECTIVE BOND CHARGES
Comparing 6k values for O - H and N-H bonds, it can be seen that they are quite close in magnitude. This is in accordance with expectations because of the similarity of the two bonds.
0.054 0 0
0.048 0 0
0.043 0 0
0
'/0.034
0 0.054 0
0 0.048 0
0 0.043 0
0 0.034 0
0 0 -0.111
0 0 -0.322
0 0 -0.466
0 0 -0.945
-0.001 0 0.036
-0.026 0 0.051
-0.045 0 0.063
-0.103 0 0.083
0 0.095 0
0 0.085 0
0 0.084 0
0 0.089 0
rl
0.045 0 -0.083
0.040 0 -0.067
0.036 0 -0.050
0.035 0 0.004
0.071 0.041 -0.018
0.057 0.048 -0.026
0.052 0.056 -0.031
0.041 0.083 -0.041
a Cartesian reference system and numbering of bonds are shown in Fig. 3.
CH3I
CH3Br
CH3CI
CH3F
R
0.041 0.023 0.031
0.048 0.002 0.045
0.056 -0.013 0.054
0.083 -0.055 0.072
r2
-0.023 0.039 -0.083
-0.020 0.035 -0.067
-0.018 0.031 -0.050
-0.018 0.031 0.004
0.071 -0.041 -0.018
0.057 -0.048 -0.026
0.052 -0.056 -0.031
0.041 -0.083 -0.041
Table 14. Experimental D(v) matrices for methyl halides (in units of electrons)°
-0.041 0.023 -0.031
-0.048 0.002 -0.045
-0.056 -0.013 -0.054
-0.083 -0.055 -0.072
r3
-0.023 t -0.039 -0.083 [
-0.020 t -0.035 -0.067/
-0.018 ) -0.031 -0.050
-0.018 -0.031 0.004
7, O <
Effective bond charges from experimental IR intensities
751
Table 15. Experimental absolute gas-phase IR intensities of XzCY molecules
Molecule H2CO
At
F~CO
At
vi
Ai
vi
Ai
(cm -t )
(km mol -t )
(cm -t )
(km mol -t )
Ref.
1 2 3
2782 1746 1500
75.5 73.99 11.15
Bt
1 2 3
1928 965 626
381.74 56.44 7.04
Bt
B2
B2
CI2CO
At
1 2 3
1827 567 285
245.26 14.48 0.07
Bi
FzCS
At
1 2 3
1368 787 526
390.34 8.92 6.72
B1
1 2 3
1137 505 220
210.80 13.81 0
B1
CI2CS
A1
Bz
B2
B2
4 5 6
2843 1249 1167
87.6 9.94 6.49
38
4 5 6
1249 584 774
370.79 5.20 30.64
36
4 5 6
850 440 580
376.45 0.18 4.90
36
4 5 6
1189 417 622
201.54 0.25 1.33
37
4 5 6
816 294 473
162.93 0.30 2.35
37
Fig. 4. Cartesian reference system and definitioon of internal coordinates for X2CY molecules.
Table 16. Geometry data and symmetry coordinates for X2CY molecules rcv (/~)
rcx (.~)
axcx~°)
/~o(D) °
1.203 1.174 1.166 1.56 1.56
1.099 1.312 1.746 1.32 1.75
116.5 108 111.3 112.5 111.3
-2.35 c -0.95 -1.18 -0.05 -0.28
Geometry H2CO b F2CO a CI2CO° F2CSd CIECSd
Symmetry coordinates" A1 SI = (Arl + Ar2)/V~
$2= AR s3 = ( 2 z a - A # , - A/~9/X/-6
BI
$4 = ( A r t - Ar2)/V~ s~ = (A/~t - A / ~ 2 ) / V ~
B2 $6 = Ay / "From Ref. [9] unless indicated. b From Ref. [38]. c From Ref. [41]. d From Ref. [37]. "Internal coordinates are defined in Fig. 4. IF is an oubof-plane angle.
752
B. GALABOVet al. Table 17. Dipole moment derivatives with respect to symmetry vibrational coordinates for X2CY molecules (in units of D A -I or D rad-~)" Sj
$2
S
$4
$5
$6
1.297 0 0
-0.424 0 0
0 -0.293 0
H2CO 0 0 1.059
0 0 -3.741
0 0 0.081
0 0 4.57
0 0 -3.97
0 0 -1.43
5.246 0 0
- 1.762 0 0
0 1.198 0
0 0 2.4
0 0 -4.7
0 0 -0.69
5.07 0 0
-2.2 0 0
0 0.596
0
0 0 4.83
0 0 -3.07
0 0 - 1.81
4.798 0 0
-0.619 0 0
0 0.282 0
0 0 -3.7
0 0 -0.71
4.601 0 0
-0.806 0 0
F2CO
CIzCO
F2CS
CI2CS (~ 3.7
i -
) .449
"The symmetry coordinates are defined in Table 16.
Analysis of the data for the hydrocarbon series collected in Table 6 reveals a tendency towards higher 6k values with increased s-character of the carbon valence orbitals, beginning with 0.162 e for methane (CSp3-H), 0.179 e for the CsP2-H 6k value in ethene, and ending with much higher effective charges for the acidic CSP-H bonds in ethyne and propyne. The same trend was found for the C-H bond charges evaluated from 6-31G** ab initio MO calculations [1]. The Csp3-H effective bond charge, as obtained for a Table 18. Experimental D(v) matrices for X2CY molecules (in units of electrons) a R
rl
r2
H2CO -0.017 0 0
0 0.125 0
0 0 -0.779
-0.152 0 -0.142
0 0.130 0
-0.083 0 -0.066
-0.152 0 0.142
0 0.130 0
0.083 0 -0.066
-0.323 0 0
0 0.282 0
0 0 -0.827
-0.714 0 -0.381
0 0.215 0
-0.340 0 -0.620
-0.714 0 0.381
0 0.215 0
0.340 0 -0.620
-0.377 0 0
0 0.213 0
0 0 -0.979
-0.702 0 -0.235
0 0.126 0
-0.327 0 -0.283
-0.702 0 0.235
0 0.126 0
0.327 0 -0.283
-i.113
0 0.040 0
0 0 -0.639
-0.624 0 -0.397
0 0.042 0
-0.337 0 -0.686
-0.624 0 0.397
0 0.042 0
0.337 0 -0.686
-0.126 0 0
0 -0.044 0
0 0 -0.770
-0.592 0 -0.391
0 -0.036 0
-0.336 0 -0.393
-0.592 0 0.391
0 -0.036 0
0.336 0 -0.393
F2CO
C12CO
F2CS
CI2CS
a Cartesian reference system and numbering of bonds are shown in Fig. 4.
)
Effective bond charges from experimental IR intensities
753
F "~ 0.8-
CH3Ce~ g
0.4-
CH3Br
/
O.O 2.~ . . . . . . ~'.~ . . . . . .
'~;G . . . . . . .
ELECTRONEGATIVITY
;'.~' . . . . .
'~;
.......
[Paullng units]
Fig. 5. Plot of the dependence between 6c_x ( X = F, CI, Br, I) and the electronegativity of halogen atoms.
number of molecules, does not appear to be very sensitive to environmental changes in the series of hydrocarbons and methyl halides, with variations in the range 0.129 (CHaBr) to 0.163 e (CHaF). Much more pronounced variations in ~k values are found for the polar carbonhalogen, carbon-oxygen and carbon-sulfur bonds. The C-X effective bond charge in methyl halides changes from 0.946 e in CH3F, 0.470 e in CH3CI, 0.329 e in CH3Br to 0.135 e in CH3I. This is in full agreement with expectations and the values evidently may be related to the electronegativity of the halogen atoms. This dependence is shown in Fig. 5. The C = O effective bond charges are higher than the respective C=S values in the sulfur analogs. This finding is also in accord with the expected lower polarity of the C=S bonds due to the lower electronegativity of the sulfur atom. Comparing 6k data for lower polarity bonds (C-H) to the much more polar C--O, C=S, C-F, C-CI and C-Br bonds, it is seen that higher bond polarity is reflected in much higher effective bond charges, with values varying with expectations in most cases. The analysis of the data for the effective bond charges as obtained from experimental gas-phase intensity data for a number of molecules reveals some definite trends of changes. The variations found may, in most cases, be related to the polar properties of the bonds considered. As already stressed, the effective bond charges are solely determined by purely vibrational distortions of the molecules. The data obtained show that these quantities may, very possibly, be regarded as experimental parameters associated with the intrinsic electric properties of valence bonds.
REFERENCES
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
B. Galabov, T. Dudev and S. l!ieva, Spectrochim. Acta 49A, 373 (1993). J. F. Biarge, J. Herranz and J. Morcillo, An. Quire. Set. A57, 81 (1961). W. B. Person and J. H. Newton, J. Chem. Phys. 61, 1040 (1974). V. T. Aleksanyan and S. Kh. Samvelyan, in Vibrational Spectra and Structure (Edited by J. R. Durig), Vol. 14, p. 256. Elsevier, Amsterdam (1985). J. C. Decius and G. B. Mast, J. Molec. Spectrosc. 70, 294 (1978). B. S. Averbukh, J. Molec. Spectrosc. 117, 179 (1986). B. L. Crawford Jr, J. Chem. Phys. 20, 977 (1952). A. D Dickson, I. M. Mills and B. L. Crawford Jr, J. Chem. Phys. 27, 445 (1957). A. J. van Straten and W. M. A. Smit, J. Molec. Spectrosc. 56, 484 (1975). E. B. Wilson Jr, J. C. Decius and P. C. Cross, Molecular Vibrations. McGraw-Hill, New York (1955). L. S. Mayants and B. S. Averbukh, J. Molec. Spectrosc. 22, 197 (1967). S. Clough, Y. Beers, G. Klein and L. Rothman, J. Chem. Phys. 59, 2254 (1973).
SA(A)51:5-E
754 [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] 28] 29] 30] 31] 32] 33] 34] 35] [36] [37] [38] [39] [40] [41]
B. GALABOVet al. Th. Koops, T. Visser and W. M. A. Smit, J. Molec. Struct. 96, 203 (1983). B. Zilles and W. B. Person, J. Chem. Phys. 79, 65 (1983). W. S. Benedict, N. Gailar and E. K. Plyler, J. Chem. Phys. 24, 1139 (1956). L. E. Sutton, lnteratomic Distances, Spec. Publ. No. 11. The Chemical Society, London (1958). I. M. Mills, in Infrared Spectroscopy and Molecular Structure (Edited by M. Devies). Elsevier. Amsterdam (1963). J. L. Duncan and I. M. Mills, Spectrochim. Acta 20, 523 (1964). J. H. G. Bode and W. M. A. Smit, J. Phys. Chem. 84, 198 (1980). T. Nakanaga, S. Kondo and S. Saeki, J. Chem. Phys. 70, 2471 (1979). W. M. A. Smit, A. J. van Straten and T. Visser, J. Molec. Struct. 48, 177 (1978). J. H. G. Bode, W. M. A. Smit, T. Visser and H. D. Verkruijsse, J. Chem. Phys. 72, 6560 (1980). J. L. Duncan, I. J. Wright and D. van Lerberghe, J. Molec. Spectrosc. 42, 463 (1972). G. Strey and I. M. Mills, J. Molec. Spectrosc. 59, 103 (1976). J. L. Duncan, D. C. McKean, P. D. Mallinson and R. McCulloch, J. Molec. Spectrosc. 46, 232 (1973). J. L. Duncan, D. C. McKean and P. D. Mallinson, J. Molec. Spectrosc. 45, 221 (1973). J. L. Duncan, D. C. McKean and G. D. Nivellini, J. Molec. Struct. 32, 255 (1976). A. L. McClellan, Tables of Experimental Dipole Moments. Freeman, San Francisco (1963). S. Kondo and S. Saeki, J. Chem. Phys. 76, 809 (1982). S. Kondo, I. Koga, T. Nakanaga and S. Saeki, Bull. Chem. Soc. Japan 56, 416 (1983). A. J. van Straten and W. M. A. Smit, J. Chem. Phys. 67, 970 (1977). C. E. Blom and A. Muller, J. Molec. Spectrosc. 70, 449 (1978). J. L. Duncan, A. Allan and D. C. McKean, Molec. Phys. 18, 289 (1970). J. L. Duncan, D. C. McKean and G. K. Speirs, Molec. Phys. 24, 553 (1972). J. Aldous and I. M. Mills, Spectrochim. Acta 19, 1567 (1963). M. J. Hopper, J. W. Russel and J. Overend, J. Chem. Phys. 48, 3765 (1968). M. J. Hopper, J. W. Russel and J. Overend, Spectrochim. Acta 28A, 1215 (1972). T. Nakanaga, S. Kondo and S. Saeki, J. Chem. Phys. 76, 3860 (1982). J. Overend and L. C. Hall, Proc. Int. Syrup. Molec. Struct. Spectrosc., Tokyo, p. 212 (1962). J. L. Duncan and P. D. Mallinson, Chem. Phys. Lett. 23, 597 (1973). M. AUegrini, J. W. C. Johnes and A. R. W. McKellar, J. Molec. Spectrosc. 67, 476 (1977).
Pergamon 0584-8539(94)01298-2
Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0584-8539/95 $9.50 + 0.00
Effective bond charges from experimental IR intensities BORIS GALABOV, TODOR D U D E V a n d SONYA ILIEVA Department of Chemistry, University of Sofia, 1126 Sofia, Bulgaria
(Received 15 July 1994; accepted 26 September 1994) Abstract--Experimental gas-phase IR absorption intensities for water, ammonia, methane, ethene, ethyne, propyne, methyl fluoride, methyl chloride, methyl bromide, methyl iodide, formaldehyde, F2CO, CI2CO, F2CS and CI2CS are transformed into quantities termed effective bond charges (6~) following a recently developed formalism. The comparison of 6k values for O--H, N-H, C-H, C-X (X = F, CI, Br, I), C = O and C=S bonds reveals trends of changes that can be associated with the valence state and electronegativities of constituent atoms and also with polarities and electronic polarizabilities of the respective bonds.
INTRODUCTION
IN A recent paper we described a new approach in interpreting vibrational absorption intensities [1]. The formulation employs as initial data vibrational intensities transformed into atomic polar tensors (APTs) [2, 3]. APTs are particularly appropriate representations of the dipole changes inflicted by vibrational distortions since these quantities may be obtained in a simple way from experiments, on the one hand, and are also standard results of ab initio molecular orbital calculations. Thus, direct comparisons between experimental and theoretical dipole moment derivatives are readily available. The physical interpretation of these quantities is, however, hampered by the implicit presence of rotational contributions into the APT elements. Additional difficulties arise from the existence of a considerable number of dependencies between the elements of the APT matrix of a molecule [4-6]. Vibrational absorption intensities in the gas-phase are determined by the fluctuations of the electric charges in molecules accompanying vibrational motion. It is therefore of considerable interest to extract from these experimental quantities molecular parameters characterizing the electric charge properties of molecules. To obtain such information it is necessary to remove from the initial dipole moment derivatives all non-vibrational contributions and also eliminate the redundancies present. Such an approach was proposed recently and the formulation developed lead to the determination of quantities called effective bond charges [1]. Data from 6-31G** ab initio calculations on six molecules were analysed in the previous study. In the present paper bond charges from experimental gas-phase absolute IR intensities on an extended series of molecules are evaluated. The interest is to analyse the trends of changes of these quantities for different types of chemical bonds and, thus, assess the potential of the procedure developed in deriving quantities associated with the intramolecular charge distribution and its dynamics with molecular motion.
EFFECTIVE BOND CHARGES
APTs free from rotational contributions can be obtained from the relation, in matrix notation [1]:
Px(o) = PsUB -- RsUB.
(1)
The elements of Px(v) contain derivatives of the Cartesian components of the molecular dipole moment with respect to atomic Cartesian displacement coordinates that refer to a molecule-fixed system. Ps is a matrix containing dipole moment derivatives with respect to symmetry coordinates and Rs is a matrix containing rotational correction terms that eliminate the contribution arising from the zero angular momentum condition [7-9]. The 739
B. GALABOV et al.
740
elements of Rs can be determined using available methods [7-9]. U and B are the standard matrices used in normal coordinate analysis [10]. The elements of Px(o) are related by nine redundancy conditions [4-6]: N
Z
P"x(V) = 03
(2)
a=I
where P~ is the APT of the ath atom, N is the number of atoms and 03 is a 3 x 3 zero matrix. These redundancies can be removed by representing the dipole derivatives into a bond Cartesian displacement coordinate space [11]. These coordinates are defined in terms of atomic Cartesian displacements by the expression [11]: X~k) - -
( A X ( a k) - -
Ax[~))i + (Ay~0 - Ay ~*))j+
( A z ( a k) -
Az~k))k
(3)
or
Xgk)= Axgk)i+ Ay~k)j+ Az?)k,
(4)
where a and b are indexes of the initial (a) and terminal (b) atoms of the kth bond, and i, j and k are unit vectors along the reference Cartesian frame. The respective dipole derivative tensor for the kth bond has the form
Ok(v)= d x(o)
d z(v)
(5)
d x(O) d Ao) The elements of Dk(V) refer also to a molecule-fixed Cartesian system. Arranged in a row, these form the following matrix: O ( v ) = ( D I ( v ) D z ( v ) . . . D k ( v ) . . . DN-I(V)).
(6)
The elements of D(v) are easily obtained from the respective rotation-free atomic polar tensor matrix Px(V): D(v) = Px(v)C-l.
(7)
The transformation matrix C -1 has a rather simple structure with elements zero or unity appropriately placed [1]. Effective bond charges are the invariants with respect to reorientation of the Cartesian reference system of the tensors Dk(v) 6 2 = Tr(Ok(V). lJk(u)),
(8)
where l)k(u) is the transpose of Dk(V). The quantities 6k are expected to reflect, in a generalized way, electrical properties of the respective bonds. In the following, 6k values for various types of bonds in a series of simple molecules are calculated from experimental gas-phase IR intensity data.
RESULTS H20 a n d NH3 Experimental gas-phase intensities for H20 [12] and NH3 [13] were used to derive 6k quantities for O-H and N-H bonds, respectively. These are given in Table 1. The first step in IR intensity analysis is the transformation of the experimental intensities into dipole moment derivatives with respect to normal coordinates. As is well known, only absolute values of these quantities can be obtained from experiments. Therefore, the signs of Op/OQi derivatives for the molecules treated have been fixed by quantum mechanical calculations [13, 14]. In analysing intensities it is always preferable to further transform the Op/OQi quantities into dipole moment derivatives with respect to symmetry vibrational coordinates. This is of particular importance in the determination of
Effective bond charges from experimental IR intensities Table 1. Observed absolute gas-phase intensities of H 2 0 and NH3 v~ (cm-1)
Molecule H20
NH3
IR
Ai (kin mol -l)
A1
1 2
3657 1597
2.24 53.6
B2
3
3756
44.6
A1
1 2
3337 950
7.6 138
E
3 4
3444 1627
3.8 31.7
band
Ref. 12
13
Table 2. G e o m e t r y data and s y m m e t r y coordinates for H 2 0 and N H 3
Geometry H20 ~ NH3 b
ron =0.9572 A , , / - H O H = 104.5 ° rNn = 1 . 0 1 1 6 / ~ , / _ H N H = 106.67 °
Symmetry coordinates~ H20
NH3
Al
St = (Arl + A r2)/~'2 S2 = A0
B2
$3 = (Arl -- Ar2)/X/2
Al
$1 = (Arl + Ar2+ Ar3)/V3 $2 = (Act1 + Aa2 + Aa3)/%/3
E'
$3~ = (2Arl - Ar2 - Ar3)/V~ S~ = (2Aal - Aa2 -- Aa3)/V6
E ft
S3b = (Ar2 - Ar3)/V~ (Aa2 - Aa3)lVr2
S4b= F r o m ref. [15]. b F r o m ref. [16]. c Internal coordinates are defined in Fig. 1.
zI x
w
×
Fig. 1, Cartesian reference systems, n u m b e r i n g of atoms and definition of internal coordinates for H 2 0 and NH3.
741
B. GALABOVet al.
742
Table 3. Ps matrices for H20 and NH~ (in units D/~ i or D rad -I) H20
(o
o
Si
52
0
-0.234
-/
53
~.992'
0.726
0
/
x Y z
NH3
Si
$2
[~ 0.29
0 0 1.62
S3~
S~
-0.195-0.366 0 0 0 0
S3b
S4b
0 -0.195 0
0 -0.366 0
The symmetry coordinates employed are defined in Table 2.
r o t a t i o n a l c o r r e c t i o n t e r m s a p p e a r i n g as e l e m e n t s o f the Rs m a t r i x [ E q n (1)]. T h e g e o m e t r y d a t a a n d t h e definition o f s y m m e t r y c o o r d i n a t e s e m p l o y e d in the c a l c u l a t i o n s a r e given in T a b l e 2. T h e o r i e n t a t i o n o f m o l e c u l e s in the C a r t e s i a n r e f e r e n c e f r a m e s is s h o w n in Fig. 1. T h e t r a n s f o r m a t i o n o f Op/OQi into Op/OSj d e r i v a t i v e s is c a r r i e d o u t with t h e r e s p e c t i v e n o r m a l c o o r d i n a t e m a t r i c e s Ls. T h e s e a r r a y s a r e o b t a i n e d f r o m n o r m a l c o o r d i n a t e c a l c u l a t i o n s e m p l o y i n g the v a l e n c e force fields o f MILLS [17] for w a t e r a n d DUNCAN a n d MILLS [18] for a m m o n i a . T h e values o f d i p o l e m o m e n t d e r i v a t i v e s with r e s p e c t to s y m m e t r y c o o r d i n a t e s f o r m i n g t h e Ps a r r a y s for the two m o l e c u l e s a r e given in T a b l e 3. T h e e l e m e n t s o f the r e s p e c t i v e Rs m a t r i c e s are e v a l u a t e d by e m p l o y i n g t h e h e a v y i s o t o p e m e t h o d [9], w e i g h t i n g the h e a v y a t o m s by a f a c t o r of 1000. PsBs, RsBs, Px(v) a n d D ( v ) m a t r i c e s for t h e s e m o l e c u l e s a r e given in T a b l e s 4 a n d 5. T h e c a l c u l a t e d 6~ v a l u e s [ E q n (8)] for the O - H a n d N - H b o n d s a r e p r e s e n t e d in T a b l e 6. T h e v a l u e s o b t a i n e d will b e discussed in t h e s u b s e q u e n t sections.
Methane, ethene, ethyne and propyne It was o f i n t e r e s t to f o l l o w t h e c h a n g e s o f effective b o n d c h a r g e s in C - H b o n d s as a f u n c t i o n o f t h e v a r y i n g h y b r i d i z a t i o n o f the c a r b o n a t o m a n d c h a n g e s in e n v i r o n m e n t . E x p e r i m e n t a l g a s - p h a s e I R i n t e n s i t i e s for m e t h a n e [19], e t h e n e [20], e t h y n e [21] a n d p r o p y n e [22] u s e d in e v a l u a t i n g the 6k q u a n t i t i e s for the r e s p e c t i v e C - H b o n d s a r e s u m m a r i z e d in T a b l e 7. T h e g e o m e t r y d a t a a n d the definition o f s y m m e t r y c o o r d i n a t e s for t h e s e m o l e c u l e s a r e given in T a b l e 8. C a r t e s i a n r e f e r e n c e s y s t e m s a n d the definition o f i n t e r n a l c o o r d i n a t e s for t h e series o f f o u r h y d r o c a r b o n s s t u d i e d a r e s h o w n in Fig. 2.
Table 4. Experimental PsBs, RsBs, Px(v) and D(u) matrices for HzO (in units of electrons)a
PsBs =
-0.231 0 0
01 0 0 0
asB $
-0.018 0 0
0 0 0
Px(V) =
-0.213 0 0
0 0 0
0 0 -0.292 0 0 0 0 0 -0.292
H2 0 0 0
0 . 0 8 9 0.115 0 0 0 . 1 4 6 0.069
/43 0 0 0
-0.089 / 0 0.146
0.009 0 0
0 0 0
0 . 0 0 7 0.009 0 0 0 0
0 0 0
-0.007 I 0 0
0.106 0 -0.069
0 0 0
0 . 0 8 2 0.107 0 0 0.146 0.069
0 0 0
-0.082/ 0 0.146 /
r2
t
0
0.146/
0.115 0 -0.069
rt
oO o0O8 oo.lo7 oO
D(v)= ~ -0.069
0
0 . 1 4 6 0.069
a 1 e = 1.602 x 10-19C. The numbering of atoms and bonds and Cartesian reference frame are shown in Fig. 1.
0 -0.028 0
0 -0.132 0
-0.028 0 0
1-0.132 0 0
RsBs =
D(o) =
0 0 -0.547
0 0 0
0 0 -0.547
0 0.080 0
0.009 0 -0.112 0 0.080 0
r~
0 0.009 0
0.009 0 0
0.009 0 -0.112
0 0.089 0
0.018 0 -0.112
H2
0.036 0 0.182
0.036 0 0.182
0.008 0 0
0.044 0 0.182
0.062 0.031 0.056
0.062 0.031 0.056
0.009 0 0
0.071 0.031 0.056
H3
0.031 0.027 -0.097
r2
0.031 0.027 -0.097
0 0.009 0
0.031 0.036 -0.097
a The numbering of atoms and bonds and Cartesian reference system are given in Fig. 1.
Px(v) =
0 -0.160 0
-0.160 0 0
PsBs =
Nl
-0.018 0.031 0.182
-0.018 0.031 0.182
-0.004 0.007 0
-0.022 0.038 0.182
0.062 -0.031 0.056
0.062 -0.031 0.056
0.009 0 0
0.071 -0.031 0.056
Table 5. Experimental PsBs, RsBs, Px(o) and D(v) matrices for NH3 (in units of electrons)a
-0.031 0.027 0.097
r3
-0.031 0.027 0.097
0 0.009 0
-0.031 0.036 0.097
H4
/
-0.018~ -0.031 ] 0.182]
-0.018 -0.031 0.182
-0.004' -0.007 0
-0.022' -0.038 0.182
--,,1 4~
o~
~r O
744
B. GALABOVel al. Table6. Effective bond charges from experimental IR intensities (in units of electrons) Bond
Molecule
O-H N-H C-H
H20 NH 3 CH4 CH2=CH2 CH--CH CHa-=C-CH3b
6,
CH3F CH3CI CH3Br CH3I H2CO
0.210 0.231 0.162 0.179 0.352 0.349 (a) 0.139 (b) 0.163 0.130 0.129 0.139 0.267
C-F
CH3F F2CO F2CS
0.946 1.096 1.064
C-CI
CH3CI C12CO CI2CS
0.470 0.866 0.879
C-Br
CH3Br
0.329
C-I
CH3I
0.135
C=O
H2CO F2CO C12CO
0.789 0.931 1.070
C=S
F2CS CI2CS
0.650 0.781
Table 7. Observed absolute gas-phase IR and band intensities of methane, ethene, ethyne and propyne vi (cm J)
Molecule
Ai (km mol l)
Ref.
CH4
F2
3 4
3019 1311
65.5 31.8
19
CH2=CH2
Bj. B2,,
7 9 10 ll 12
949 3105 826 2989 1443
84.4 26.0 0.03 14.3 10.4
20
3295 730
76.244 194.888
21
43.2 19.5 5.2 1.42 0.65 15.4 17.8 0.25 88.5 15.6
22
B3~ CH-=CH
X~ FI,
3 5
CH3-C---CH
A~
1 2 3 4 5 6 7 8 9 10
E
31335.1 2910 2142 1390.6 930.1 2!)80.8 1450.9 1036 638.6 329.2
Effective bond charges from experimental IR intensities
745
Table 8. Geometry data and symmetry coordinates for methane, ethene, ethyne and propyne
Geometry Methane a Ethene b Ethyne c Propyned
rc, = 1.093 A, a . c , = 109.471 ° rcc = 1.339/~, rcH = 1.085/~, aHcn= 117.83° rcc = 1.203/~, rcn = 1.060 ,~ rc,c = 1.2073 A, rc4: = 1.4596 ,~, rH_c~= 1.060 A rCH(CH3)= 1.096/~, aHCH= 108.28 °
Symmetry coordinates "'f Methane
F2
S3x= (Arl - Ar2 -- Ar3 + A&)/2
S3y = (-Ar~ + Ar 2- Ar3+ Ar4)/2 S3z = (Ar I + Ar 2- Ar 3- A&)/2 S4x-~ (Aa23 -- Aat4)/V~ S4y -~ (Aa13 -- aa24)/V'2 $4~= (Aa34 - Aal2)/V2 Ethene
Blu Bz~
$7 = r0 cos(a/2) (At/I + Ar]E)/V2g' h $9 = (At1 - At2 - Ar 3+ Ar4)/2 S10 ~- r0(Aq~ 1 - A ~ 2 - A ~ 3 + A ~ 4 ) / 2 g
B3~
Sn = (At1 + Ar2 - Ar3 - Ar4)/2 St2 = r0(2Aat - 2Aa2 - ASt - Aq~2+ Aq~3+ A$4)/X/~g
Ethyne
X, n.
S 3=
Propyne
At
St = (Art + Ar2 + Ar3)/V~ S2 = a(Aal + Aa2 + Aa3) - b(Aflt + Aft2+ Aft3) a = 0.41675, b = 0.39956 $3 = AR $4 = AT $5 = Ar'
E'
$6~= (2Arl - Ar2 - Ar3)/X/6 STx= (2Aat - Aa2 - Aa3)/V6
(Aq - Ar2)/V2 $5~ = (a$x + A~')/N/2
&, = (2A#, - A#2 - A~3)/VZ
Sgx= A¢x S1o:¢ = A ~ ) x
E"
S6y= (Ar2 - Ar3)/N/2 STy= (Aa2 -- Aa3)/V2
Sgy= A~y Stay = A~py a From Ref. [18]. b From Ref. [23]. c From Ref. [24]. dFrom Ref. [25]. e Symmetry coordinates describing the IR-active vibrations only are given. f Internal coordinates are defined in Fig. 2. g r0 = 1.085/~. h r/ is an out-of-plane angle.
T h e Op/OQi q u a n t i t i e s a r e t r a n s f o r m e d i n t o d i p o l e m o m e n t d e r i v a t i v e s w i t h r e s p e c t t o s y m m e t r y c o o r d i n a t e s with the aid of t h e r e s p e c t i v e n o r m a l c o o r d i n a t e t r a n s f o r m a t i o n m a t r i c e s . I n t h e i r e v a l u a t i o n , t h e f o r c e f i e l d s o f DUNCAN a n d MILLS f o r m e t h a n e [18], o f DUNCAN et al. f o r e t h a n e [26], o f STREY a n d MILLS f o r e t h y n e [24] a n d o f DUNCAN et al. f o r p r o p y n e [27] w e r e e m p l o y e d . T h e e l e m e n t s o f t h e r e s p e c t i v e Ps m a t r i c e s a r e c o l l e c t e d in T a b l e 9. M e t h a n e , e t h e n e a n d e t h y n e d o n o t p o s s e s s a p e r m a n e n t d i p o l e m o m e n t . Therefore, no rotational terms appear. In the case of propyne, having a dipole moment o f - 0 . 7 5 D [28], a r e f e r e n c e h e a v y i s o t o p e C * H a - C * - = C H w i t h m a s s e s o f t h e r e s p e c t i v e c a r b o n a t o m s m u l t i p l i e d b y 1000 is u s e d t o d e r i v e t h e e l e m e n t s o f Rs f o r t h e v i b r a t i o n s b e l o n g i n g to t h e E s y m m e t r y class. D(v) m a t r i c e s for t h e h y d r o c a r b o n s s t u d i e d are given in T a b l e 10. T h e c a l c u l a t e d 6k v a l u e s f o r t h e C - H b o n d s a r e g i v e n in T a b l e 6.
746
B. GALABOV et al.
zI x ~
01
R
I"1
@ /~,,,
Yl Z
cp~
q>x
%
%
Z
Fig. 2. Cartesian reference systems and definition of internal coordinates for methane, ethene, ethyne and propyne. Table 9. Ps matrices for methane, ethene, ethyne and propyne° (in units D/~-t or D rad -~) Methane S~ ( -i.7502
S3y
$3~
0 -0.7502 0
0 0 -0.7502
$4~
$9
Sl0
SI1
o
o0
S4y
0.38180 0 0.3818 0 0
$4~ 0 ) 0 0.3818
Ethene $7
(:
o
-0.71 0
0.05 0
0.63
S12
ot
0 0.27
y z
Ethyne
$3
( 0
$5~
1.4918
Ssy
0
0 1.3258
0 0
-1.4918 0
S1 0 0 0.618
S2 0 0 0.089
S3 0 0 -0.052
) x y z
Propyne
s,~
s,..
-1.128 0 0
-1.107 0 0
s6y
0 -0.400 0
S4 0 0 - 1.228
Ss 0 0 0.871
sT,
0 0.404 0
S~ -0.400 0 0
S,, 0.404 0 0
ss,
sg,
S.o,
0
0
-0.212 0
° The symmetry coordinates employed are defined in Table 8.
-1.128 0
-0.212 0 0
0
X
-1.107 0
y Z
0.068 -0.020 0.064
r2
0 -0.025 0
R
0 -0.207 0
R
0 0.132 0
-0.011 0.023 -0.013
0 0 0.245
0 0 -0.195
0 0 -0.016
R
0.058 -0.068 -0.037
-0.257 0 0
-0.207 0 0
-0.141 0 0
-0.068 -0.020 -0.064
r3
0 -0.257 0
T
0 0.207 0
rl
0 -0.066 0.081
r2
-0.003 0.066 0.066
0.066 -0.003 -0.066
-0.066 0.066 -0.003
rI
0.066 -0.003 0.066
-0.011 -0.023 -0.013
0 0 -0.437
0 0 0.195
0 0.034 0.008
rl
0.066 -0.066 -0.003
0.211 0 0
-0.059 0 0.074
-0.207 0 0
-0.141 0 0
-0.003 -0.066 -0.066
"Cartesian reference systems and numbering of bonds are shown in Fig. 2.
0.058 0.068 -0.037
-!.025
Propyne
0.207 0 0
Ethyne
- i 516
Ethene
-0.003
Methane
0 0.211 0
r'
0 0.097 0
r~
0 0.207 0
r2
0 -0.066 -0.081
-0.066 -0.003 -0.066
r3
0 0 0.181
0.027 0 -0.013
J
0 1 0 0.195
0 -0.034 0.008
r2
-0.066 -0.066 -0.003
0.141 0 0
-0.003 -0.066 0.066
0 -0.066 0.081
-0.066 -0.003 0.066
F4
0 0.034 0.008
r3
0.066 t 0.066 -0.003
Table 10. Experimental D(v) matrices for methane, ethene, ethyne and propyne (in units of electrons)"
0.141 0 0
0 -0.066 -0.081
0.008 !
034/
r4
¢D
¢D
B
~r O t~
m
B. GALABOV et al.
748
Table 11. Observed absolute gas-phase IR band intensities of methyl halides vi (cm-l)
Molecule
Ai (kin m o V i)
vi (era-i)
Ai (kin tool-l)
Ref.
CH3F
A1
1 2 3
2863.2 1460 1048.6
24.7 0.9 95
E
4 5 6
3005.8 1468 1182.4
61 8.7 2.6
29
CH3CI
Ai
1 2 3
2967.8 1355 732.9
19.15 8.41 23.69
E
4 5 6
3038.9 1452.1 1017.3
10.77 11.38 3.85
30
CH3Br
Aj
1 2 3
2972 1305 611
16.452 15.388 11.186
E
4 5 6
3056 1445 952
5.196 12.591 7.237
31
CH3I
Al
1 2 3
2970 1251 533
11.03 20.66 1.93
E
4 5 6
3061 1440 880
2.15 10.59 8.91
8
xI Z
a2
R
G
2
Fig. 3. Cartesian reference system and definition of internal coordinates for methyl halides.
Table 12. G e o m e t r y data and s y m m e t r y coordinates for methyl halides
Geometry CH3 Fb CH3CI c CH3BI"b CH3 Ib
rcn (A)
rcx (A)
ancn ~°}
Po (D) °
1.095 1.095 1.084 1.083
1.382 1.780 1.935 2.136
110.5 110.83 111.33 111.67
-1.81 -1.87 - 1.80 -1.62
Symmetry coordinates d AI $1 = (Arl + Ar2 + A r 3 ) / ~ 3 $2 = [k(Aa, + Aa2 + Aa3) - (Afll + A~2 + fl3)]/[3(1 + k2)] ~/2 k = - 3 sinfl cos fl/sin a S3= A R
E'
S4,, = (2Arl - Ar2 -- Ar3)/V'6 S5, = (2Aaj - A a 2 - Aa3)/%/6 s~ = (2A#, -
A132-- A133)/X/8
° From Ref. [9]. b From Ref. [34], c From Ref. [35]. a For the definition of the internal coordinates, see Fig. 3.
E"
S4b = ( Ar2 - A r 3 ) / V ~ S5b = ( A a 2 -- ACt3)/V2 s~ = (A~2-
A~3)/X/~
Effective bond charges from experimental IR intensities
749
Table 13. Dipole moment derivatives with respect to symmetry vibrational coordinates for methyl halides (in units of D A -l or D rad 1)a
Si
$2
S3
S~
S~
$6,
S4b
Ssbb
S~
CH3F
0 0.64
0
0 0.20
0 -4.54
0 0 -0.182
0 0 -2.237
07 0 9 0 0
0 0
00 0 0
0
0
0 -0.386 0
0 0.285 0
-0.72 0
0.29 0
i)
.02
CH3CI [~ 0.625
-0.3860.285 0 0 0 0
-0.166 0 0
-0.281
-0.260
0 1 -0.166 0
CHjBr /~
0
0
0
0
0.576-0.317
-1.546
0 0 0.492
0 0 -0.533
0.295
0
0
0
0
0 81
0
0
0
0
0
0 0
0
0
\ 60
)
CH3I 0 0 -0.454
-0.136 0 0
0.347 0 0
-0.380 0 0
0 -0.136 0
0 0.347 0
0 / -0.380 0
)
aThe symmetry coordinates are defined in Table 12.
Methyl halides
Experimental gas-phase IR intensity data of KONDO and SAEKI [29] for methyl fluoride, KONDO et al. [30] for methyl chloride, VAN STRATEN and SMIT [31] for methyl bromide and of DICKSONet al. [8] for methyl iodide were used in the analysis. These data are presented in Table 11. The normal coordinate transformation matrices Ls are calculated from the force fields of BLOM and MULLER ( C H 3 F [32]), of DUNCAN et al. (CH3CI [33]) and of DUNCAN et al. (CH3Br and CH3I [34]). Definitions of internal and symmetry coordinates and molecular geometry data are given in Fig. 3 and Table 12. The Ps matrices containing Op/OSj derivatives for the series of methyl halide molecules are given in Table 13. The determination of the elements of the Rs matrices for vibrations belonging to the non-totally symmetric E class is performed by using hypothetical heavy isotopes with masses of the heavy atoms multiplied by 1000. The D(v) matrices for these molecules are presented in Table 14. The calculated effective bond charges for C-H and C-X (X=F, CI, Br, I) are summarized in Table 6. X2CY molecules Experimental absolute gas-phase IR intensities of HOPPER et al. [36, 37] for F2CO, F2CS, C12CO and CI2CS, and of NAKANAGA et al. [38] for H2CO were used. The respective Ai values are summarized in Table 15. The Op/OQi values obtained from the experimental IR intensities are further reduced to Op/OSj dipole moment derivatives with Ls matrices evaluated from the force fields of OVEREND and HALL [39] for F2CO and C12CO, of HOPPER et al. [37] for F2CS and CI2CS and of DUNCAN and MALUNSON[40] for H2CO. Internal and symmetry coordinates and geometry data are defined in Fig. 4 and Table 16. The Ps arrays employed in the calculations are given in Table 17. The D(u) matrices evaluated for the X2CY molecules studied are presented in Table 18. The C-X and C-Y effective bond charges obtained are shown in Table 6.
DISCUSSION OF THE EFFECTIVE BOND CHARGES
Comparing 6k values for O - H and N-H bonds, it can be seen that they are quite close in magnitude. This is in accordance with expectations because of the similarity of the two bonds.
0.054 0 0
0.048 0 0
0.043 0 0
0
'/0.034
0 0.054 0
0 0.048 0
0 0.043 0
0 0.034 0
0 0 -0.111
0 0 -0.322
0 0 -0.466
0 0 -0.945
-0.001 0 0.036
-0.026 0 0.051
-0.045 0 0.063
-0.103 0 0.083
0 0.095 0
0 0.085 0
0 0.084 0
0 0.089 0
rl
0.045 0 -0.083
0.040 0 -0.067
0.036 0 -0.050
0.035 0 0.004
0.071 0.041 -0.018
0.057 0.048 -0.026
0.052 0.056 -0.031
0.041 0.083 -0.041
a Cartesian reference system and numbering of bonds are shown in Fig. 3.
CH3I
CH3Br
CH3CI
CH3F
R
0.041 0.023 0.031
0.048 0.002 0.045
0.056 -0.013 0.054
0.083 -0.055 0.072
r2
-0.023 0.039 -0.083
-0.020 0.035 -0.067
-0.018 0.031 -0.050
-0.018 0.031 0.004
0.071 -0.041 -0.018
0.057 -0.048 -0.026
0.052 -0.056 -0.031
0.041 -0.083 -0.041
Table 14. Experimental D(v) matrices for methyl halides (in units of electrons)°
-0.041 0.023 -0.031
-0.048 0.002 -0.045
-0.056 -0.013 -0.054
-0.083 -0.055 -0.072
r3
-0.023 t -0.039 -0.083 [
-0.020 t -0.035 -0.067/
-0.018 ) -0.031 -0.050
-0.018 -0.031 0.004
7, O <
Effective bond charges from experimental IR intensities
751
Table 15. Experimental absolute gas-phase IR intensities of XzCY molecules
Molecule H2CO
At
F~CO
At
vi
Ai
vi
Ai
(cm -t )
(km mol -t )
(cm -t )
(km mol -t )
Ref.
1 2 3
2782 1746 1500
75.5 73.99 11.15
Bt
1 2 3
1928 965 626
381.74 56.44 7.04
Bt
B2
B2
CI2CO
At
1 2 3
1827 567 285
245.26 14.48 0.07
Bi
FzCS
At
1 2 3
1368 787 526
390.34 8.92 6.72
B1
1 2 3
1137 505 220
210.80 13.81 0
B1
CI2CS
A1
Bz
B2
B2
4 5 6
2843 1249 1167
87.6 9.94 6.49
38
4 5 6
1249 584 774
370.79 5.20 30.64
36
4 5 6
850 440 580
376.45 0.18 4.90
36
4 5 6
1189 417 622
201.54 0.25 1.33
37
4 5 6
816 294 473
162.93 0.30 2.35
37
Fig. 4. Cartesian reference system and definitioon of internal coordinates for X2CY molecules.
Table 16. Geometry data and symmetry coordinates for X2CY molecules rcv (/~)
rcx (.~)
axcx~°)
/~o(D) °
1.203 1.174 1.166 1.56 1.56
1.099 1.312 1.746 1.32 1.75
116.5 108 111.3 112.5 111.3
-2.35 c -0.95 -1.18 -0.05 -0.28
Geometry H2CO b F2CO a CI2CO° F2CSd CIECSd
Symmetry coordinates" A1 SI = (Arl + Ar2)/V~
$2= AR s3 = ( 2 z a - A # , - A/~9/X/-6
BI
$4 = ( A r t - Ar2)/V~ s~ = (A/~t - A / ~ 2 ) / V ~
B2 $6 = Ay / "From Ref. [9] unless indicated. b From Ref. [38]. c From Ref. [41]. d From Ref. [37]. "Internal coordinates are defined in Fig. 4. IF is an oubof-plane angle.
752
B. GALABOVet al. Table 17. Dipole moment derivatives with respect to symmetry vibrational coordinates for X2CY molecules (in units of D A -I or D rad-~)" Sj
$2
S
$4
$5
$6
1.297 0 0
-0.424 0 0
0 -0.293 0
H2CO 0 0 1.059
0 0 -3.741
0 0 0.081
0 0 4.57
0 0 -3.97
0 0 -1.43
5.246 0 0
- 1.762 0 0
0 1.198 0
0 0 2.4
0 0 -4.7
0 0 -0.69
5.07 0 0
-2.2 0 0
0 0.596
0
0 0 4.83
0 0 -3.07
0 0 - 1.81
4.798 0 0
-0.619 0 0
0 0.282 0
0 0 -3.7
0 0 -0.71
4.601 0 0
-0.806 0 0
F2CO
CIzCO
F2CS
CI2CS (~ 3.7
i -
) .449
"The symmetry coordinates are defined in Table 16.
Analysis of the data for the hydrocarbon series collected in Table 6 reveals a tendency towards higher 6k values with increased s-character of the carbon valence orbitals, beginning with 0.162 e for methane (CSp3-H), 0.179 e for the CsP2-H 6k value in ethene, and ending with much higher effective charges for the acidic CSP-H bonds in ethyne and propyne. The same trend was found for the C-H bond charges evaluated from 6-31G** ab initio MO calculations [1]. The Csp3-H effective bond charge, as obtained for a Table 18. Experimental D(v) matrices for X2CY molecules (in units of electrons) a R
rl
r2
H2CO -0.017 0 0
0 0.125 0
0 0 -0.779
-0.152 0 -0.142
0 0.130 0
-0.083 0 -0.066
-0.152 0 0.142
0 0.130 0
0.083 0 -0.066
-0.323 0 0
0 0.282 0
0 0 -0.827
-0.714 0 -0.381
0 0.215 0
-0.340 0 -0.620
-0.714 0 0.381
0 0.215 0
0.340 0 -0.620
-0.377 0 0
0 0.213 0
0 0 -0.979
-0.702 0 -0.235
0 0.126 0
-0.327 0 -0.283
-0.702 0 0.235
0 0.126 0
0.327 0 -0.283
-i.113
0 0.040 0
0 0 -0.639
-0.624 0 -0.397
0 0.042 0
-0.337 0 -0.686
-0.624 0 0.397
0 0.042 0
0.337 0 -0.686
-0.126 0 0
0 -0.044 0
0 0 -0.770
-0.592 0 -0.391
0 -0.036 0
-0.336 0 -0.393
-0.592 0 0.391
0 -0.036 0
0.336 0 -0.393
F2CO
C12CO
F2CS
CI2CS
a Cartesian reference system and numbering of bonds are shown in Fig. 4.
)
Effective bond charges from experimental IR intensities
753
F "~ 0.8-
CH3Ce~ g
0.4-
CH3Br
/
O.O 2.~ . . . . . . ~'.~ . . . . . .
'~;G . . . . . . .
ELECTRONEGATIVITY
;'.~' . . . . .
'~;
.......
[Paullng units]
Fig. 5. Plot of the dependence between 6c_x ( X = F, CI, Br, I) and the electronegativity of halogen atoms.
number of molecules, does not appear to be very sensitive to environmental changes in the series of hydrocarbons and methyl halides, with variations in the range 0.129 (CHaBr) to 0.163 e (CHaF). Much more pronounced variations in ~k values are found for the polar carbonhalogen, carbon-oxygen and carbon-sulfur bonds. The C-X effective bond charge in methyl halides changes from 0.946 e in CH3F, 0.470 e in CH3CI, 0.329 e in CH3Br to 0.135 e in CH3I. This is in full agreement with expectations and the values evidently may be related to the electronegativity of the halogen atoms. This dependence is shown in Fig. 5. The C = O effective bond charges are higher than the respective C=S values in the sulfur analogs. This finding is also in accord with the expected lower polarity of the C=S bonds due to the lower electronegativity of the sulfur atom. Comparing 6k data for lower polarity bonds (C-H) to the much more polar C--O, C=S, C-F, C-CI and C-Br bonds, it is seen that higher bond polarity is reflected in much higher effective bond charges, with values varying with expectations in most cases. The analysis of the data for the effective bond charges as obtained from experimental gas-phase intensity data for a number of molecules reveals some definite trends of changes. The variations found may, in most cases, be related to the polar properties of the bonds considered. As already stressed, the effective bond charges are solely determined by purely vibrational distortions of the molecules. The data obtained show that these quantities may, very possibly, be regarded as experimental parameters associated with the intrinsic electric properties of valence bonds.
REFERENCES
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
B. Galabov, T. Dudev and S. l!ieva, Spectrochim. Acta 49A, 373 (1993). J. F. Biarge, J. Herranz and J. Morcillo, An. Quire. Set. A57, 81 (1961). W. B. Person and J. H. Newton, J. Chem. Phys. 61, 1040 (1974). V. T. Aleksanyan and S. Kh. Samvelyan, in Vibrational Spectra and Structure (Edited by J. R. Durig), Vol. 14, p. 256. Elsevier, Amsterdam (1985). J. C. Decius and G. B. Mast, J. Molec. Spectrosc. 70, 294 (1978). B. S. Averbukh, J. Molec. Spectrosc. 117, 179 (1986). B. L. Crawford Jr, J. Chem. Phys. 20, 977 (1952). A. D Dickson, I. M. Mills and B. L. Crawford Jr, J. Chem. Phys. 27, 445 (1957). A. J. van Straten and W. M. A. Smit, J. Molec. Spectrosc. 56, 484 (1975). E. B. Wilson Jr, J. C. Decius and P. C. Cross, Molecular Vibrations. McGraw-Hill, New York (1955). L. S. Mayants and B. S. Averbukh, J. Molec. Spectrosc. 22, 197 (1967). S. Clough, Y. Beers, G. Klein and L. Rothman, J. Chem. Phys. 59, 2254 (1973).
SA(A)51:5-E
754 [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] 28] 29] 30] 31] 32] 33] 34] 35] [36] [37] [38] [39] [40] [41]
B. GALABOVet al. Th. Koops, T. Visser and W. M. A. Smit, J. Molec. Struct. 96, 203 (1983). B. Zilles and W. B. Person, J. Chem. Phys. 79, 65 (1983). W. S. Benedict, N. Gailar and E. K. Plyler, J. Chem. Phys. 24, 1139 (1956). L. E. Sutton, lnteratomic Distances, Spec. Publ. No. 11. The Chemical Society, London (1958). I. M. Mills, in Infrared Spectroscopy and Molecular Structure (Edited by M. Devies). Elsevier. Amsterdam (1963). J. L. Duncan and I. M. Mills, Spectrochim. Acta 20, 523 (1964). J. H. G. Bode and W. M. A. Smit, J. Phys. Chem. 84, 198 (1980). T. Nakanaga, S. Kondo and S. Saeki, J. Chem. Phys. 70, 2471 (1979). W. M. A. Smit, A. J. van Straten and T. Visser, J. Molec. Struct. 48, 177 (1978). J. H. G. Bode, W. M. A. Smit, T. Visser and H. D. Verkruijsse, J. Chem. Phys. 72, 6560 (1980). J. L. Duncan, I. J. Wright and D. van Lerberghe, J. Molec. Spectrosc. 42, 463 (1972). G. Strey and I. M. Mills, J. Molec. Spectrosc. 59, 103 (1976). J. L. Duncan, D. C. McKean, P. D. Mallinson and R. McCulloch, J. Molec. Spectrosc. 46, 232 (1973). J. L. Duncan, D. C. McKean and P. D. Mallinson, J. Molec. Spectrosc. 45, 221 (1973). J. L. Duncan, D. C. McKean and G. D. Nivellini, J. Molec. Struct. 32, 255 (1976). A. L. McClellan, Tables of Experimental Dipole Moments. Freeman, San Francisco (1963). S. Kondo and S. Saeki, J. Chem. Phys. 76, 809 (1982). S. Kondo, I. Koga, T. Nakanaga and S. Saeki, Bull. Chem. Soc. Japan 56, 416 (1983). A. J. van Straten and W. M. A. Smit, J. Chem. Phys. 67, 970 (1977). C. E. Blom and A. Muller, J. Molec. Spectrosc. 70, 449 (1978). J. L. Duncan, A. Allan and D. C. McKean, Molec. Phys. 18, 289 (1970). J. L. Duncan, D. C. McKean and G. K. Speirs, Molec. Phys. 24, 553 (1972). J. Aldous and I. M. Mills, Spectrochim. Acta 19, 1567 (1963). M. J. Hopper, J. W. Russel and J. Overend, J. Chem. Phys. 48, 3765 (1968). M. J. Hopper, J. W. Russel and J. Overend, Spectrochim. Acta 28A, 1215 (1972). T. Nakanaga, S. Kondo and S. Saeki, J. Chem. Phys. 76, 3860 (1982). J. Overend and L. C. Hall, Proc. Int. Syrup. Molec. Struct. Spectrosc., Tokyo, p. 212 (1962). J. L. Duncan and P. D. Mallinson, Chem. Phys. Lett. 23, 597 (1973). M. AUegrini, J. W. C. Johnes and A. R. W. McKellar, J. Molec. Spectrosc. 67, 476 (1977).