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An ab initio study of the harmonic and anharmonic force field and fundamental vibrational frequencies of performic acid
JOURNAL
OF MOLECULAR
SPECTROSCOPY
84,
256-271 (1980)
An Ab Initio Study of the Harmonic and Anharmonic Field and Fundamental Vibrational Frequencies of Performic Acid
Force
CHARLES W. BOCK AND MENDEL TRACHTMAN Chemistry Department,
Philadelphia College of Textiles & Science,
Philadelphia,
Pennsylvania
19144
AND PHILIP GEORGE Biology Department,
Universiry of Pennsylvania,
Philadelphia,
Pennsylvania
19147
The harmonic and anharmonic force fields and fundamental vibrational frequencies of performic acid are studied ab initio in the 4-31G basis set using geometries fully optimized at this level. The frequencies predicted for the cis-cis conformer are compared with those derived from spectroscopic observations on the most stable form. An extensive comparison is made between the changes in diagonal and off-diagonal quadratic and cubic force constants, and diagonal stretching quartic constants, in going from the chain to the ring structure in performic and formic acid, and features which these changes have in common are seen to support the view that there is a hydrogen bonding type of interaction in rrans-formic acid despite its unfavorable geometry. cis-cis and cis-trans
1. INTRODUCTION
The most extensively investigated hydrogen bonding is that in which the two electronegative atoms and the hydrogen are collinear, or nearly collinear-namely, intermolecular bonding, e.g., in the H,O dimer, the [F-H--F]ion and the formic acid dimer, and intramolecular bonding which results in the formation of sixand seven-membered rings, e.g., in the enol form of malonaldehyde and in the maleate mono-anion, respectively (l-3). Infrared spectroscopy has been the experimental technique most commonly used to establish its presence (4, 5), and the concentration dependence of the “X-H” peak in solvents such as carbon tetrachloride or hexane has been invaluable in showing whether it is inter- or intramolecular in nature. However, the finding that with formic acid and performic acid the most stable monomeric conformer is the one in which the H of the O-H group and the 0 of the C=O group are in close proximity suggests that a hydrogen-bonding type of interaction may be stabilizing these particular conformers, even though the rings are smaller, containing four and five atoms, respectively, with the H-atom lying at best some 0.7-1.0 A off the line joining the two O-atoms (6, 7). Ab initio studies have been mainly concerned with calculating the geometry of hydrogen-bonded structures and the bonding energy (5,8,9). To a lesser extent 0022-2852/80/110256-16$02.00/O Copyright
0
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256
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
0
H\/
O\O
H'-
“1
/ :: I
b
ACID
257
0
I
0
d
FIG. 1. The Structures of (a) the Cis-Cis, and (b) the Cis-Tram Conformers of Performic Acid, and (c) the Truns- and (d) the C&Conformers of Formic Acid (la).
the change in the various force constants has been investigated, e.g., the O-H stretching force constant (5, 8). In a previous paper we reported the complete harmonic and anharmonic force fields and the fundamental vibrational frequencies calculated ab initio for both the tram- and c&planar conformers of formic acid,’ and traced the changes in the force field as the H of the O-H group and the 0 of the C=O group come into close proximity. The present paper extends these studies to per-formic acid, see Figs. la and b (6). Although it presents no problem in carrying out the calculations and making the comparison between the cis-cis conformer, which would have a five-membered H-bonding ring, and the cis-tram conformer, which has the O-H group rotated 180” about the O-O bond axis, it has to be remembered that at present there is no conclusive experimental evidence as to the actual structure of the most stable form (7). An analysis of the average dipole moment of several long chain peracids was shown to favor a nonplanar structure in which the hydroxyl hydrogen is twisted out of the plane by about 72” but still in fairly close proximity to the 0 of the C=O group (II -13). This analysis has been questioned on the grounds that the assumption that bond moments taken from other molecules will provide good values for the peracids does not seem justified (14). In addition, the bond moment for the O--H bond was not taken into account (15). Moreover, semiempirical calculations, IEHT and PCILO (14), and ab initio calculations using several basis sets-STO-3G, 4-3 lG, 4-3 1G plus bond functions, (9,5) with and without polarization functions-all find the cis-cis planar structure to be the most stable conformer as might have been expected (7,14). Quadratic and selected cubic and quartic force constants are computed using the 4-31G basis set for the cis-cis and cis-tram conformers of performic acid. Corresponding values for the two conformers are compared among themselves and with the values for the analogous constants for tram- and &-formic acid (6). Harmonic and anharmonic vibrational frequencies are calculated for both pet-formic acid conformers using the procedure of Hoy et al. (26), and the values for the cis-cis conformer are compared with those derived from spectroscopic observations on the most stable form (17). ’ Using Hocking’schoice of the two H-atoms as reference, (IO), see Figs. lc and d.
the vans-conformer
is the more stable
258
BOCK,TRACHTMAN,ANDGEORGE 2.COMPUTATIONALMETHODS
The SCF wavefunctions and forces were computed using the Arkansas version (18) of the TEXAS program written by Pulay (19), utilizing the widely used nearly double 5 4-31G basis set with no scale factors (20). The energies, E(q), and forces f(q), were obtained for the 4-31G optimized geometries for both conformers and at small displacements Aq, from these geometries. The force constants were then obtained numerically from the energies and forces. The displacements were chosen to lie along individual internal coordinates, and the harmonic force constants determined from the usual two-point difference formula f’rJ
=
[f&h
-
&J)
.ffJ
=
-.fdSo
+
AqJ)l/+qJI
(1)
and [f)lJ
+
f;t1!2,
(2)
wheref( is the ith component of the force vector. Equation (2) ensures that the harmonic force constant matrix is symmetric. As suggested by Schlegel et al. (21), the diagonal stretching force constants were computed by fitting a fourth-degree polynomial to the energies and forces at three points: fir = 2Mq, + Aqr) - 2E(q,) + &-I, - Aqr)l/)hi/’
- Lfdqo- Aqd -f&o + W1/2\ 41.
(3)
This reduces errors due to large anharmonic effects. I Aqr1 was chosen as 0.05 A for bond stretching, and 2” for in-plane bending and out-of-plane torsional coordinates. The cubic force constants j& and were computed using the three-point difference formula ftJJ
hJJ
=
-
[fdqo
+
hi)
-
2.fdqo)
+
f&o
-
AeW 1A%12.
(4)
The remaining cubic constantsftil, (i # j Z k) were assumed to be small, and were taken as zero in the frequency calculations (22). The diagonal stretching quartic force constants,hiii, were computed from the fourth-degree polynomial used above for the quadratic diagonal stretching constants, where frtti = IV[fl(qo - Aq,) - fi(qo + AqiW 1ho 1
- [Nqo + W - 2E(qd + Wq, - WY) 4,) 2H)Aqrj2. (5) All remaining quartic constants were assumed to be small, and taken as zero in the frequency calculations (21). The harmonic frequencies and normal coordinates were calculated by the Wilson F-G method (22). In order to make anharmonicity corrections, the force constants were transformed from curvilinear internal coordinates to linear normal coordinates using the procedure of Hoy et al. (16), except that the derivatives of the L matrix needed for the nonlinear transformation were computed numerically rather than analytically, as described by Schlegel et al. (21).
VIBRATIONAL
FREQUENCIES
259
OF PERFORMIC ACID
TABLE I Geometry of the Cis-Tram and Cis-Cis Conformers of Performic Acid [Figs. lb and a], and the Cis- and Tram-Conformers of Formic Acid [Figs. Id and c] Formic Acid
Performic Acid
cis
trans 1.343
Structural Parameter
cis-trans
cis-cis
c-o
1.360
1.350
1.352
c=o
1.190
1.200
1.194
1.202
O-H
0.973
0.984
0.956
0.972
C-H
1.082
1.079
1.105
1.097
o-o
1.457
1.458
126.9
123.6
122.1
124.9
107.1
109.9
114.6
111.0
111.8
l&3.6
99.0
104.5 109.7
106.7
__~--____
The energies of the vibrational levels, E(v), were then expanded series in the vibrational quantum numbers,
as a power
E(v) = 2 W&, + 112) + c Xrs(V, + 1/2)(V, + 112) + * * ‘, r
C-8
where W, are the harmonic frequencies. The second-order perturbation formulas for asymmetric-top molecules given by Mills (23) were used in the calculation of the anharmonicity constants X,,. 3. GEOMETRY
In the absence of any experimental geometry for either the cis-cis or cis-tram conformer of pet-formic acid (Figs. la and b), the values for the bond lengths and bond angles calculated using the 4-31G basis set with full geometry optimization, see Table I, have been employed in the force constant studies. In comparing these force constants with those for rrans- and cis-formic acid (Figs. lc and d), it must be borne in mind that the formic acid values were obtained using experimental geometries (10). The 4-31G optimized geometries for formic acid are, however, quite close to the experimental-on average to within 0.003 A in the bond lengths and 0.5” in the bond angles- except in the case of the C-H bond length and the LCOH bond angle, which differ by about 0.018 A and 6.8”, respectively. Hence the only force constants likely to be much affected are those involving these structural elements. Even so, the use of these different geometries in no way affects the internal comparison of the cis-tram and cis-cis constants for pet-formic acid, and the cis and rrans constants for formic acid, to see whether there are significant and consistent trends as the H of the H-O group is rotated into position for an optimal
260
BOCK, TRACHTMAN,
AND GEORGE
H-bonding.type of interaction. This rotation, however, involves the O-O bond axis in pet-formic acid and the C-O bond axis in formic acid, so the changes in overall geometry are not strictly the same in the two cases. 4. FORCE FIELD
The quadratic, cubic, and quartic force constants computed for the cis-cis and cis-truns conformers of pet-formic acid using the 4-3 1G basis set are listed in Table II. Before looking at the values in detail it may be recalled that harmonic force constant matrices generated by ab initio calculations show systematic deviations with respect to the experimental force field, particularly the diagonal constants (24). Calculated values using the 4-31G or comparable basis sets have been found to overestimate diagonal stretching constants by about 5- 10% depending on the geometry employed, and in-plane diagonal bending constants by about 10% (24-34). Although off-diagonal elements obtained from experiment are usually less accurate (24, 34), the calculated values usually agree to within about 10%. Hence, while calculated values taken separately can be expected to be in only fair agreement with experiment, trends in values for molecules that have a similar structure are nevertheless quite reliable and informative comparisons can be made. In a recent study of trans-formic acid using the 6-3 1G basis set Ha et al. (34) found that only minor corrections to the calculated force field were needed to reach agreement with experiment, and so the present results for pet-formic acid should be of help in arriving at reliable experimental force fields for its cis-cis and cistrans conformers. To facilitate comparison of the changes in the force constants that are common to per-formic acid (PFA) and formic acid (FA) in going from the chain to the ring structure, i.e., from b to a and from d to c in Fig. 1, the values have been brought together in Table III. These changes can be rationalized in the following way. The traditional valence bond approach, or a consideration of the effect of the hydrogen on the spatial distribution of the molecular orbitals when it comes into the vicinity of the two oxygens, would lead one to expect bonding to some extent between the H of the OH group and the 0 of the C=O group, and hence electron delocalization in the ring compared to the chain structure. As a consequence one would anticipate an enhancement of the mechanical strength of the formal C-O bond, and a diminution in the strength of the formal C=O and O-H bonds. This sort of effect is borne out by the changes in bond lengths for both acids as shown in Table I. C-O decreases in length indicating a strengthening, while C=O and O-H (35) increase in length indicating a weakening: O-O in PFA also increases in length, indicating a weakening in the ring structure. The changes in the bond angles, however, show no such regularities, which could be due to the difference in ring size. Turning first to the diagonal stretching constants, all three sets of values show the characteristics one would predict on the basis of these mechanical changes: (i) fc_o,c_o
(chain <.fc_o,c_o
(ii) f,--,c=o
(chain) >fc=o,c=o
(iii) fo_-H,O_u (chain) >fo_u,o_u
(ring): both PFA and FA, (ring): both PFA and FA, (ring): both PFA and FA.
VIBRATIONAL FREQUENCIES
261
OF PERFORMIC ACID
TABLE i1 Force Constant9 A.
for CM_%’ and Cis-Trunsb Performic Acid Computed from the 4-31G Basis Set’
Quadratic
For&
c-o
c=o
Constants o-o
fij
O-H
C-H
C=O
14.812 15.653
C-O
1.628 1.366
6.770 6.574
o-o
0.002 -0.012
0.116 0.094
5.467 5.644
O-H -0.152 -0.066
0.158 0.044
-0.032 -0.172
7.263 7.920
C-H
0.201 0.072
0.094 0.166
-0.078 -0.070
0.002 -0.009
6.129
0.385 0.037
0.785 0.701
-0.271 -0.193
0.032 -0.005
-0.136 -0.146
0.084 -0.106
0.562 0.522
0.662 0.521
0.037 0.002
0.012 0.042
0.126 0.004
-0.173 -0.008
0.672 0.660
0.216 0.066
0.488 0.532
0.033 0.053
-0.043 -0.014
TOCOO
TCOOH
THCOO
TOCOO
0.562 0.440
TCOOH
0.087 0.004
THCOO
-0.382 -0.396
5.981 2.552 2.307 0.098
0.024
1.843 1.457
-0.013 0.011
-0.136 -0.081
-0.014 0.190
1.222 1.090
0.045 0.054
0.711 0.706
0.177 0.146
0.013 0.050
1.395 1.460
0.039 0.0014d 0.004 -0.006
0.504 0.505
In addition, since the H--O interaction can be presumed to be attractive in nature, one would expect all diagonal bending constants internal to the ring to be larger for the ring compared to the corresponding bending constants for the chain structure. This is the case with PFA, for which (iv)
~LOCO,LOCO
(find
> fL~~~,L~~~
(chain)
but not FA, which could be due to a smaller attractive interaction in the fourmembered ring, or features of the calculation procedure, e.g., the relatively small basis set employed, the absence of polarization functions, or correlation energy effects. Similar relationships hold for the force constants that are specific to each acid, see Table IV. In the case of PFA electron delocalization would be expected to diminish the mechanical strength of the formal O-O bond along with the formal O-H and C=O bonds, and accordingly: 64
fo-o,~-~
(chain)
> fo-O,O-o
(ring).
0.31 0.26
0.06 0.06
1.54 1.57
0.00
0.00
0.00
ace
7oCoo
TCOOE
%COO
0.41 0.16
-
1.15 1.61
C-E -
&Co
0.14 0.08
o-a -
-0.70 -0.60
0.57 -0.12
-2.11 -1.60
-2.64 -1.83
-0.67 -0.77
-0.24 -0.20
-1.13 -1.23
0.10 0.16
-
*o
-3.40 -1.96
c-o
Force
3.05 -39.35 2.86 -41.39
99.40 -103.84
-
c=o
Cubic
c-o -
i) C=O
(j)
B.
0.00 -0.02 -35.75 -35.04
-48.48 -51.81 0.00 0.16 0.14 0.00
-0.44 .-l-41
0.02 -0.04
0.58 0.32
-0.11 -0.14
-2.36 -2.27
-2.22 -1.80
-0.05 -0.03
0.98 0.52
-26.19 -26.95
0.10 0.11
-0.02 0.01
0.73 -0.10 -0.01 0.02
0.07 0.12
0.69 0.00
-0.13 -0.14
0.30 0.33
0.19 -0.09
0.26 0.18
C-H 0.63 0.72
O-H
f. Ijj
-0.20 0.02
-0.30 -0.31
O-O
Constants
1.02 1.05
0.09 0.09
-2.37 -0.96
-3.97 -1.89
-0.39 -0.39
0.38 -0.01
-0.21 0.00
-0.68 -0.02
-7.83 -4.27
-3.36 -1.48
0.09 0.02
0.05 -0.08
-3.41 -2.10
0.01 0.02
-1.74 -1.05
-0.79 -0.03
0.22 0.02
0.00 -0.01
-0.34 -0.37
-2.10 -1.55
0.00 -0.18
-3.86 -2.73
-3.68 -2.40 -0.41 -0.10
-0.98
0.14
-0.22 -0.27
0.01 -0.05
-0.20 -0.19
0.85 0.26
-0.16 -0.05
-0.14 0.03
0.08
0.23
0.99
-0.17 -0.16
0.14 0.01
0.04 -0.01
-0.10 -0.09
-0.09 -0.09
-0.21 -0.03
-0.02 -0.01
0.26 -0.02
0.10 0.02
0.10 0.11
-0.01 0.00
0.01 0.30
0.26 0.25
-0.19 -0.19
-0.00 -0.01
-0.06 -0.06
-0.22 -0.21
-0.21 -0.11
-0.29 -0.12 -0.22 -0.12
-0.48 -0.52
THCOO
0.19 0.01
TcOOH
-0.44 -0.98
ToCoo
1.02
-0.70 -0.70
0.02 -0.01
-0.15 -0.24
-0.94 -1.01
-0.94
0.09
-0.70 0.22
-3.85 -3.20
II-Continued
TABLE
263
VIBRATIONAL FREQUENCIES OF PERFORMIC ACID TABLE II-Continued C.
Quartlo
c-o
523.0 564.1
c-o
246.3 226.7
o-o
117.6 110.1
O-H
309.4 336.4
C-H
167.6 163.5
a.
Quadratic rtretch, force
Conrtantr
Foroe
constants
and bend-bend
in mdyn/R2,
stretch-stretch-stretch,
constants
b.
The upper numbers are for
c.
See reference
d.
If
and probably
respectively.
cis-cir-performic
(z)
the
stretch-bend-bend puartic
stretching
acid,
and the lower
. value
spurious
of
0.001
(r&9
~LOOH,LOOH Wng)
is
used in place
Fermi resonance
With regard to the bending constants
(vii)
and mdyn and mdyn n” for
the cis-trans-conformer.
a rounded-off
.LCOO,XOO
Cubic
respectively.
in mdyn/i3.
numbers for
(vi)
mdyn/i
constants
stretch-stretch-bend,
and bend-bend-bend constants
in mdyn/R, mdyn and mdyn R for the rtretch-
force constants stretch-bend
fiiii
0.0014,
a severe
arises.
internal to the ring,
?LCOO,~COO > ~LOOIUOOH
(Chain), (Chain),
and likewise with FA, (viii)
YLHOC,LHOC (ring> > ~LHOC,LHOC (Chain).
Furthermore, one would expect it to be more difficult for rotation to occur about the C-O and O-O bonds in the ring form of PFA, and about the C-O bond in the ring form of FA. The values for the torsional constants in Table IV bear this out, i.e., with PFA (ix) fiOcOO,lOc,,,, (ring) > fT,,c00,70c,,0 (chain), (4
f’COOH,TCOOH (ring) > fTCOOH.TCOOH (chain).
In the case structures, membered If indeed
of FA, however, f7,,,_,C0,7HOC0 is almost the same for the chain and ring which again could be due to less attractive interaction in the fourring or features of the calculation procedure. attractive interaction is greater in the five-membered ring of PFA,
264
BOCK, TRACHTMAN,
AND GEORGE
then one would expect the changes in the various force constants that are common to both acids to be larger for PFA. This is the case for three of the four relationships set out above, i.e., for ~c-_o,c-_o,~~=o.c=o, andfLoco,LOCo. Forfo_-H.o_-H the change is greater for FA, but this could be attributed to a repulsive interaction operative in cis-FA due to the close approach of the two hydrogens to within about 1.8 A, see Fig. Id, which is appreciably less than the sum of their Van der Waal radii (7,36). It is obvious from Fig. lb that no such repulsive interaction could be present in cis-trans-PFA. Several changes in quadratic off-diagonal constants follow the same sort of trend. andfc=O,iOCO all increase in going from the chain For example, fc=o,c-O, ~~=o,oH to the ring structure, the increase being larger for PFA indicative of greater coupling between these structural elements in the five-membered ring. Among the cubic diagonal constants, (xi) fc=o,c=o,c=o (xii)
_LOCO,~OCO,~OCO
(chain)
>~c~,c=o,c=o
(chain)
(ring):
> f L~~~,L~~~,L~~~
both (ring):
PFA both
and WA
F& and
FA
with the changes again greater in the case of PFA. However withfo--H,O--H,O--H the change is greater for FA, while fc_o,c_o,c-o increases for FA but decreases for PFA. Among the cubic off-diagonal constants the much larger increases with for PFA are quite striking. And finally the ~c=o,c-O,C-o and ~C=O.~OCO,~OCO quartic constants fc=o,c=o,c=o,c=o and fo_~,o_-H,o_-H,o_-H decrease, and increases, likewise in accord with the general trends. fc-o,c-o.c-OS-0 5. VIBRATIONAL
FREQUENCIES
The frequencies predicted for cis-cis and cis-tram pet-formic acid using the 4-3 1G basis set are listed in Table V together with current experimental assignments for the most stable form. The frequencies predicted for trans- and cis-formic acid using the same basis set have been included for comparison, along with the experimental values for the trans-conformer. Brooks and Haas (37) have calculated sets of frequencies for cis-cis pet-formic and peracetic acid using normal coordinate analysis and an assumed percarboxyl geometry. Perfect agreement between the calculated and observed values was obtained, but this was a consequence of having more force constants to adjust than the number of frequencies, and so no independent comparisons are possible. In general the values in Table V predicted ab initio are consistently larger than experiment for both per-formic and formic acid. For trans-formic acid the difference in values ranges from 28 to 124 cm-‘, with an average difference of 80 + 33 cm-‘. For per-formic acid, omitting the values for the C-O stretch, the difference between the values calculated for the cis-cis structure and the experimental values for the most stable form ranges from 36 to 152 cm-‘, with an average difference of 86 f 29 cm-‘. The C-O stretch is the only frequency for which the calculated is less than the experimental value, and, since the values for trans-formic acid do not show this discrepancy, it suggests that the experimental assignment of 1243 cm-’ for per-formic acid may be too high. There would appear to be some doubt with regard to this assignment, both the magnitude and the actual identifi-
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
ACID
TABLE III Changes in Force Constants Common to Performic Acid and Formic Acid in going from the Chain to the Ring Structure [Figs. lb + a and d + c]
constant
Performic Acid
Formic Acid
fc=o,c=o
decreases 15.65 -L 14.81
decreases 15.37 + 14.84
fC-O,C-O
increases 6.57 + 6.77
increases 7.23 + 7.45
f 0-H,O-H
decreases 7.92 + 7.26
decreases 8.78 + 7.96
f C-H,C-H
increases 5.98 + 6.13
increases 5.16 + 5.51
f
increases 2.31 + 2.55
decreases 2.35 + 2.32
cHCO,
decreases 1.46 + 1.40
decreases 1.59 + 1.50
fC=O,C-O
increases 1.37 + 1.63
increases 1.22 + 1.31
f C=O,O-H
increases -0.07 + -0.15
increases -0.04 + -0.06
fc-0,0-H
increases 0.04 -, 0.16
increases 0.01 + 0.23
f C=O,C-H
increases 0.07 + 0.20
decreases 0.36 + 0.27
f C-O,C-H
decreases 0.17 -L 0.09
decreases 0.19 + 0.12
f 0-H,C-H
decreases -0.01 + 0.00
sign changes 0.01 + -0.04
f c=o,
increases 0.04 + 0.39
increases 0.07 + 0.18
f c-o,
increases 0.70 -L 0.79
decreases 0.76 -+ 0.48
f OH,
-/+ sign change - 0.01 + 0.03
+/- sign change 0.07 * -0.10
f C-H,
decreases - 0.15 + -0.14
decreases -0.19 + -0.16
f C=O,
decreases - 0.51 -L -0.47
decreases -0.54 + -0.48
f C-O,
decreases 0.53 + 0.49
increases 0.47 -. 0.52
f 0-H,
increases - 0.01 + -0.04
sign changes -0.06 +. 0.04
f C-H,
same
increases 0.02 -c 0.04
f
same 0.71 +
Force
Quadratic:
f
Quadratic:
diagonal
off diagonal
0.05 -t 0.05 0.71
decreases 0.77 + 0.73
265
BOCK, TRACHTMAN, TABLE
Force Constant
AND GEORGE
III-Continued
Performic Acid
Formic Acid
fc-o,c-o,c-0
decreases -103.84 + 79.40
decreases -101.29 + -97.91
fc-o,c-o,c-0
decreases - 41.39 --39.35
increases - 45.47 + -46.03
decreases - 51.81 + -48.48
decreases - 58.06 + -51.83
increases - 35.04+-35.75
increases - 31.11 + -32.64
Cubic:
diagonal
fc-H,C-&C-H
coca,
coca,
increases - 1.89-c- 3.97
increases - 1.32 -. - 1.53
f
decreases - 0.27+-
decreases - 0.40 + - 0.27
f
Cubic:
0.22
off-diagonal
fC=O,C-o,c-0
increases
- 1.96 .+ - 3.40
increases - 2.20 -c - 2.32
+/- sign change 0.02 * - 0.20
-
decreases 0.72 + 0.63
decreases 0.68 + 0.63
increases
decreases -3.22 -. -3.10
-2.66 + -3.05
-/+ sign change 0.05 -, 0.02
changes sign -0.09 + 0.19
increases
decreases 0.33 + 0.30
decreases 0.34 -L 0.27
changes sign 0.08 + -0.14
decreases -0.23 + -0.06
increases -0.20 + -0.24
increases -0.69 + -1.28
decreases -0.02 + -0.00
decreases -0.07 + -0.03
decreases -1.61 + -1.15
decreases -1.96 - -1.69
fC-H,C-O,C-0
decreases -0.77 -c -0.67
decreases -0.75 -L -0.68
fC-H,O-H,O-H
decreases -0.16 + 0.00
changes sign 0.09 + -0.05
increases -3.20 + -3.65
increases -3.59 + -3.76
decreases -0.98 -c -0.94
decreases -1.13 -L -1.03
increases -2.40 + -3.66
decreases -2.26 -c -2.09
decreases -1.01 + -0.94
decreases -1.17 + -1.03
fC-0,0-H,O-H
fC=O,
coca,
fc-o,coco,
0.26 -L 0.29
VIBRATIONAL
FREQUENCIES TABLE
Force Constant Cubic:
OF PERFORMIC
267
III-Continued
Performic Acid
off-diagonal
ACID
Formic Acid
(cont'd)
f 0-H,
changes sign -0.01 .+ 0.38
changes sign -0.23 + 0.13
f 0-H,
-/t sign change -0.01 + 0.02
t/- sign change 0.07 + -0.22
same - 0.39
+ - 0.39
decreases - 0.46 +
- 0.43
f C-H,
same - 0.70
* - 0.70
increases - 0.59 +
- 0.71
f
increases - 0.16 + - 0.41
increases - 0.51 .
- 0.52
increases - 1.83 + - 2.64
decreases - 1.61 +
- 1.28
increases 0.00 +
changes sign 0.07 + - 0.06
tOCO,C-H,C-H
decreases - 0.14 + - 0.13
increases - 0.18 +
- 0.19
decreases 1.57 +
1.54
decreases 1.60 +
1.48
f
increases - 0.60 + - 0.70
decreases - 0.74 +
- 0.67
f
+/- sign change 0.02 + - 0.01
-/+ sisn chance - 0.07- 0.07
decreases 0.11 +
0.10
decreases 0.25 +
0.06
f
decreases 1.02 +
0.99
increases 1.08 +
1.09
f
decreases 1.05 i.
1.02
decreases 1.09 +
1.07
fC=O,C=O,C=O,C=O
decreases 564 +
523
decreases 534 +
511
fC-O,~c-O,C-O,C-O
increases
246
increases 230 +
245
fO-H,O-H,O-H,O-H
decreases 336 -.
309
decreases 370 +
337
increases 184 +
188
increases 165 +
172
f C-H,
f f f f
f
Ouartic
0.14
(fiiiij
fC-H,C-H,C-H,C-H
227
+
cation (17). The band is weak in any case, and with peracetic acid there are three very strong bands in this region, i.e., at 1229, 1239, and 1248 cm-l. Among the calculated values themselves several points may be noted. With regard to the change in frequency in going from the chain to the ring structure: (i) vo__H decreases
substantially,
by 139 cm-’ with PFA and 190 cm-’ with FA,
268
BOCK, TRACHTMAN,
AND GEORGE
TABLE IV Changes in Quadratic Diagonal Force Constants Specific to Performic Acid and to Formic Acid in going from the Chain to the Ring Structures [Figs. lb + a, and d + c, respectively] Force Constants
Performic Acid
fo-0,0-o
decreases 5.64 + 5.41
f
increases 1.46 + 1.84
f
increases 1.09 + 1.22
f
increases 0.95 + 1.01
f 'ocoo,Tocoo
increases 0.44 + 0.56
f
increases 0.00 + 0.40
TCOOH,TCOOH
Formic Acid
same 0.51 -L 0.50 f
increases 0.50 - 0.51
'HOCO,'HOCO
increases
f THOCH,THOCH
0.44 + 0.50
and (ii) I+=~ decreases to a lesser extent, by 96 cm-’ with PFA and 54 cm-l with FA, on the other hand, (iii) ~~0~0 increases by 5 1 cm-’ in the case of PFA, but decreases by 46 cm-’ in the case of FA. Comparing the frequencies
of PFA and FA directly,
(iv) vo__His almost the same for chain PFA and ring FA, i.e., 3621 and 3629 cm-‘, respectively, on the other hand, (v) vcEo is very similar for the two chain structures, i.e., 1921 and 1936 cm-’ for PFA and FA, respectively, and (vi) vc_o is also very similar for the two chain structures, i.e., 1188 and 1190 cm-’ for PFA and FA, respectively, whereas (vii) vc_o is very different for the two ring structures, i.e., 1232 and 1140 cm-’ for PFA and FA, respectively, and (viii) vLoco is much larger for both the chain and the ring structures of PFA compared to FA, i.e., 810 and 861 cm-‘, respectively, for PFA, and 699 and 653 cm-‘, respectively, for FA. 6. CONCLUDING
REMARKS
Pimental and McClellan (2) pointed out 20 years ago that while the structural data for crystals support the premise that a linear arrangement of “A-H---B” is energetically favored, in intramolecular hydrogen bonding (and in smaller poly-
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
269
ACID
TABLE V Harmonic and Anharmonic Frequencies (cm-‘) of Cis-Cis and Cis-Trans Performic Acid, and Cis- and Trans-Formic Acid (6), Calculated Using the 4-31G Basis Set Performic
Acid Cis-Trans
Cis-Cis
Harmonic
Anharmonic
Harmonic
Experimenta
"
Anharmonic
O-H
3367
3606
3482
3167
3621
C-H
2967
3348
3139
3303
3171
C=O
1739
1881
1825
1946
1921
C-O
1243
1250
1232
1257
1188
O-O
859
941
930
940
921
1453
1539
1489
1527
1448
1340
1484
1432
1485
1402
810
880
861
829
810
345
341
319
309
1138
1133
1144
1149
TOCOo
410
411
300
299
TCOOH
141
143
50
58
rHCOO
Formic wan* Exveriment
"
Harmonic
Acid trans Anharmonic
cis Harmonic
Anharmonic
O-H
3570
3769
3629
3963
3819
C-H
2944
3170
3047
3063
2766
C=0
1776
1909
188.X
1973
1936
C-O
1105
1150
1140
1210
1190
1387
1510
1490
1547
151s
'o=c-0
625
659
653
709
699
1223
1366
1347
1396
1362
TWCOH
1033
1163
1157
1133
1128
563
561
464
463
'OCOH
a.
642(553)'
The
data
refers
to the most
atable
form,
see
Introduction.
merit units) the linear arrangement may be obtainable only with strains in other degrees of freedom, and a compromise nonlinear minimum energy configuration will result. Further experimental studies since then have tended to accentuate the contrast between intermolecular and intramolecular bonding. For example, it appears from Olovsson and Jonsson’s (35) recent tabulation of neutron diffraction data for 3 15 intermolecular hydrogen bonds with N or 0 as the donor and N, 0 or Cl as the acceptor that the A-H---B angle lies between 165 and 180” in about 86% of the cases. The angle is less than 120” for only 8 N-H---O bonds, and only 1 O-H---O bond. In addition, the O/O distance in 170 O-H---O bonds lies between
270
BOCK, TRACHTMAN,
AND GEORGE
2.50 and 2.94 A in about 85% of the cases. Only 15 O/O distances are 2.49 A or less, and 2.40 A is the lower limit. According to these criteria, intramolecular bonding in the cis-cis structure of performic acid with an O-H---O angle of about 116” and an O/O distance of about 2.6 A would rank as an extreme case. But the tuans-structure of formic acid has a far smaller O-H---O angle of about 68” and an O/O distance of about 2.3 A, well outside the above limits. The finding that in going from the chain to the ring structure there are significant changes in force constants common to both performic and formic acid serves to support the view that there is nevertheless a hydrogen bonding type of interaction in trans-formic acid despite its adverse geometrical features. The present studies thus corroborate the ab initio charge density calculations of Peyerimhoff and Buenker (38) which show electron density in the region between the 0 of the C=O group and the H of the O-H group that can be construed as a bonding interaction. RECEIVED:
October
18, 1979 REFERENCES
I. J. D. BERNAL, The function of the hydrogen bond in solids and liquids, in “Hydrogen Bonding” (D. Hadzi, Ed.), Pergamon, New York, 1959, pp. 7-32, especially p. 8. 2. G. C. PIMENTAL AND A. L. MCCLELLAN, “The Hydrogen Bond,” Freeman, San Francisco, Calif., 1960. 3. “The Hydrogen Bond” (P. Schuster, G. Zundel, and C. Sandorfy, Eds.), Vols. I-III, NorthHolland, Amsterdam, 1976. 4. N. SHEPPARD,Infrared spectroscopy and hydrogen bonding-band widths and frequency shifts, in “Hydrogen Bonding” (D. Hadzi, Ed.), p. 85- 105, Pergamon, New York, 1959. 5. P. A. KOLLMAN AND L. C. ALLEN, Chem. Rev. 72, 283-303 (1972), especially pp. 293-294. See also D. HADZI AND S. BRATOS,Vibrational spectroscopy of the hydrogen bond, Chap. 12 in Vol. II of Ref. (3), above. 6. C. W. BOCK, M. TRACHTMAN,AND P. GEORGE,J. Mol. S~ecfrmc. 80, 131-144 (1980). 7. C. W. BOCK, P. GEORGE,AND M. TRACHTMAN,.I. Mol. Struct. in press. 8. P. SCHUSTER,Energy surfaces for hydrogen bonded systems, Chap. 2 in Vol. I of Ref. (J), above. 9. P. A. KOLLMAN, Hydrogen bonding and donor-acceptor interactions, in “Applications of Electronic Structure Theory” (H. F. Schaefer, III, Ed.), Plenum, New York, 1977. 10. (a) W. H. HOCKING,~. NaturforschA 31, 1113-1121(1976);(b)E. BJARNOVANDW. H. HOCKING, Z. Nafurforsch A 33,610-618 (1978); (c)G. H. KWEI AND R. F. CURL, JR.,J. Chem. Phys. 32, 1592- 1594 (1960). II. J. R. RITTENHOUSE,W. LOSUNEZ, D. SWERN, AND J. G. MILLER, .I. Amer. Chem. Sot. 80, 4850-4852 (1958). 12. W. LOBLINEZ, R. RITTENHOUSE,AND J. G. MILLER,J. Amer. Chem. Sot. 80,3505-3509 (1958). 13. M. T. ROGERSAND T. W. CAMPBELL,J. Amer. Chem. Sot. 74, 4742-4743 (1952). 14. L. M. HJELMELANDAND G. H. LOEW, Chem. Phys. Left. 32, 309-314 (1975). IS. B. PLESNICAR,M. TASEVSKI,AND A. AZMAN, J. Amer. Chem. Sot. 100, 743-746 (1978). 16. A. R. HOY, I. M. MILLS, AND G. STREY, Mol. Phys. 24, 1265-1290 (1972). 17. P. GIGUERE AND A. WEINGARTSHOFEROLMOS, Canad. J. Chem. 30, 821-830 (1952). 18. H. SELLERS,personal communication. 19. P. PULAY, Theor. Chim. Acta 50, 299-312 (1979). 20. R. DITCHFIELD, W. J. HEHRE, AND J. A. POPLE, J. Chem. Phys. 54, 724-728 (1971). 21. H. B. SCHLEGEL,S. WOLFE, AND F. BERNARDI,J. Chem. Phys. 67, 4181-4193 (1977). 22. E. B. WILSON, JR., J. C. DECIUS. AND P. C. CROSS, “Molecular Vibrations,” McGraw-Hill,
New York, 1955. 23. I. M. MILLS, in “Molecular Spectroscopy-Modern Research” Mathews, Eds.), Academic Press, New York, 1972.
(K. Narahari Rao and C. W.
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
ACID
271
24. P. PULAY, Direct use of the gradient for investigating molecular energy surfaces, in “Applications of Electronic Structure Theory” (H. F. Schaefer, III, Ed.), pp. 153-185, Plenum, New York, 1977. 25. C. W. BOCK, P. GEORGE, AND M. TRACHTMAN, J. Mol. Spectrosc, 78, 248-256 (1979). 26. C. W. BOCK, P. GEORGE, AND M. TRACHTMAN, J. Mol. Spectrosc. 78, 298-308 (1979). 27. C. E. BLOM, C. ALTONA, AND A. OSKAM, Mol. Phys. 34, 557-571 (1977). 28. C. E. BLOM AND C. ALTONA, Mol. Phys. 31, 1377-1391 (1976). 29. C. E. BLOM AND C. ALTONA, Mol. Phys. 34, 177-192 (1977). 30. C. E. BLOM AND C. ALTONA, Mol. Phys. 33, 875-885 (1977). 31. G. FOGARASIAND P. PULAY, Mol. Phys. 33, 1565-1570 (1977). 32. P. FULAY, Mol. Phys. 21, 329-339 (1971). 33. P. PULAY, A. RUOFF, AND W. SAWODNY, Mol. Phys. 30, 1123-1131 (1975). 34. T. K. HA, R. MEYER, AND H. H. GUNTHARD, Chem. Phys. Lett. 59, 17-20 (1978). 35. I. OLOVSSON AND P.-G. JONSON, X-ray and neutron diffraction studies of hydrogen bonded systems, Chap. 8, Vol. II of Ref. (3), above. 36. E. L. ELLEL, “Sterochemistry of Carbon Compounds,” p. 206, McGraw-Hill, New York, 1962. 37. W. V. F. BROOKSAND C. M. HAAS, J. Phys. Chem. 71, 650-655 (1967). 38. S. D. PEYERIMHOFFAND R. J. BUENKER,J. Chem. Phys. 50, 1846-1861 (1969).
OF MOLECULAR
SPECTROSCOPY
84,
256-271 (1980)
An Ab Initio Study of the Harmonic and Anharmonic Field and Fundamental Vibrational Frequencies of Performic Acid
Force
CHARLES W. BOCK AND MENDEL TRACHTMAN Chemistry Department,
Philadelphia College of Textiles & Science,
Philadelphia,
Pennsylvania
19144
AND PHILIP GEORGE Biology Department,
Universiry of Pennsylvania,
Philadelphia,
Pennsylvania
19147
The harmonic and anharmonic force fields and fundamental vibrational frequencies of performic acid are studied ab initio in the 4-31G basis set using geometries fully optimized at this level. The frequencies predicted for the cis-cis conformer are compared with those derived from spectroscopic observations on the most stable form. An extensive comparison is made between the changes in diagonal and off-diagonal quadratic and cubic force constants, and diagonal stretching quartic constants, in going from the chain to the ring structure in performic and formic acid, and features which these changes have in common are seen to support the view that there is a hydrogen bonding type of interaction in rrans-formic acid despite its unfavorable geometry. cis-cis and cis-trans
1. INTRODUCTION
The most extensively investigated hydrogen bonding is that in which the two electronegative atoms and the hydrogen are collinear, or nearly collinear-namely, intermolecular bonding, e.g., in the H,O dimer, the [F-H--F]ion and the formic acid dimer, and intramolecular bonding which results in the formation of sixand seven-membered rings, e.g., in the enol form of malonaldehyde and in the maleate mono-anion, respectively (l-3). Infrared spectroscopy has been the experimental technique most commonly used to establish its presence (4, 5), and the concentration dependence of the “X-H” peak in solvents such as carbon tetrachloride or hexane has been invaluable in showing whether it is inter- or intramolecular in nature. However, the finding that with formic acid and performic acid the most stable monomeric conformer is the one in which the H of the O-H group and the 0 of the C=O group are in close proximity suggests that a hydrogen-bonding type of interaction may be stabilizing these particular conformers, even though the rings are smaller, containing four and five atoms, respectively, with the H-atom lying at best some 0.7-1.0 A off the line joining the two O-atoms (6, 7). Ab initio studies have been mainly concerned with calculating the geometry of hydrogen-bonded structures and the bonding energy (5,8,9). To a lesser extent 0022-2852/80/110256-16$02.00/O Copyright
0
1960 by Academic
All rights of reproduction
Press,
Inc.
in any form reserved.
256
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
0
H\/
O\O
H'-
“1
/ :: I
b
ACID
257
0
I
0
d
FIG. 1. The Structures of (a) the Cis-Cis, and (b) the Cis-Tram Conformers of Performic Acid, and (c) the Truns- and (d) the C&Conformers of Formic Acid (la).
the change in the various force constants has been investigated, e.g., the O-H stretching force constant (5, 8). In a previous paper we reported the complete harmonic and anharmonic force fields and the fundamental vibrational frequencies calculated ab initio for both the tram- and c&planar conformers of formic acid,’ and traced the changes in the force field as the H of the O-H group and the 0 of the C=O group come into close proximity. The present paper extends these studies to per-formic acid, see Figs. la and b (6). Although it presents no problem in carrying out the calculations and making the comparison between the cis-cis conformer, which would have a five-membered H-bonding ring, and the cis-tram conformer, which has the O-H group rotated 180” about the O-O bond axis, it has to be remembered that at present there is no conclusive experimental evidence as to the actual structure of the most stable form (7). An analysis of the average dipole moment of several long chain peracids was shown to favor a nonplanar structure in which the hydroxyl hydrogen is twisted out of the plane by about 72” but still in fairly close proximity to the 0 of the C=O group (II -13). This analysis has been questioned on the grounds that the assumption that bond moments taken from other molecules will provide good values for the peracids does not seem justified (14). In addition, the bond moment for the O--H bond was not taken into account (15). Moreover, semiempirical calculations, IEHT and PCILO (14), and ab initio calculations using several basis sets-STO-3G, 4-3 lG, 4-3 1G plus bond functions, (9,5) with and without polarization functions-all find the cis-cis planar structure to be the most stable conformer as might have been expected (7,14). Quadratic and selected cubic and quartic force constants are computed using the 4-31G basis set for the cis-cis and cis-tram conformers of performic acid. Corresponding values for the two conformers are compared among themselves and with the values for the analogous constants for tram- and &-formic acid (6). Harmonic and anharmonic vibrational frequencies are calculated for both pet-formic acid conformers using the procedure of Hoy et al. (26), and the values for the cis-cis conformer are compared with those derived from spectroscopic observations on the most stable form (17). ’ Using Hocking’schoice of the two H-atoms as reference, (IO), see Figs. lc and d.
the vans-conformer
is the more stable
258
BOCK,TRACHTMAN,ANDGEORGE 2.COMPUTATIONALMETHODS
The SCF wavefunctions and forces were computed using the Arkansas version (18) of the TEXAS program written by Pulay (19), utilizing the widely used nearly double 5 4-31G basis set with no scale factors (20). The energies, E(q), and forces f(q), were obtained for the 4-31G optimized geometries for both conformers and at small displacements Aq, from these geometries. The force constants were then obtained numerically from the energies and forces. The displacements were chosen to lie along individual internal coordinates, and the harmonic force constants determined from the usual two-point difference formula f’rJ
=
[f&h
-
&J)
.ffJ
=
-.fdSo
+
AqJ)l/+qJI
(1)
and [f)lJ
+
f;t1!2,
(2)
wheref( is the ith component of the force vector. Equation (2) ensures that the harmonic force constant matrix is symmetric. As suggested by Schlegel et al. (21), the diagonal stretching force constants were computed by fitting a fourth-degree polynomial to the energies and forces at three points: fir = 2Mq, + Aqr) - 2E(q,) + &-I, - Aqr)l/)hi/’
- Lfdqo- Aqd -f&o + W1/2\ 41.
(3)
This reduces errors due to large anharmonic effects. I Aqr1 was chosen as 0.05 A for bond stretching, and 2” for in-plane bending and out-of-plane torsional coordinates. The cubic force constants j& and were computed using the three-point difference formula ftJJ
hJJ
=
-
[fdqo
+
hi)
-
2.fdqo)
+
f&o
-
AeW 1A%12.
(4)
The remaining cubic constantsftil, (i # j Z k) were assumed to be small, and were taken as zero in the frequency calculations (22). The diagonal stretching quartic force constants,hiii, were computed from the fourth-degree polynomial used above for the quadratic diagonal stretching constants, where frtti = IV[fl(qo - Aq,) - fi(qo + AqiW 1ho 1
- [Nqo + W - 2E(qd + Wq, - WY) 4,) 2H)Aqrj2. (5) All remaining quartic constants were assumed to be small, and taken as zero in the frequency calculations (21). The harmonic frequencies and normal coordinates were calculated by the Wilson F-G method (22). In order to make anharmonicity corrections, the force constants were transformed from curvilinear internal coordinates to linear normal coordinates using the procedure of Hoy et al. (16), except that the derivatives of the L matrix needed for the nonlinear transformation were computed numerically rather than analytically, as described by Schlegel et al. (21).
VIBRATIONAL
FREQUENCIES
259
OF PERFORMIC ACID
TABLE I Geometry of the Cis-Tram and Cis-Cis Conformers of Performic Acid [Figs. lb and a], and the Cis- and Tram-Conformers of Formic Acid [Figs. Id and c] Formic Acid
Performic Acid
cis
trans 1.343
Structural Parameter
cis-trans
cis-cis
c-o
1.360
1.350
1.352
c=o
1.190
1.200
1.194
1.202
O-H
0.973
0.984
0.956
0.972
C-H
1.082
1.079
1.105
1.097
o-o
1.457
1.458
126.9
123.6
122.1
124.9
107.1
109.9
114.6
111.0
111.8
l&3.6
99.0
104.5 109.7
106.7
__~--____
The energies of the vibrational levels, E(v), were then expanded series in the vibrational quantum numbers,
as a power
E(v) = 2 W&, + 112) + c Xrs(V, + 1/2)(V, + 112) + * * ‘, r
C-8
where W, are the harmonic frequencies. The second-order perturbation formulas for asymmetric-top molecules given by Mills (23) were used in the calculation of the anharmonicity constants X,,. 3. GEOMETRY
In the absence of any experimental geometry for either the cis-cis or cis-tram conformer of pet-formic acid (Figs. la and b), the values for the bond lengths and bond angles calculated using the 4-31G basis set with full geometry optimization, see Table I, have been employed in the force constant studies. In comparing these force constants with those for rrans- and cis-formic acid (Figs. lc and d), it must be borne in mind that the formic acid values were obtained using experimental geometries (10). The 4-31G optimized geometries for formic acid are, however, quite close to the experimental-on average to within 0.003 A in the bond lengths and 0.5” in the bond angles- except in the case of the C-H bond length and the LCOH bond angle, which differ by about 0.018 A and 6.8”, respectively. Hence the only force constants likely to be much affected are those involving these structural elements. Even so, the use of these different geometries in no way affects the internal comparison of the cis-tram and cis-cis constants for pet-formic acid, and the cis and rrans constants for formic acid, to see whether there are significant and consistent trends as the H of the H-O group is rotated into position for an optimal
260
BOCK, TRACHTMAN,
AND GEORGE
H-bonding.type of interaction. This rotation, however, involves the O-O bond axis in pet-formic acid and the C-O bond axis in formic acid, so the changes in overall geometry are not strictly the same in the two cases. 4. FORCE FIELD
The quadratic, cubic, and quartic force constants computed for the cis-cis and cis-truns conformers of pet-formic acid using the 4-3 1G basis set are listed in Table II. Before looking at the values in detail it may be recalled that harmonic force constant matrices generated by ab initio calculations show systematic deviations with respect to the experimental force field, particularly the diagonal constants (24). Calculated values using the 4-31G or comparable basis sets have been found to overestimate diagonal stretching constants by about 5- 10% depending on the geometry employed, and in-plane diagonal bending constants by about 10% (24-34). Although off-diagonal elements obtained from experiment are usually less accurate (24, 34), the calculated values usually agree to within about 10%. Hence, while calculated values taken separately can be expected to be in only fair agreement with experiment, trends in values for molecules that have a similar structure are nevertheless quite reliable and informative comparisons can be made. In a recent study of trans-formic acid using the 6-3 1G basis set Ha et al. (34) found that only minor corrections to the calculated force field were needed to reach agreement with experiment, and so the present results for pet-formic acid should be of help in arriving at reliable experimental force fields for its cis-cis and cistrans conformers. To facilitate comparison of the changes in the force constants that are common to per-formic acid (PFA) and formic acid (FA) in going from the chain to the ring structure, i.e., from b to a and from d to c in Fig. 1, the values have been brought together in Table III. These changes can be rationalized in the following way. The traditional valence bond approach, or a consideration of the effect of the hydrogen on the spatial distribution of the molecular orbitals when it comes into the vicinity of the two oxygens, would lead one to expect bonding to some extent between the H of the OH group and the 0 of the C=O group, and hence electron delocalization in the ring compared to the chain structure. As a consequence one would anticipate an enhancement of the mechanical strength of the formal C-O bond, and a diminution in the strength of the formal C=O and O-H bonds. This sort of effect is borne out by the changes in bond lengths for both acids as shown in Table I. C-O decreases in length indicating a strengthening, while C=O and O-H (35) increase in length indicating a weakening: O-O in PFA also increases in length, indicating a weakening in the ring structure. The changes in the bond angles, however, show no such regularities, which could be due to the difference in ring size. Turning first to the diagonal stretching constants, all three sets of values show the characteristics one would predict on the basis of these mechanical changes: (i) fc_o,c_o
(chain <.fc_o,c_o
(ii) f,--,c=o
(chain) >fc=o,c=o
(iii) fo_-H,O_u (chain) >fo_u,o_u
(ring): both PFA and FA, (ring): both PFA and FA, (ring): both PFA and FA.
VIBRATIONAL FREQUENCIES
261
OF PERFORMIC ACID
TABLE i1 Force Constant9 A.
for CM_%’ and Cis-Trunsb Performic Acid Computed from the 4-31G Basis Set’
Quadratic
For&
c-o
c=o
Constants o-o
fij
O-H
C-H
C=O
14.812 15.653
C-O
1.628 1.366
6.770 6.574
o-o
0.002 -0.012
0.116 0.094
5.467 5.644
O-H -0.152 -0.066
0.158 0.044
-0.032 -0.172
7.263 7.920
C-H
0.201 0.072
0.094 0.166
-0.078 -0.070
0.002 -0.009
6.129
0.385 0.037
0.785 0.701
-0.271 -0.193
0.032 -0.005
-0.136 -0.146
0.084 -0.106
0.562 0.522
0.662 0.521
0.037 0.002
0.012 0.042
0.126 0.004
-0.173 -0.008
0.672 0.660
0.216 0.066
0.488 0.532
0.033 0.053
-0.043 -0.014
TOCOO
TCOOH
THCOO
TOCOO
0.562 0.440
TCOOH
0.087 0.004
THCOO
-0.382 -0.396
5.981 2.552 2.307 0.098
0.024
1.843 1.457
-0.013 0.011
-0.136 -0.081
-0.014 0.190
1.222 1.090
0.045 0.054
0.711 0.706
0.177 0.146
0.013 0.050
1.395 1.460
0.039 0.0014d 0.004 -0.006
0.504 0.505
In addition, since the H--O interaction can be presumed to be attractive in nature, one would expect all diagonal bending constants internal to the ring to be larger for the ring compared to the corresponding bending constants for the chain structure. This is the case with PFA, for which (iv)
~LOCO,LOCO
(find
> fL~~~,L~~~
(chain)
but not FA, which could be due to a smaller attractive interaction in the fourmembered ring, or features of the calculation procedure, e.g., the relatively small basis set employed, the absence of polarization functions, or correlation energy effects. Similar relationships hold for the force constants that are specific to each acid, see Table IV. In the case of PFA electron delocalization would be expected to diminish the mechanical strength of the formal O-O bond along with the formal O-H and C=O bonds, and accordingly: 64
fo-o,~-~
(chain)
> fo-O,O-o
(ring).
0.31 0.26
0.06 0.06
1.54 1.57
0.00
0.00
0.00
ace
7oCoo
TCOOE
%COO
0.41 0.16
-
1.15 1.61
C-E -
&Co
0.14 0.08
o-a -
-0.70 -0.60
0.57 -0.12
-2.11 -1.60
-2.64 -1.83
-0.67 -0.77
-0.24 -0.20
-1.13 -1.23
0.10 0.16
-
*o
-3.40 -1.96
c-o
Force
3.05 -39.35 2.86 -41.39
99.40 -103.84
-
c=o
Cubic
c-o -
i) C=O
(j)
B.
0.00 -0.02 -35.75 -35.04
-48.48 -51.81 0.00 0.16 0.14 0.00
-0.44 .-l-41
0.02 -0.04
0.58 0.32
-0.11 -0.14
-2.36 -2.27
-2.22 -1.80
-0.05 -0.03
0.98 0.52
-26.19 -26.95
0.10 0.11
-0.02 0.01
0.73 -0.10 -0.01 0.02
0.07 0.12
0.69 0.00
-0.13 -0.14
0.30 0.33
0.19 -0.09
0.26 0.18
C-H 0.63 0.72
O-H
f. Ijj
-0.20 0.02
-0.30 -0.31
O-O
Constants
1.02 1.05
0.09 0.09
-2.37 -0.96
-3.97 -1.89
-0.39 -0.39
0.38 -0.01
-0.21 0.00
-0.68 -0.02
-7.83 -4.27
-3.36 -1.48
0.09 0.02
0.05 -0.08
-3.41 -2.10
0.01 0.02
-1.74 -1.05
-0.79 -0.03
0.22 0.02
0.00 -0.01
-0.34 -0.37
-2.10 -1.55
0.00 -0.18
-3.86 -2.73
-3.68 -2.40 -0.41 -0.10
-0.98
0.14
-0.22 -0.27
0.01 -0.05
-0.20 -0.19
0.85 0.26
-0.16 -0.05
-0.14 0.03
0.08
0.23
0.99
-0.17 -0.16
0.14 0.01
0.04 -0.01
-0.10 -0.09
-0.09 -0.09
-0.21 -0.03
-0.02 -0.01
0.26 -0.02
0.10 0.02
0.10 0.11
-0.01 0.00
0.01 0.30
0.26 0.25
-0.19 -0.19
-0.00 -0.01
-0.06 -0.06
-0.22 -0.21
-0.21 -0.11
-0.29 -0.12 -0.22 -0.12
-0.48 -0.52
THCOO
0.19 0.01
TcOOH
-0.44 -0.98
ToCoo
1.02
-0.70 -0.70
0.02 -0.01
-0.15 -0.24
-0.94 -1.01
-0.94
0.09
-0.70 0.22
-3.85 -3.20
II-Continued
TABLE
263
VIBRATIONAL FREQUENCIES OF PERFORMIC ACID TABLE II-Continued C.
Quartlo
c-o
523.0 564.1
c-o
246.3 226.7
o-o
117.6 110.1
O-H
309.4 336.4
C-H
167.6 163.5
a.
Quadratic rtretch, force
Conrtantr
Foroe
constants
and bend-bend
in mdyn/R2,
stretch-stretch-stretch,
constants
b.
The upper numbers are for
c.
See reference
d.
If
and probably
respectively.
cis-cir-performic
(z)
the
stretch-bend-bend puartic
stretching
acid,
and the lower
. value
spurious
of
0.001
(r&9
~LOOH,LOOH Wng)
is
used in place
Fermi resonance
With regard to the bending constants
(vii)
and mdyn and mdyn n” for
the cis-trans-conformer.
a rounded-off
.LCOO,XOO
Cubic
respectively.
in mdyn/i3.
numbers for
(vi)
mdyn/i
constants
stretch-stretch-bend,
and bend-bend-bend constants
in mdyn/R, mdyn and mdyn R for the rtretch-
force constants stretch-bend
fiiii
0.0014,
a severe
arises.
internal to the ring,
?LCOO,~COO > ~LOOIUOOH
(Chain), (Chain),
and likewise with FA, (viii)
YLHOC,LHOC (ring> > ~LHOC,LHOC (Chain).
Furthermore, one would expect it to be more difficult for rotation to occur about the C-O and O-O bonds in the ring form of PFA, and about the C-O bond in the ring form of FA. The values for the torsional constants in Table IV bear this out, i.e., with PFA (ix) fiOcOO,lOc,,,, (ring) > fT,,c00,70c,,0 (chain), (4
f’COOH,TCOOH (ring) > fTCOOH.TCOOH (chain).
In the case structures, membered If indeed
of FA, however, f7,,,_,C0,7HOC0 is almost the same for the chain and ring which again could be due to less attractive interaction in the fourring or features of the calculation procedure. attractive interaction is greater in the five-membered ring of PFA,
264
BOCK, TRACHTMAN,
AND GEORGE
then one would expect the changes in the various force constants that are common to both acids to be larger for PFA. This is the case for three of the four relationships set out above, i.e., for ~c-_o,c-_o,~~=o.c=o, andfLoco,LOCo. Forfo_-H.o_-H the change is greater for FA, but this could be attributed to a repulsive interaction operative in cis-FA due to the close approach of the two hydrogens to within about 1.8 A, see Fig. Id, which is appreciably less than the sum of their Van der Waal radii (7,36). It is obvious from Fig. lb that no such repulsive interaction could be present in cis-trans-PFA. Several changes in quadratic off-diagonal constants follow the same sort of trend. andfc=O,iOCO all increase in going from the chain For example, fc=o,c-O, ~~=o,oH to the ring structure, the increase being larger for PFA indicative of greater coupling between these structural elements in the five-membered ring. Among the cubic diagonal constants, (xi) fc=o,c=o,c=o (xii)
_LOCO,~OCO,~OCO
(chain)
>~c~,c=o,c=o
(chain)
(ring):
> f L~~~,L~~~,L~~~
both (ring):
PFA both
and WA
F& and
FA
with the changes again greater in the case of PFA. However withfo--H,O--H,O--H the change is greater for FA, while fc_o,c_o,c-o increases for FA but decreases for PFA. Among the cubic off-diagonal constants the much larger increases with for PFA are quite striking. And finally the ~c=o,c-O,C-o and ~C=O.~OCO,~OCO quartic constants fc=o,c=o,c=o,c=o and fo_~,o_-H,o_-H,o_-H decrease, and increases, likewise in accord with the general trends. fc-o,c-o.c-OS-0 5. VIBRATIONAL
FREQUENCIES
The frequencies predicted for cis-cis and cis-tram pet-formic acid using the 4-3 1G basis set are listed in Table V together with current experimental assignments for the most stable form. The frequencies predicted for trans- and cis-formic acid using the same basis set have been included for comparison, along with the experimental values for the trans-conformer. Brooks and Haas (37) have calculated sets of frequencies for cis-cis pet-formic and peracetic acid using normal coordinate analysis and an assumed percarboxyl geometry. Perfect agreement between the calculated and observed values was obtained, but this was a consequence of having more force constants to adjust than the number of frequencies, and so no independent comparisons are possible. In general the values in Table V predicted ab initio are consistently larger than experiment for both per-formic and formic acid. For trans-formic acid the difference in values ranges from 28 to 124 cm-‘, with an average difference of 80 + 33 cm-‘. For per-formic acid, omitting the values for the C-O stretch, the difference between the values calculated for the cis-cis structure and the experimental values for the most stable form ranges from 36 to 152 cm-‘, with an average difference of 86 f 29 cm-‘. The C-O stretch is the only frequency for which the calculated is less than the experimental value, and, since the values for trans-formic acid do not show this discrepancy, it suggests that the experimental assignment of 1243 cm-’ for per-formic acid may be too high. There would appear to be some doubt with regard to this assignment, both the magnitude and the actual identifi-
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
ACID
TABLE III Changes in Force Constants Common to Performic Acid and Formic Acid in going from the Chain to the Ring Structure [Figs. lb + a and d + c]
constant
Performic Acid
Formic Acid
fc=o,c=o
decreases 15.65 -L 14.81
decreases 15.37 + 14.84
fC-O,C-O
increases 6.57 + 6.77
increases 7.23 + 7.45
f 0-H,O-H
decreases 7.92 + 7.26
decreases 8.78 + 7.96
f C-H,C-H
increases 5.98 + 6.13
increases 5.16 + 5.51
f
increases 2.31 + 2.55
decreases 2.35 + 2.32
cHCO,
decreases 1.46 + 1.40
decreases 1.59 + 1.50
fC=O,C-O
increases 1.37 + 1.63
increases 1.22 + 1.31
f C=O,O-H
increases -0.07 + -0.15
increases -0.04 + -0.06
fc-0,0-H
increases 0.04 -, 0.16
increases 0.01 + 0.23
f C=O,C-H
increases 0.07 + 0.20
decreases 0.36 + 0.27
f C-O,C-H
decreases 0.17 -L 0.09
decreases 0.19 + 0.12
f 0-H,C-H
decreases -0.01 + 0.00
sign changes 0.01 + -0.04
f c=o,
increases 0.04 + 0.39
increases 0.07 + 0.18
f c-o,
increases 0.70 -L 0.79
decreases 0.76 -+ 0.48
f OH,
-/+ sign change - 0.01 + 0.03
+/- sign change 0.07 * -0.10
f C-H,
decreases - 0.15 + -0.14
decreases -0.19 + -0.16
f C=O,
decreases - 0.51 -L -0.47
decreases -0.54 + -0.48
f C-O,
decreases 0.53 + 0.49
increases 0.47 -. 0.52
f 0-H,
increases - 0.01 + -0.04
sign changes -0.06 +. 0.04
f C-H,
same
increases 0.02 -c 0.04
f
same 0.71 +
Force
Quadratic:
f
Quadratic:
diagonal
off diagonal
0.05 -t 0.05 0.71
decreases 0.77 + 0.73
265
BOCK, TRACHTMAN, TABLE
Force Constant
AND GEORGE
III-Continued
Performic Acid
Formic Acid
fc-o,c-o,c-0
decreases -103.84 + 79.40
decreases -101.29 + -97.91
fc-o,c-o,c-0
decreases - 41.39 --39.35
increases - 45.47 + -46.03
decreases - 51.81 + -48.48
decreases - 58.06 + -51.83
increases - 35.04+-35.75
increases - 31.11 + -32.64
Cubic:
diagonal
fc-H,C-&C-H
coca,
coca,
increases - 1.89-c- 3.97
increases - 1.32 -. - 1.53
f
decreases - 0.27+-
decreases - 0.40 + - 0.27
f
Cubic:
0.22
off-diagonal
fC=O,C-o,c-0
increases
- 1.96 .+ - 3.40
increases - 2.20 -c - 2.32
+/- sign change 0.02 * - 0.20
-
decreases 0.72 + 0.63
decreases 0.68 + 0.63
increases
decreases -3.22 -. -3.10
-2.66 + -3.05
-/+ sign change 0.05 -, 0.02
changes sign -0.09 + 0.19
increases
decreases 0.33 + 0.30
decreases 0.34 -L 0.27
changes sign 0.08 + -0.14
decreases -0.23 + -0.06
increases -0.20 + -0.24
increases -0.69 + -1.28
decreases -0.02 + -0.00
decreases -0.07 + -0.03
decreases -1.61 + -1.15
decreases -1.96 - -1.69
fC-H,C-O,C-0
decreases -0.77 -c -0.67
decreases -0.75 -L -0.68
fC-H,O-H,O-H
decreases -0.16 + 0.00
changes sign 0.09 + -0.05
increases -3.20 + -3.65
increases -3.59 + -3.76
decreases -0.98 -c -0.94
decreases -1.13 -L -1.03
increases -2.40 + -3.66
decreases -2.26 -c -2.09
decreases -1.01 + -0.94
decreases -1.17 + -1.03
fC-0,0-H,O-H
fC=O,
coca,
fc-o,coco,
0.26 -L 0.29
VIBRATIONAL
FREQUENCIES TABLE
Force Constant Cubic:
OF PERFORMIC
267
III-Continued
Performic Acid
off-diagonal
ACID
Formic Acid
(cont'd)
f 0-H,
changes sign -0.01 .+ 0.38
changes sign -0.23 + 0.13
f 0-H,
-/t sign change -0.01 + 0.02
t/- sign change 0.07 + -0.22
same - 0.39
+ - 0.39
decreases - 0.46 +
- 0.43
f C-H,
same - 0.70
* - 0.70
increases - 0.59 +
- 0.71
f
increases - 0.16 + - 0.41
increases - 0.51 .
- 0.52
increases - 1.83 + - 2.64
decreases - 1.61 +
- 1.28
increases 0.00 +
changes sign 0.07 + - 0.06
tOCO,C-H,C-H
decreases - 0.14 + - 0.13
increases - 0.18 +
- 0.19
decreases 1.57 +
1.54
decreases 1.60 +
1.48
f
increases - 0.60 + - 0.70
decreases - 0.74 +
- 0.67
f
+/- sign change 0.02 + - 0.01
-/+ sisn chance - 0.07- 0.07
decreases 0.11 +
0.10
decreases 0.25 +
0.06
f
decreases 1.02 +
0.99
increases 1.08 +
1.09
f
decreases 1.05 i.
1.02
decreases 1.09 +
1.07
fC=O,C=O,C=O,C=O
decreases 564 +
523
decreases 534 +
511
fC-O,~c-O,C-O,C-O
increases
246
increases 230 +
245
fO-H,O-H,O-H,O-H
decreases 336 -.
309
decreases 370 +
337
increases 184 +
188
increases 165 +
172
f C-H,
f f f f
f
Ouartic
0.14
(fiiiij
fC-H,C-H,C-H,C-H
227
+
cation (17). The band is weak in any case, and with peracetic acid there are three very strong bands in this region, i.e., at 1229, 1239, and 1248 cm-l. Among the calculated values themselves several points may be noted. With regard to the change in frequency in going from the chain to the ring structure: (i) vo__H decreases
substantially,
by 139 cm-’ with PFA and 190 cm-’ with FA,
268
BOCK, TRACHTMAN,
AND GEORGE
TABLE IV Changes in Quadratic Diagonal Force Constants Specific to Performic Acid and to Formic Acid in going from the Chain to the Ring Structures [Figs. lb + a, and d + c, respectively] Force Constants
Performic Acid
fo-0,0-o
decreases 5.64 + 5.41
f
increases 1.46 + 1.84
f
increases 1.09 + 1.22
f
increases 0.95 + 1.01
f 'ocoo,Tocoo
increases 0.44 + 0.56
f
increases 0.00 + 0.40
TCOOH,TCOOH
Formic Acid
same 0.51 -L 0.50 f
increases 0.50 - 0.51
'HOCO,'HOCO
increases
f THOCH,THOCH
0.44 + 0.50
and (ii) I+=~ decreases to a lesser extent, by 96 cm-’ with PFA and 54 cm-l with FA, on the other hand, (iii) ~~0~0 increases by 5 1 cm-’ in the case of PFA, but decreases by 46 cm-’ in the case of FA. Comparing the frequencies
of PFA and FA directly,
(iv) vo__His almost the same for chain PFA and ring FA, i.e., 3621 and 3629 cm-‘, respectively, on the other hand, (v) vcEo is very similar for the two chain structures, i.e., 1921 and 1936 cm-’ for PFA and FA, respectively, and (vi) vc_o is also very similar for the two chain structures, i.e., 1188 and 1190 cm-’ for PFA and FA, respectively, whereas (vii) vc_o is very different for the two ring structures, i.e., 1232 and 1140 cm-’ for PFA and FA, respectively, and (viii) vLoco is much larger for both the chain and the ring structures of PFA compared to FA, i.e., 810 and 861 cm-‘, respectively, for PFA, and 699 and 653 cm-‘, respectively, for FA. 6. CONCLUDING
REMARKS
Pimental and McClellan (2) pointed out 20 years ago that while the structural data for crystals support the premise that a linear arrangement of “A-H---B” is energetically favored, in intramolecular hydrogen bonding (and in smaller poly-
VIBRATIONAL
FREQUENCIES
OF PERFORMIC
269
ACID
TABLE V Harmonic and Anharmonic Frequencies (cm-‘) of Cis-Cis and Cis-Trans Performic Acid, and Cis- and Trans-Formic Acid (6), Calculated Using the 4-31G Basis Set Performic
Acid Cis-Trans
Cis-Cis
Harmonic
Anharmonic
Harmonic
Experimenta
"
Anharmonic
O-H
3367
3606
3482
3167
3621
C-H
2967
3348
3139
3303
3171
C=O
1739
1881
1825
1946
1921
C-O
1243
1250
1232
1257
1188
O-O
859
941
930
940
921
1453
1539
1489
1527
1448
1340
1484
1432
1485
1402
810
880
861
829
810
345
341
319
309
1138
1133
1144
1149
TOCOo
410
411
300
299
TCOOH
141
143
50
58
rHCOO
Formic wan* Exveriment
"
Harmonic
Acid trans Anharmonic
cis Harmonic
Anharmonic
O-H
3570
3769
3629
3963
3819
C-H
2944
3170
3047
3063
2766
C=0
1776
1909
188.X
1973
1936
C-O
1105
1150
1140
1210
1190
1387
1510
1490
1547
151s
'o=c-0
625
659
653
709
699
1223
1366
1347
1396
1362
TWCOH
1033
1163
1157
1133
1128
563
561
464
463
'OCOH
a.
642(553)'
The
data
refers
to the most
atable
form,
see
Introduction.
merit units) the linear arrangement may be obtainable only with strains in other degrees of freedom, and a compromise nonlinear minimum energy configuration will result. Further experimental studies since then have tended to accentuate the contrast between intermolecular and intramolecular bonding. For example, it appears from Olovsson and Jonsson’s (35) recent tabulation of neutron diffraction data for 3 15 intermolecular hydrogen bonds with N or 0 as the donor and N, 0 or Cl as the acceptor that the A-H---B angle lies between 165 and 180” in about 86% of the cases. The angle is less than 120” for only 8 N-H---O bonds, and only 1 O-H---O bond. In addition, the O/O distance in 170 O-H---O bonds lies between
270
BOCK, TRACHTMAN,
AND GEORGE
2.50 and 2.94 A in about 85% of the cases. Only 15 O/O distances are 2.49 A or less, and 2.40 A is the lower limit. According to these criteria, intramolecular bonding in the cis-cis structure of performic acid with an O-H---O angle of about 116” and an O/O distance of about 2.6 A would rank as an extreme case. But the tuans-structure of formic acid has a far smaller O-H---O angle of about 68” and an O/O distance of about 2.3 A, well outside the above limits. The finding that in going from the chain to the ring structure there are significant changes in force constants common to both performic and formic acid serves to support the view that there is nevertheless a hydrogen bonding type of interaction in trans-formic acid despite its adverse geometrical features. The present studies thus corroborate the ab initio charge density calculations of Peyerimhoff and Buenker (38) which show electron density in the region between the 0 of the C=O group and the H of the O-H group that can be construed as a bonding interaction. RECEIVED:
October
18, 1979 REFERENCES
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