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Molecular orbital studies of the conformation of peroxyacetic acid
‘.
Voitime’32, number 2
CHEMICAL
PHYSICS
.
iEl--l-ERS
.15.4+
1975
: ‘.
:
i%fOLECULARORBlTALSTUDlESCiFTkECONFORMATIONdFPEROXYACETiC Leonard M. HJELMELMD
ACID
and Gild_aH. LoEW
Department of Genetics, Stqnfod Stan-ford, C!ali/ornia 94305, USA
University Medical School,
Received 3 January 1975
A conformatior,d r&hods. The tot&y moment results.
study of peroxyacetic acid has been performed using both STO-3G and PCLO moIecuk orbital planar, cis conformer is obtained by both methods and is consistent with X-ray, infrwed;and dipole :
1. Introduction
conformation of the perpxycarboxyl group in which the consti&ent atoms all lay in a sitigle plane, with the exception of the hydrogen, which wad rotated Detailed investigation of peracid conformation was out of the plane by 72O abuut the peroxide bond. -This begun in 1950, when a dilutiqn study of the,infrared spectrum of peroxypropionic acid incarbon tetra-. conformation is currently accepted as being experi.chloride led to the prbposal of a five m.embered intermentally verified because of the agreement obtained . nally hydrogen bonded,ring as the cpnformatioxi of with the experimental dipole moment. Such a.structur& however, seems inconsistent with the peroxycarboxyl group [I]. Subsiquent infrared the,infrared data,.which -Hould be more easily accomstudies of peroxyacetic acid in both the liquid and vamodafed by a completely planar conformation of the por states revealed similar O-H stretching frequencies. peroxycarboxyl group. A normal coordinate analysis around 3310 cfi:I, characteristic of the hydrogen’ bonded state [2]. Hi&ly purified long &in fatty perof the force constants for an.ti planar conformation of the peroxycarboxyl group shows excellent agreeacids showed essentially nb free hydroxyl absorptions in their.high resolution infrared spectra over a range’ ment with the infrared’spectra ofperoxyacetic and peroxyformic acids 171 -‘Extended. HiickeI theory of concentrations between 3.0X 10-l&olar and 6.0 x io-3 molar in either carbon tetrachloride or molecular orbital calculations qf a_lIplanar conformation an.d the non-planar conformation suggested by hexane, strengthening the conclusion that these mole- .. .the dipole moment studies aIso predicted the p!anar cules exist as monomeric, intramolecularly hydrogen conformation to &slightly more stable [S] . Crystal bonded sp&ies in the liquid and vapor states 131: _ structures of peroxypelargonic acid and o-nitroperoxyTo further kxamine the conformati& of the peroxyl .b&zoic,acid confirm the planar nature of the peroxy&boxy1 group/studies were initiated on,the dipole carboxyl group, with the.exceptibm of the hydrogen moments’of peracids. Vatious long ch+--fatty peracattim which is rotated out of the pIane due to inter.ids were all found, to have a’dipole moment of 2.3i molecul& hidrogen bonds not piesent in the liquid !+ 0.04) debye [4]. Ugini this expe&nent$ value for qFvapor st&ks [9, !O]. Rui, the confo?mation of the dipolk momeni; an assumed geometry for the peroxycarboxyl group, and a set of bond inoi$nt val- ‘. p&acids has not been conclusively determined. ues takefl f:?m stubies of various otjier per&ides [5,‘6]; To further exam& the con.fomaiion of the per.._ a vector Sum method was used lo calculate corifoma-% -’ oxyctirboxyl.group, we iia$urid&-taken an extensive tions ,whidli:wotild reproduce the experimensal rno-..:” - ‘s.et.of CO~~OJ+II+O~C~~UI~G~& ofpecckyacetic ,,m&t. The r&At., of this study &a~ qk proposal of a:‘:. ,. acid.usjng abinitio.and semi-empirical MO techniques.’
f_ .'. :
,.'
.' ',. :
.,
. ...,, !.,. '. _,-.y ., _', ,, .. , .,:.. '_.~', :.
_' ., /. .,
369
Volume 32, number 2
..
CHEMICALPHYSICSLET-f-MS
..
2. Method of calculation and results
,:
1.5April
1975
..
2.1. i&hods. The molecular orbital methods we have chosen for the conformational studies are KILO (perturbative .,donfiguration interaction using localized orbit&) and STO-3G [ 11,121. PCILO is a semi-empirical method -which was explicitly developed for the conformational analysis of large molecules and STO-3G is an ab initio method in which the radial function of each Slatertype orbital (STO) is replaced by a least-squares-fitted combination of three gaussian-type orbitals. A Mulliken population
titialysis was pcrfomed
with
the results
Fig. 1. Torsion anglesvvied in’conformationalstudy of peroxyacetic
acid.
b&d angles and lengths which were used by Swern to correlate his proposed conformation with the dipole moments of long chain fatty peracids. Structures II and III represent the bond lengths and angles taken from the crystal structure of peroxypelargonic acid, and differ only in the O-H bond length. The O-H bond lengh and O-O-H V&XIC~ZU& wore not reported and as a result we obtained the O-O-H angle from the onitroperoxybenzoic acid crystal structure and varied the O-H bond length between the dues of 1.02 A suggested by infrared studies (structure II) and I .I 0 ,$ reTorted in the o-nitroperoxybenzoic acid structure I(structure III). We reasoned that the bond lengths and angles from peroxypelargonic acid were the more.reliable for our &culations since ,both sterically and electronically the aliphatic pel.argonic group (CH3-(CH,),-) better resembles the methy group than does the o-nitrophenyl moiety.
of
each method [13]‘. A refined dipole moment was calculated with the ~ ‘-STO-63iG** bzsis se; [14]. This is a double zeta qual-ity basis set in which polarization functions (d type for C and 0, and p type for H) have,been added..IEHT (iterative extended Hiickel theory) and INDO (incomplete neglect of differential overlap) were addition.ally employed to calculate the dipole moment of selected .structures ElS, 161. All five methods have been sxtensively described in the literature and will not be further discussed here. ‘2.2. Iizputge0,mh-k
2.3. Results “.
‘To study the rotational conformations of peroxyacetic acid (fig. l), we have used three different input geometries in order to include the most reasonable structurei which have been reported in the literature.
To investigate the gross conformation21 behavior of peroxyacetic acid, a set of nested rotations about ail three rotational axes was performed with PCILO on structure 1. 71 wk, set at 0’ or 60’ while r2 and 73
Table 1 gives the bond len@hs and valence angles of each of these structures. Structure I represents the Tabk j
Input gepmetries used for peroqyxetic
acid’calculatio~s
ca-c
-
1.49.,’
c&~-o
‘, .:.. .-. ,r y : 11. I ‘..
1.27 1.23 .‘I:23
,. 1.49
..
.’
c=o
1154
1 Il 1 111 _
III,
_’ -.,
.: ,a) ~&lengths ., .,.ii‘& .“..’ . ,., _I : :.$lg’:::’ ‘.’ : :’ ..: : : ,, ., ‘, ..‘_ .‘.
a)
‘-
y-T-0.
.1.35 1.35 ,.1;35
1.49 1.44. 1.43
‘. Lo/-O
O\
:
-
:112.0” 112.0”
.o
1.02 1.02 1.10
H.
,H
- : 105” ! :... .’ -
::.1120.
;
: 112”
,:
: ., ,.
,‘,.‘,
‘, :.
‘C
;
..
”
109;:y ..
-.: _,‘:.1: I ....,.
1.09 1.09
C’Q
109s~ 109.5”
..
.: :
:
,..
.’ ‘.
C-H
O-H
,0-o
,105;
i2S”. 121.6O 121.6:
125” 126.2” 128.2”
. :
c-o
{ ., -._:,
.’
“_:..
: ” :
,:~.‘,...’ ,I;’ .,,:I’ ,_., ‘: ;‘, .’ : .‘_ .. _ :
I ,, _,
_
Volume 32, number 2
: CHEMICAL PHYSICS LETTERS
1.5 April 1975
Table 2 Gross
rotational
behavior a) of structure I of pcroxyacetic
acid
71 = 0,60” ‘2
73
0”
0.0
60” 120” 180” 24V 300”
2.9 3.7 3.3 3.7
=
o”
72
=
60”
6.0 7.3 7.0 6.5 6.4 5.7
2.9
‘2 = 120’
72 = 180” -.
7.2= 24s
72 = 300”
10.3 10.3
31.2
8.6
1.4 5.3 7.4 12.9
10.4 8.6 7.6 7.6 8.6
5.9 5.9 6.3 6.5 7.0
10.1
7.2
12.9
7.8 7.1 8.6
a) Relative energy in kcal mole-‘. were simultaneously varied between 0” and 300” by increments of 60’. Conformers ufhere rl = 60” were universally calculated to be about 0.5 kcal mole-l less stable than the 7 = 0” conformers. This difference is within the :epioducibility of the results and consequently conformers differing only in rotations about ~1 must be considered energetically equivalent. The enera obtained for each conformer of structure I generated by rotations about 72 and TV; relative to the lowest enera state is given in table 2. The planar form, where 72 = 73 = 0”, was calculated to be the most energetically favorable conformer. Diviations in the planarity oi the peroxycarboxyl group by rotations about ~2 caused the most significant destabilization with a maximum of 30 kcal mole-l for the 72 = 180°, .r3 = o” c_aseas cqmpared with the all planar conformer. The possibility of stable conformations resulting from small deviations in the planarity of the peroxy
values were not large, i.e., less than 5 kcal mole-l _ Thus;using structure I and PCILO, we calculate the all planar conformation of the peroxycarboxyl group
carboxyl
to be the most stzblc. ‘I$is result is in aweement
group
was also tested
3y a set of PCILO
Table 3
llcet$led rotational behavior al of
structure I of
peroxyacctic
TI = 0,60” =
o0
r,=36”
73
r*
270” 288”
3.5 3.3
3.1
4.5
3.3
4.1
306”
2.8
2.6
3.4
324=
1.9
1.7
2.9
342’ 360”
0.5 0.0
0.7 0.9
2.6 3.1
‘2
=
18”
a) Relative energy in kcal mole-‘.
cal-
with
the previous EHTcalculation and easiIyaccommodates the infrved data, but therefore contra&tits the results
culations with structure I. Rotations about r2 from 0’ to 36’ in increments of 18” were nested with rotations about 73 from 270” to 0” in increments-of -18”. These calculations were performed for both the 71 7 0” and 71 = 50” cases, which again proved to be energeti+ly’ equivalent. Tne combination of rotational angles used allowed .puck+g of the peioxycarboxyl ,tig v$ile maintaining the closest possible distance between the
Swem obtained from his dipole moment studies. The two crystal structures, while com%-ming a rz = 0” structure, provide no insight into the placement of the hydrogen atom, due to intermo!ecujar hydrogen bonds not found in the liquid and vapor states. To further study the position,of the peroxide hy-
carboxj4 oxygen and hydrogen atoms involved in the ... .. proposed hydrogen b&d. .The energies pf each conformer relative ‘to the low:
energy arid rotational behavioc about the peroxide bond calculations were performed with the crystal
drogen atom and the effect ofinput geometry on
est energy conformer are giveri in table. 3’:The a$~planar ‘. peroxycarboxyl’group was again,calculated .to be thk most stable. Deviations fro~:&u+ity in 71 and ~2 -, were unif$nly i& stable, although the relative’energy ,” ‘..:: .
:
:-,;
_.
.:
structures
(t1 and III) as well. as the Swem structure
‘. I
‘...
(I).
Both the WILO and STOJG methods were used to, cJculate *e relative energies of five conConners penerated ,by ‘set ting rl = ri = 0” Fd rotating 7-3.from 0” ;
-.,
.’
. . .
.-
311
’
‘-_VohIme.32, number 2 :
-‘.CH&ICAL
PHYSICS Lg+‘ERS
,,’
15 April 1975.
;.
,.-
47-
‘459
.’
.:
930
.
AC-O-O-H
, IBP
1350 OlHiDRAL
: io
0
of 45’.
lS0’. in increments
.mole-l
:
drogen
.
:, The two me thdds agree less well for calculations invbfving structure I. Both methods do give r3 = 0” as the ininimum energy conformer, with‘another relative minimum at.73 = 1809, but the shapes of the calculated barriers tie different. .’ -. ‘Bond densities c&ulated by STO-3G for the hy-‘ ..
I 135’
91p OIHEDRAL
I 180’
,MGLE
Fig. 4. Peroxide rotational barrier in peroxyacetic acid C&Ulated with cr]stXl geometry and OH bond length = 1.10 A. _.
The r&ulfs of these calculations
are shown in figs. ‘,2,3 and 3; Additional points in fig. 2 viere provided by the previous cakulatibs on structure I with PCILQ. -PCI.LO and STO-3G are ii-agreement for both crystal ~&iictuhis (II and III), giving 73 = 0”. as the only minimum and the calculated rotationa! barrier as 3-4 kdall ,’
450 AC-O-o-n,
acid E&U-
:’
_”
ANGLE
‘&. 2. Per&de iotational barrier in perosyncetic ‘@ted with Sw@Fngeometry:
;RILO-
., ‘.
0
”
bond
between
the carbonyl
oxygen
and the
hydrogen in structures I,‘II and III are listed in table 4. Hydrogen,bonding decreased rapidly as the hydrogen
wkrotated
out of the plane, and essentially vanished
in the bans tionfoker.(r3.= 180”). Both methods yield the cry.94 geometry with an C-I-I bond langth of 1.02 w as .the most stable of the three structures. Relative energies are &en in table 5. Dipole moments.of the most stable all planar conformer were calculated by PCILO and STO-3G for each of the three structures as well as l?TDO and IEHT for ~structures I and 11 and ST063lG** for struct& II. ” ‘. Results are given in table 6. 2,4. Riscussim
.’ -,
: ..
The. theoretical treatment of-peroxide conforma..tion is a.no&iously difficult’problem. In his treatmix& of ?he 3mfmrmti& oEsm& 1-110Ie~tirsxvi& &e STO-?G method, Pople concluded that hydrogen per-
4 -WLO
1 3-
!? 2 .3,2_ 3, .L--. 3 ; :_ E:m, &I-. .q,: ‘. ‘1 : _.: :. --*
..
: -STO-3G
.. Table 4. Vqriatiofi of liydrogen bondingwi~ acetic acid a) :, ,,
, ‘,
4
:
.’
:,.
.’
I
: .I
.p ..,-,.. ,’ &m. ..-
do*-,’
’
1eo*
13s.
.r, .’
AiLO-d+y
DIHEDRAL
bNGLE
‘, II
.,
“.
;‘&!,3. Peroxide rotational btier in peroxyacetic atid calcu-, ,ht$ v$h,&ystal &oinetzy Yid‘O-H bond length =l.OZ,A. ‘, . _p :. ‘_ -:. +,:_ :‘:’ : I ,;;_ :.: _.;,: .j: -._. l’,, : .’ _:.. : -. . . ; . :,_ . . .. ,__ .. ..-
0”.,’ ‘. _,
.-
.’
2746 b) -12.6.0
”
‘45”. 1.6.30 2.96
.:
,I ,; conform,a&n in peioxy-. :
;..YO”-....
,139
0.64
‘0.26
0.40
0.03
‘MO” 0.18 .’ .o.oo,
‘0.06. ” ; 0.00 I ., .: ,. ;. .’ ... 3) .iTO.3G;&&s. : ’ :‘, b) B$d density in frktions of el~c+&s~X~~03. : ;;,.. -. ;_-. .:. : .,-,-:; . ._ ,.: _. ..‘, ,‘, 13.70,
‘-%I.,
,.,.
..’
-. 4.06
‘. 0.46 ...; .. ’ ’
:
:
Volume 32,.nu&ber 2
CHEhIICALPtiYSICS LETTERS
1s April 1975 :
-Table5 : Relative en&giesn) of three planar conformers
to be in agreement with the ‘total dipoIe moment by. a vector sum method. The O-H moment thus calcukited must therefore be suspect on the basis of an assumed geometry for hydrogen peroxide which differs considerably_from the currently accepted values. The accuracy of the dipole moment method for
of pcroxyacetic
acid
ST03G,
PCILO a)
I
11
3.2 :3.6
0.0 0.0
..
5.0 2.0
kcal rn~le-~.
ST013G
1:
of structures I, II
PCILO
INDQ
IEHT
STO-631Gf*
1.52
2.17
2.35
3.4
-
1.46
2.06
2.24
2.14
2.16
1.43
2.04
-
-
-
The existence of a minimum at 111.5” for hydrogen ‘peroxide is usually attributed to a gauche effect, ini’olving repulsive interactions of the nonbonding electrons on the peroxide oxygens, and as such is very sensitive to the local geometry of the peroxide group. The peracids exhibit significant differences in this respect. The O-O-H valence angle in hydrogen peroxide has bEen de&i-iTine~ +x7be *So [ 181, whik the pemidc. valence &de in the peroxypelargonic crystal structure : is 112’..Differences in the iotational barriers between these two percxides are therefore not surprising:’ The structural information concerning hydrogen
peroxide also bears directly on the validity of the di; pole moment methods which have be& previou’sly +ed td infer the conformation of the peroxyc++yl group as well as other peroxides [S, 63: Jn these meth: qds, hydrogen peroxide was first assumed @‘have a dihedial z&le’qf 100” and an Q-0-ivalence-angle of
105”. Froni this geometry;hnd the eQeriine&al.dip@le moment,,an O_fi bond rnement was’calculated so &’ ‘.
.-.
‘.
OIL@her
grounds. First, the assumpiioh that bond moments taken from other molecul&s will provide good values for the p&acids does not seem justified. The C-K and C-O bond moments were obtained from studies of di-n-propyl ether, while the C=O moment.was taken from.previous
oxide represented a worst case .[171. The experimental dihedral angle of 111 So could not be reproduced by -STO-3G, but was obtained by using-a more extended basis set. For the less accurate calculations, including the semi-empirical methods, the very small Pans barrier Was replaced by a single minimum at 180’. These methods do, however, reproduce the general shape of .’ the rotational barrier.
.’
the case of peracids could also be questioned
”
Table 6 Dipole moment of the alI planar conformer and III
I
III
work on ketones,
ail of which are mole-
cules of substantially different eIectronic structure. In addition to these assumptions concerning bond moments, the geometry which was used to create the vector model
for the conformational
analysis
also
varied considerably from the crystal struct~ires which we&subsequently reporteci. @though the molecular orbital techniques give better description of tite electronic distribution than bond moments borrowed from other molecules, even these methods often fail to give very accurate dipoIe moment values. STO-3G, for example, underestimates the dipole moment of several oxygen containicg compounds, even though this value is caIcuIated as an exact integral [ 191. These problems are invariably due to the size and nature of the basis set used in ab initio calculations, and to the methods’of calculation of both the dipd!e moment and the chzge distribution in the more approxi!qate &eories [201. In a study
of the dipole
moments
of 34 small mole-
cules with a double zeta gaussian basis set, Snyder four@ the root -mean-square deviation from the experimental momenis to be 0.6 D [21] _When polarization i*n&ons weze added; tic ,ms detiztion drqped In, 0.36 D. Tine author suggests that very accurate dipole moments can only be calculated v.ith near HartreeFock basis’sets and’extensive configuration interaction. In view of thi spread of .dipoie moment values we ob-
taine,d for the same structure us&five molecuIar
different
orbital methods
(table 6) we felt thai.the use of variation in-dipole moment to predict the conformatioh of perbxyacetic acid would be unreliable] !t shoul’d-bk noted, though, that dipole moment values froin IEH? are ,~+~uaJly soAewh,at too’.&&, while INDO
values are very reasonable, despite the approximations
inherent’in this method- &se obsetiations :_ _..‘:. _I,.. _., ,,’ .’ ‘. _:.-. -_. ” _, ‘1. ,__ _’ ..:’ ,, .‘. : .. ,. ,, : ..
together 313
.
,. CHEhlICAL PHY ;F .,:. “_.’ . ., ‘. .. .. .Refer+es~ -’ .‘; _:. ‘._ -. ,I ..” v&i.dut c&ufated dipolk moments suggest that the :. ,. ;_ 1.’ : : .’ ,’ @ planai st$cture is’cqnsistent with the’experimentrrl :_. :.‘. .,’ .,, ;, [ l] -B.S. i&&rent, i.E. PT&I’u&&I, NM. EmanucI annd I.(:.::~~~~~‘rno~~n~ of2.32 0. .. N.G._Yaio&vskii, Dokl.’ Akad. Nauk SSsR 70 (1950? ‘- T’fieresuIts presented% table 4 indicate that $n.if.. 1025. 1’ ‘_‘.~jcnnt~hy&ogenbonding occurs or.ly in ci$‘confokma12) P.A. Giguere and A. ~~~~~~tihofe~-~~~s, Can. I. ‘, tipn. Thkm&tiuti hydrogen bond densities were cal-, : .Chem. !p (1952)821. ‘.. .’ : .‘, cul@ed’to be 1:3%‘tif a nor&i carbon hydrogen, [3] D. Swem, L.D. :Vitn&ei, C.RbEddy and W.E. Pa&r, ,I: Am. Cfrem.So~. 77 (1955) 5537.; -. ..-bo&d, which corresponds roufly to 1-3 kcal:&ole-I. ‘.(.VOlu&. 32, number z
-_ . .
-. The rapid’attenu&on ofthe extent of H-bondingin .’ ‘_+Gfitiotijblanarconformersis clnsiskt witi?the inferdnce p’ ij plariar structure from the’ IR data.
1413-R. Ritlenhduse, Hi.‘Lobuncz.D. $wern and J& Millir, J. Am Chqn. Sac, 80 (1958) 4850.. [5] W. Lobunez, 3-R. Rittenhouse and J.G. Mill&r,J. km. ‘.
Chem.
Sac:
80 (1958).35&i.
[6] M.T. R=.ers and,T.W.Campbell, J. Am:Chem. Sot. 74
.‘:;‘Ik.c&lusion-it isapparknt that the:& planar arr&ig~men~ df the’peioxycarboxyl group, and thus of peioxyadetic’acid, should be reconsidered as the min.- ~i.ryni energy conformer. This conclksion is based ori ,’ the energy resulk. for all three stn.ctures tested, which ga$*t: aU’&nar confoimer as’the most stable. 7’he :‘inf&red data, which show a single hydrogen bonded O-H,stret.qhing band,‘are also mo?e easily accommo..clated by the aI1 planar structure. In additio;, our re_sdts indicate- the possibility,of
‘2.32 D for ,.,
a dipole moment
of
the all planar strticture. (, ;
:
..
:
‘Acknowledgemknt
.
.’
..
,: ..: ,’,I. The authors wkh to thank Dr;.Qeorge’Lie’z&d the
‘IBM-Corpora&n for iheir assistance and the c&nputer ,:.,time [email protected] the STO-631G*‘? c&uIaticns. One : of us, Leon&d M. H;telmeland, gratefully acknowledges support fo; this work froin a’n Upjohn Graduate Fel.‘lowship. We also wish to’ac@owled~e the helpful as-” sistance of Mr. D&&d Berkdwitz and Dr. Peter. Kollman’:
._
‘.
:,
(1952) 4742. [7] W.V.F. ,Brooks and C;M. &as, JZhys. Chem. 71 (1967) 650.. ‘. : [S] T.,Yonei:awa, H. Kaio. a@ 0. Y&namolo, Bull. Chem. .‘Soc. Japan 40 (1967) 307. iP] ?. Belits.$us and G.A, Jeffrey; Act; Cry% 18 (196.5) ‘, 45% (IO] M. Sax, Ii. B&rs+s and s. (Shu,‘Adt;l Cryst. 18 (1965) 252. [ 1l] S. Diner, J.P: k&eu, F. JoId; and M. GilIiert,.‘IheoFei. : chim. Acta 1.5 (1969) 100. ‘. [ 121 W.J. tiehre, R.F, Stewart and J.A. Poplc, 3. Chem. P?IYS.51 (1969) 2657. 1131 R.S. Mulliken, J. Chem. Phys. 23 (195!),Z%33. [14]
P-C. Hariharvl
and3.A.
Ppple.
Theoret.
Chim.
Akt
28
‘.
(1973)213. .. (151 M. 2enie.r and’M. G&e&n,
Theorot. &m. Acta? (1966) 44. [ 161.J.k. PapIe a@ D.L. Reveridge, Approtiate mde~tir’ orbital tkebry (McGraw-Hill, New York, 1970). [l;] hi+. Ncutan, W-A; Lathan, WJ. Hehre and J.A; Pople, J. Chem. Phys; 52 (1970) 4064. [18] @.H: i&t, R.A. Leacock, C.W. Peters and’ K.T. Hecht, ,.’ J. Chem. Phys,42 (1965) 1931: [19] !qJ. Hetie tind3.A. Pople, 3. Am. C&em. Sot. 9i (197Oj (zO]
?gC’i&~k-Pet& and A:‘Pul.iman; The&et. (shim; Acta..
11 (1960159. 1, : .. [21] L;G. Snyder,‘J: Chem. Phys. 6!.(1974)
,.
.:-
‘. I
., __
‘.
747. .’
..
Voitime’32, number 2
CHEMICAL
PHYSICS
.
iEl--l-ERS
.15.4+
1975
: ‘.
:
i%fOLECULARORBlTALSTUDlESCiFTkECONFORMATIONdFPEROXYACETiC Leonard M. HJELMELMD
ACID
and Gild_aH. LoEW
Department of Genetics, Stqnfod Stan-ford, C!ali/ornia 94305, USA
University Medical School,
Received 3 January 1975
A conformatior,d r&hods. The tot&y moment results.
study of peroxyacetic acid has been performed using both STO-3G and PCLO moIecuk orbital planar, cis conformer is obtained by both methods and is consistent with X-ray, infrwed;and dipole :
1. Introduction
conformation of the perpxycarboxyl group in which the consti&ent atoms all lay in a sitigle plane, with the exception of the hydrogen, which wad rotated Detailed investigation of peracid conformation was out of the plane by 72O abuut the peroxide bond. -This begun in 1950, when a dilutiqn study of the,infrared spectrum of peroxypropionic acid incarbon tetra-. conformation is currently accepted as being experi.chloride led to the prbposal of a five m.embered intermentally verified because of the agreement obtained . nally hydrogen bonded,ring as the cpnformatioxi of with the experimental dipole moment. Such a.structur& however, seems inconsistent with the peroxycarboxyl group [I]. Subsiquent infrared the,infrared data,.which -Hould be more easily accomstudies of peroxyacetic acid in both the liquid and vamodafed by a completely planar conformation of the por states revealed similar O-H stretching frequencies. peroxycarboxyl group. A normal coordinate analysis around 3310 cfi:I, characteristic of the hydrogen’ bonded state [2]. Hi&ly purified long &in fatty perof the force constants for an.ti planar conformation of the peroxycarboxyl group shows excellent agreeacids showed essentially nb free hydroxyl absorptions in their.high resolution infrared spectra over a range’ ment with the infrared’spectra ofperoxyacetic and peroxyformic acids 171 -‘Extended. HiickeI theory of concentrations between 3.0X 10-l&olar and 6.0 x io-3 molar in either carbon tetrachloride or molecular orbital calculations qf a_lIplanar conformation an.d the non-planar conformation suggested by hexane, strengthening the conclusion that these mole- .. .the dipole moment studies aIso predicted the p!anar cules exist as monomeric, intramolecularly hydrogen conformation to &slightly more stable [S] . Crystal bonded sp&ies in the liquid and vapor states 131: _ structures of peroxypelargonic acid and o-nitroperoxyTo further kxamine the conformati& of the peroxyl .b&zoic,acid confirm the planar nature of the peroxy&boxy1 group/studies were initiated on,the dipole carboxyl group, with the.exceptibm of the hydrogen moments’of peracids. Vatious long ch+--fatty peracattim which is rotated out of the pIane due to inter.ids were all found, to have a’dipole moment of 2.3i molecul& hidrogen bonds not piesent in the liquid !+ 0.04) debye [4]. Ugini this expe&nent$ value for qFvapor st&ks [9, !O]. Rui, the confo?mation of the dipolk momeni; an assumed geometry for the peroxycarboxyl group, and a set of bond inoi$nt val- ‘. p&acids has not been conclusively determined. ues takefl f:?m stubies of various otjier per&ides [5,‘6]; To further exam& the con.fomaiion of the per.._ a vector Sum method was used lo calculate corifoma-% -’ oxyctirboxyl.group, we iia$urid&-taken an extensive tions ,whidli:wotild reproduce the experimensal rno-..:” - ‘s.et.of CO~~OJ+II+O~C~~UI~G~& ofpecckyacetic ,,m&t. The r&At., of this study &a~ qk proposal of a:‘:. ,. acid.usjng abinitio.and semi-empirical MO techniques.’
f_ .'. :
,.'
.' ',. :
.,
. ...,, !.,. '. _,-.y ., _', ,, .. , .,:.. '_.~', :.
_' ., /. .,
369
Volume 32, number 2
..
CHEMICALPHYSICSLET-f-MS
..
2. Method of calculation and results
,:
1.5April
1975
..
2.1. i&hods. The molecular orbital methods we have chosen for the conformational studies are KILO (perturbative .,donfiguration interaction using localized orbit&) and STO-3G [ 11,121. PCILO is a semi-empirical method -which was explicitly developed for the conformational analysis of large molecules and STO-3G is an ab initio method in which the radial function of each Slatertype orbital (STO) is replaced by a least-squares-fitted combination of three gaussian-type orbitals. A Mulliken population
titialysis was pcrfomed
with
the results
Fig. 1. Torsion anglesvvied in’conformationalstudy of peroxyacetic
acid.
b&d angles and lengths which were used by Swern to correlate his proposed conformation with the dipole moments of long chain fatty peracids. Structures II and III represent the bond lengths and angles taken from the crystal structure of peroxypelargonic acid, and differ only in the O-H bond length. The O-H bond lengh and O-O-H V&XIC~ZU& wore not reported and as a result we obtained the O-O-H angle from the onitroperoxybenzoic acid crystal structure and varied the O-H bond length between the dues of 1.02 A suggested by infrared studies (structure II) and I .I 0 ,$ reTorted in the o-nitroperoxybenzoic acid structure I(structure III). We reasoned that the bond lengths and angles from peroxypelargonic acid were the more.reliable for our &culations since ,both sterically and electronically the aliphatic pel.argonic group (CH3-(CH,),-) better resembles the methy group than does the o-nitrophenyl moiety.
of
each method [13]‘. A refined dipole moment was calculated with the ~ ‘-STO-63iG** bzsis se; [14]. This is a double zeta qual-ity basis set in which polarization functions (d type for C and 0, and p type for H) have,been added..IEHT (iterative extended Hiickel theory) and INDO (incomplete neglect of differential overlap) were addition.ally employed to calculate the dipole moment of selected .structures ElS, 161. All five methods have been sxtensively described in the literature and will not be further discussed here. ‘2.2. Iizputge0,mh-k
2.3. Results “.
‘To study the rotational conformations of peroxyacetic acid (fig. l), we have used three different input geometries in order to include the most reasonable structurei which have been reported in the literature.
To investigate the gross conformation21 behavior of peroxyacetic acid, a set of nested rotations about ail three rotational axes was performed with PCILO on structure 1. 71 wk, set at 0’ or 60’ while r2 and 73
Table 1 gives the bond len@hs and valence angles of each of these structures. Structure I represents the Tabk j
Input gepmetries used for peroqyxetic
acid’calculatio~s
ca-c
-
1.49.,’
c&~-o
‘, .:.. .-. ,r y : 11. I ‘..
1.27 1.23 .‘I:23
,. 1.49
..
.’
c=o
1154
1 Il 1 111 _
III,
_’ -.,
.: ,a) ~&lengths ., .,.ii‘& .“..’ . ,., _I : :.$lg’:::’ ‘.’ : :’ ..: : : ,, ., ‘, ..‘_ .‘.
a)
‘-
y-T-0.
.1.35 1.35 ,.1;35
1.49 1.44. 1.43
‘. Lo/-O
O\
:
-
:112.0” 112.0”
.o
1.02 1.02 1.10
H.
,H
- : 105” ! :... .’ -
::.1120.
;
: 112”
,:
: ., ,.
,‘,.‘,
‘, :.
‘C
;
..
”
109;:y ..
-.: _,‘:.1: I ....,.
1.09 1.09
C’Q
109s~ 109.5”
..
.: :
:
,..
.’ ‘.
C-H
O-H
,0-o
,105;
i2S”. 121.6O 121.6:
125” 126.2” 128.2”
. :
c-o
{ ., -._:,
.’
“_:..
: ” :
,:~.‘,...’ ,I;’ .,,:I’ ,_., ‘: ;‘, .’ : .‘_ .. _ :
I ,, _,
_
Volume 32, number 2
: CHEMICAL PHYSICS LETTERS
1.5 April 1975
Table 2 Gross
rotational
behavior a) of structure I of pcroxyacetic
acid
71 = 0,60” ‘2
73
0”
0.0
60” 120” 180” 24V 300”
2.9 3.7 3.3 3.7
=
o”
72
=
60”
6.0 7.3 7.0 6.5 6.4 5.7
2.9
‘2 = 120’
72 = 180” -.
7.2= 24s
72 = 300”
10.3 10.3
31.2
8.6
1.4 5.3 7.4 12.9
10.4 8.6 7.6 7.6 8.6
5.9 5.9 6.3 6.5 7.0
10.1
7.2
12.9
7.8 7.1 8.6
a) Relative energy in kcal mole-‘. were simultaneously varied between 0” and 300” by increments of 60’. Conformers ufhere rl = 60” were universally calculated to be about 0.5 kcal mole-l less stable than the 7 = 0” conformers. This difference is within the :epioducibility of the results and consequently conformers differing only in rotations about ~1 must be considered energetically equivalent. The enera obtained for each conformer of structure I generated by rotations about 72 and TV; relative to the lowest enera state is given in table 2. The planar form, where 72 = 73 = 0”, was calculated to be the most energetically favorable conformer. Diviations in the planarity oi the peroxycarboxyl group by rotations about ~2 caused the most significant destabilization with a maximum of 30 kcal mole-l for the 72 = 180°, .r3 = o” c_aseas cqmpared with the all planar conformer. The possibility of stable conformations resulting from small deviations in the planarity of the peroxy
values were not large, i.e., less than 5 kcal mole-l _ Thus;using structure I and PCILO, we calculate the all planar conformation of the peroxycarboxyl group
carboxyl
to be the most stzblc. ‘I$is result is in aweement
group
was also tested
3y a set of PCILO
Table 3
llcet$led rotational behavior al of
structure I of
peroxyacctic
TI = 0,60” =
o0
r,=36”
73
r*
270” 288”
3.5 3.3
3.1
4.5
3.3
4.1
306”
2.8
2.6
3.4
324=
1.9
1.7
2.9
342’ 360”
0.5 0.0
0.7 0.9
2.6 3.1
‘2
=
18”
a) Relative energy in kcal mole-‘.
cal-
with
the previous EHTcalculation and easiIyaccommodates the infrved data, but therefore contra&tits the results
culations with structure I. Rotations about r2 from 0’ to 36’ in increments of 18” were nested with rotations about 73 from 270” to 0” in increments-of -18”. These calculations were performed for both the 71 7 0” and 71 = 50” cases, which again proved to be energeti+ly’ equivalent. Tne combination of rotational angles used allowed .puck+g of the peioxycarboxyl ,tig v$ile maintaining the closest possible distance between the
Swem obtained from his dipole moment studies. The two crystal structures, while com%-ming a rz = 0” structure, provide no insight into the placement of the hydrogen atom, due to intermo!ecujar hydrogen bonds not found in the liquid and vapor states. To further study the position,of the peroxide hy-
carboxj4 oxygen and hydrogen atoms involved in the ... .. proposed hydrogen b&d. .The energies pf each conformer relative ‘to the low:
energy arid rotational behavioc about the peroxide bond calculations were performed with the crystal
drogen atom and the effect ofinput geometry on
est energy conformer are giveri in table. 3’:The a$~planar ‘. peroxycarboxyl’group was again,calculated .to be thk most stable. Deviations fro~:&u+ity in 71 and ~2 -, were unif$nly i& stable, although the relative’energy ,” ‘..:: .
:
:-,;
_.
.:
structures
(t1 and III) as well. as the Swem structure
‘. I
‘...
(I).
Both the WILO and STOJG methods were used to, cJculate *e relative energies of five conConners penerated ,by ‘set ting rl = ri = 0” Fd rotating 7-3.from 0” ;
-.,
.’
. . .
.-
311
’
‘-_VohIme.32, number 2 :
-‘.CH&ICAL
PHYSICS Lg+‘ERS
,,’
15 April 1975.
;.
,.-
47-
‘459
.’
.:
930
.
AC-O-O-H
, IBP
1350 OlHiDRAL
: io
0
of 45’.
lS0’. in increments
.mole-l
:
drogen
.
:, The two me thdds agree less well for calculations invbfving structure I. Both methods do give r3 = 0” as the ininimum energy conformer, with‘another relative minimum at.73 = 1809, but the shapes of the calculated barriers tie different. .’ -. ‘Bond densities c&ulated by STO-3G for the hy-‘ ..
I 135’
91p OIHEDRAL
I 180’
,MGLE
Fig. 4. Peroxide rotational barrier in peroxyacetic acid C&Ulated with cr]stXl geometry and OH bond length = 1.10 A. _.
The r&ulfs of these calculations
are shown in figs. ‘,2,3 and 3; Additional points in fig. 2 viere provided by the previous cakulatibs on structure I with PCILQ. -PCI.LO and STO-3G are ii-agreement for both crystal ~&iictuhis (II and III), giving 73 = 0”. as the only minimum and the calculated rotationa! barrier as 3-4 kdall ,’
450 AC-O-o-n,
acid E&U-
:’
_”
ANGLE
‘&. 2. Per&de iotational barrier in perosyncetic ‘@ted with Sw@Fngeometry:
;RILO-
., ‘.
0
”
bond
between
the carbonyl
oxygen
and the
hydrogen in structures I,‘II and III are listed in table 4. Hydrogen,bonding decreased rapidly as the hydrogen
wkrotated
out of the plane, and essentially vanished
in the bans tionfoker.(r3.= 180”). Both methods yield the cry.94 geometry with an C-I-I bond langth of 1.02 w as .the most stable of the three structures. Relative energies are &en in table 5. Dipole moments.of the most stable all planar conformer were calculated by PCILO and STO-3G for each of the three structures as well as l?TDO and IEHT for ~structures I and 11 and ST063lG** for struct& II. ” ‘. Results are given in table 6. 2,4. Riscussim
.’ -,
: ..
The. theoretical treatment of-peroxide conforma..tion is a.no&iously difficult’problem. In his treatmix& of ?he 3mfmrmti& oEsm& 1-110Ie~tirsxvi& &e STO-?G method, Pople concluded that hydrogen per-
4 -WLO
1 3-
!? 2 .3,2_ 3, .L--. 3 ; :_ E:m, &I-. .q,: ‘. ‘1 : _.: :. --*
..
: -STO-3G
.. Table 4. Vqriatiofi of liydrogen bondingwi~ acetic acid a) :, ,,
, ‘,
4
:
.’
:,.
.’
I
: .I
.p ..,-,.. ,’ &m. ..-
do*-,’
’
1eo*
13s.
.r, .’
AiLO-d+y
DIHEDRAL
bNGLE
‘, II
.,
“.
;‘&!,3. Peroxide rotational btier in peroxyacetic atid calcu-, ,ht$ v$h,&ystal &oinetzy Yid‘O-H bond length =l.OZ,A. ‘, . _p :. ‘_ -:. +,:_ :‘:’ : I ,;;_ :.: _.;,: .j: -._. l’,, : .’ _:.. : -. . . ; . :,_ . . .. ,__ .. ..-
0”.,’ ‘. _,
.-
.’
2746 b) -12.6.0
”
‘45”. 1.6.30 2.96
.:
,I ,; conform,a&n in peioxy-. :
;..YO”-....
,139
0.64
‘0.26
0.40
0.03
‘MO” 0.18 .’ .o.oo,
‘0.06. ” ; 0.00 I ., .: ,. ;. .’ ... 3) .iTO.3G;&&s. : ’ :‘, b) B$d density in frktions of el~c+&s~X~~03. : ;;,.. -. ;_-. .:. : .,-,-:; . ._ ,.: _. ..‘, ,‘, 13.70,
‘-%I.,
,.,.
..’
-. 4.06
‘. 0.46 ...; .. ’ ’
:
:
Volume 32,.nu&ber 2
CHEhIICALPtiYSICS LETTERS
1s April 1975 :
-Table5 : Relative en&giesn) of three planar conformers
to be in agreement with the ‘total dipoIe moment by. a vector sum method. The O-H moment thus calcukited must therefore be suspect on the basis of an assumed geometry for hydrogen peroxide which differs considerably_from the currently accepted values. The accuracy of the dipole moment method for
of pcroxyacetic
acid
ST03G,
PCILO a)
I
11
3.2 :3.6
0.0 0.0
..
5.0 2.0
kcal rn~le-~.
ST013G
1:
of structures I, II
PCILO
INDQ
IEHT
STO-631Gf*
1.52
2.17
2.35
3.4
-
1.46
2.06
2.24
2.14
2.16
1.43
2.04
-
-
-
The existence of a minimum at 111.5” for hydrogen ‘peroxide is usually attributed to a gauche effect, ini’olving repulsive interactions of the nonbonding electrons on the peroxide oxygens, and as such is very sensitive to the local geometry of the peroxide group. The peracids exhibit significant differences in this respect. The O-O-H valence angle in hydrogen peroxide has bEen de&i-iTine~ +x7be *So [ 181, whik the pemidc. valence &de in the peroxypelargonic crystal structure : is 112’..Differences in the iotational barriers between these two percxides are therefore not surprising:’ The structural information concerning hydrogen
peroxide also bears directly on the validity of the di; pole moment methods which have be& previou’sly +ed td infer the conformation of the peroxyc++yl group as well as other peroxides [S, 63: Jn these meth: qds, hydrogen peroxide was first assumed @‘have a dihedial z&le’qf 100” and an Q-0-ivalence-angle of
105”. Froni this geometry;hnd the eQeriine&al.dip@le moment,,an O_fi bond rnement was’calculated so &’ ‘.
.-.
‘.
OIL@her
grounds. First, the assumpiioh that bond moments taken from other molecul&s will provide good values for the p&acids does not seem justified. The C-K and C-O bond moments were obtained from studies of di-n-propyl ether, while the C=O moment.was taken from.previous
oxide represented a worst case .[171. The experimental dihedral angle of 111 So could not be reproduced by -STO-3G, but was obtained by using-a more extended basis set. For the less accurate calculations, including the semi-empirical methods, the very small Pans barrier Was replaced by a single minimum at 180’. These methods do, however, reproduce the general shape of .’ the rotational barrier.
.’
the case of peracids could also be questioned
”
Table 6 Dipole moment of the alI planar conformer and III
I
III
work on ketones,
ail of which are mole-
cules of substantially different eIectronic structure. In addition to these assumptions concerning bond moments, the geometry which was used to create the vector model
for the conformational
analysis
also
varied considerably from the crystal struct~ires which we&subsequently reporteci. @though the molecular orbital techniques give better description of tite electronic distribution than bond moments borrowed from other molecules, even these methods often fail to give very accurate dipoIe moment values. STO-3G, for example, underestimates the dipole moment of several oxygen containicg compounds, even though this value is caIcuIated as an exact integral [ 191. These problems are invariably due to the size and nature of the basis set used in ab initio calculations, and to the methods’of calculation of both the dipd!e moment and the chzge distribution in the more approxi!qate &eories [201. In a study
of the dipole
moments
of 34 small mole-
cules with a double zeta gaussian basis set, Snyder four@ the root -mean-square deviation from the experimental momenis to be 0.6 D [21] _When polarization i*n&ons weze added; tic ,ms detiztion drqped In, 0.36 D. Tine author suggests that very accurate dipole moments can only be calculated v.ith near HartreeFock basis’sets and’extensive configuration interaction. In view of thi spread of .dipoie moment values we ob-
taine,d for the same structure us&five molecuIar
different
orbital methods
(table 6) we felt thai.the use of variation in-dipole moment to predict the conformatioh of perbxyacetic acid would be unreliable] !t shoul’d-bk noted, though, that dipole moment values froin IEH? are ,~+~uaJly soAewh,at too’.&&, while INDO
values are very reasonable, despite the approximations
inherent’in this method- &se obsetiations :_ _..‘:. _I,.. _., ,,’ .’ ‘. _:.-. -_. ” _, ‘1. ,__ _’ ..:’ ,, .‘. : .. ,. ,, : ..
together 313
.
,. CHEhlICAL PHY ;F .,:. “_.’ . ., ‘. .. .. .Refer+es~ -’ .‘; _:. ‘._ -. ,I ..” v&i.dut c&ufated dipolk moments suggest that the :. ,. ;_ 1.’ : : .’ ,’ @ planai st$cture is’cqnsistent with the’experimentrrl :_. :.‘. .,’ .,, ;, [ l] -B.S. i&&rent, i.E. PT&I’u&&I, NM. EmanucI annd I.(:.::~~~~~‘rno~~n~ of2.32 0. .. N.G._Yaio&vskii, Dokl.’ Akad. Nauk SSsR 70 (1950? ‘- T’fieresuIts presented% table 4 indicate that $n.if.. 1025. 1’ ‘_‘.~jcnnt~hy&ogenbonding occurs or.ly in ci$‘confokma12) P.A. Giguere and A. ~~~~~~tihofe~-~~~s, Can. I. ‘, tipn. Thkm&tiuti hydrogen bond densities were cal-, : .Chem. !p (1952)821. ‘.. .’ : .‘, cul@ed’to be 1:3%‘tif a nor&i carbon hydrogen, [3] D. Swem, L.D. :Vitn&ei, C.RbEddy and W.E. Pa&r, ,I: Am. Cfrem.So~. 77 (1955) 5537.; -. ..-bo&d, which corresponds roufly to 1-3 kcal:&ole-I. ‘.(.VOlu&. 32, number z
-_ . .
-. The rapid’attenu&on ofthe extent of H-bondingin .’ ‘_+Gfitiotijblanarconformersis clnsiskt witi?the inferdnce p’ ij plariar structure from the’ IR data.
1413-R. Ritlenhduse, Hi.‘Lobuncz.D. $wern and J& Millir, J. Am Chqn. Sac, 80 (1958) 4850.. [5] W. Lobunez, 3-R. Rittenhouse and J.G. Mill&r,J. km. ‘.
Chem.
Sac:
80 (1958).35&i.
[6] M.T. R=.ers and,T.W.Campbell, J. Am:Chem. Sot. 74
.‘:;‘Ik.c&lusion-it isapparknt that the:& planar arr&ig~men~ df the’peioxycarboxyl group, and thus of peioxyadetic’acid, should be reconsidered as the min.- ~i.ryni energy conformer. This conclksion is based ori ,’ the energy resulk. for all three stn.ctures tested, which ga$*t: aU’&nar confoimer as’the most stable. 7’he :‘inf&red data, which show a single hydrogen bonded O-H,stret.qhing band,‘are also mo?e easily accommo..clated by the aI1 planar structure. In additio;, our re_sdts indicate- the possibility,of
‘2.32 D for ,.,
a dipole moment
of
the all planar strticture. (, ;
:
..
:
‘Acknowledgemknt
.
.’
..
,: ..: ,’,I. The authors wkh to thank Dr;.Qeorge’Lie’z&d the
‘IBM-Corpora&n for iheir assistance and the c&nputer ,:.,time [email protected] the STO-631G*‘? c&uIaticns. One : of us, Leon&d M. H;telmeland, gratefully acknowledges support fo; this work froin a’n Upjohn Graduate Fel.‘lowship. We also wish to’ac@owled~e the helpful as-” sistance of Mr. D&&d Berkdwitz and Dr. Peter. Kollman’:
._
‘.
:,
(1952) 4742. [7] W.V.F. ,Brooks and C;M. &as, JZhys. Chem. 71 (1967) 650.. ‘. : [S] T.,Yonei:awa, H. Kaio. a@ 0. Y&namolo, Bull. Chem. .‘Soc. Japan 40 (1967) 307. iP] ?. Belits.$us and G.A, Jeffrey; Act; Cry% 18 (196.5) ‘, 45% (IO] M. Sax, Ii. B&rs+s and s. (Shu,‘Adt;l Cryst. 18 (1965) 252. [ 1l] S. Diner, J.P: k&eu, F. JoId; and M. GilIiert,.‘IheoFei. : chim. Acta 1.5 (1969) 100. ‘. [ 121 W.J. tiehre, R.F, Stewart and J.A. Poplc, 3. Chem. P?IYS.51 (1969) 2657. 1131 R.S. Mulliken, J. Chem. Phys. 23 (195!),Z%33. [14]
P-C. Hariharvl
and3.A.
Ppple.
Theoret.
Chim.
Akt
28
‘.
(1973)213. .. (151 M. 2enie.r and’M. G&e&n,
Theorot. &m. Acta? (1966) 44. [ 161.J.k. PapIe a@ D.L. Reveridge, Approtiate mde~tir’ orbital tkebry (McGraw-Hill, New York, 1970). [l;] hi+. Ncutan, W-A; Lathan, WJ. Hehre and J.A; Pople, J. Chem. Phys; 52 (1970) 4064. [18] @.H: i&t, R.A. Leacock, C.W. Peters and’ K.T. Hecht, ,.’ J. Chem. Phys,42 (1965) 1931: [19] !qJ. Hetie tind3.A. Pople, 3. Am. C&em. Sot. 9i (197Oj (zO]
?gC’i&~k-Pet& and A:‘Pul.iman; The&et. (shim; Acta..
11 (1960159. 1, : .. [21] L;G. Snyder,‘J: Chem. Phys. 6!.(1974)
,.
.:-
‘. I
., __
‘.
747. .’
..