LINEAR
27 July 1984
CHEhlICAL PHYSICS LETTERS
Volume 108, number 6
AND BIFURCATED
HYDRONIUM
ION COMPLEXES
WITH ELECTRON
DONORS:
AN AB INITIO STUDY * Walter H. JONES, Robert D. MARIANI and Michael L. LIVELY De[~arrment of Chemistry, The University of West Floricla. Pensacola. Florida 32511, USA
Hydronium ion complexes with C2H 2. CzHa, N,, 02, CO, HCN and NzH2 were studied with STO-3G and extended basis sets. The stability of single versi~s bifurcated hydrogen bonding decreases as the basis set is estcnded. Geometries of tllc complescs more nearly resemble the reactants rhan the products of proton transfer. Single-well proton transfer encrg curves were found for Nz. C2H2. and Czii4 complexes.
3. Results
1. Introduction In the course of a study of the mechanisms of electrophilic addition reactions, we have conducted an ab initio investigation of the energies and geometries of complexes of H,O+ with C,H,, C,H,, N,, O,, CO, HCN, and N,H,, using STO-3G and extended basis sets. We are prompted to report the results at this time because of their relevance to recent reports of structural effects on bonding in molecular complexes (e.g. ref. [I] ), and of the effect of basis set quality on the relative stabilities of single and bifurcated hydrogen bonded complexes [2] _
2. Methods Calculations were conducted
using the University
of Toronto modification (MONSTERGAUSS) of the GAUSSIAN 76 program [3] _Complete geometry optimizations were accomplished using the optimally conditioned gradient method [4] (the algorithm is described in ref. [5]). Orders of the critical points were determined by diagonalization of the Hessian matrix, computed by gradient differences. Basis sets used were STO-3G [6],3-2lC [7].6-31G [8],and 6-31G’ [9].
* Prcsentcd in part at the 29th (WC) June 9, 1983.
602
IUI’AC Congress,
Cologne
Single Izydrogen
bond complexes:
figs. 1 and 3,. (a) N,, CO, NCH, OH,. A number
Tables 1 and 2, of directions
of
approach of the parent species were analyzed; listed are the most stable complexes found, which were
zeroth order critical points on the energy surface; they show moderate-to-strong linear (@ of table 2) hydrogen bonds in the expected directions (0 of table 2) of the unshared electron pairs. Attachment to the carbon end of CO was preferred (STO-3G level)_ For Na, expansion of the basis set resulted in decreased computed stability of the complex, as is reported for other systems (e.g. refs. [13,34]). (b) C,H, and C,H,. As discussed in ref. [I 01, the n complexes involved approach of the oxygen atom of H30+ perpendicularly to the midpoint of the multiple bond. They were zeroth order critical points, and the hydrogen bonds were nearly linear. Ref. [IO] gave the optimal geometry for (H20HC2H&+; fig. 1b shows the STO-3G structure of (H,OHC,H,)+. We are currently investigating the relevance of these results to the mechanisms of electrophilic addition reactions. (c) 0, _These energy surfaces were more complicated, because two distinct minima were found. Openshell calculations (unrestricted Hartree-Fock) led to a bent geometry at the STO-3G and 3-21G levels (HB-0-Oanglesof 1 17.91°and 122.9?‘respectively), 0 009-2614/84/s (North-Holland
03.00 0 Elsevier Science Publishers Physics Publishina Division)
B.V.
Volume 108, number 6
Fig. 1. structures of 1-1x0+ complcscs: NCH: (b) C,Ilz and Czl14.
CHEMICAL PHYSICS LETTERS
(3) Nz. 02.
27 July 1984
oc. co.
1,. 3. Structures of [H30S,H, 1’ (1) singlr hydrogen bond: (b) bifurclrted Ir~drogen bond. Disrances and anplcs given arc for rhe STO-3C species. I“”
while with (H,-O-O
the 4-3 1 G basis set a nearly angle of 179.37’) structure
linear emerged.
Closed-shell calculations also resulted in two principal geometries: 3-21G and 6-31G gave an angle of 179.57”. and 4-3 IG resulted in 136.S3”. The closed-shell STO3G surface was esplored minimum at 175.17° was search revealed an elusive was the lower of the two
more thoroughly. A local readily located, but further minimum at 115.77O. which by 50 kJ mol-*. These re-
sults are interpretable as involving bonding through the In, orbital of 02,giving the approximately trigonal angle (0) for the most stable species. and the 30~ orbital of O2 for the higher energy (linear) species.
Because complexes
of molecular
oxygen are of wide-
spread interest in inorganic and biolo$cal chemistry_ investigation of H,OOz at a higher level of theory appears desirable_ Bi_tiucated hydrogen bolld complexes: Table 3 and figs. 2 and 3b.
(a) N,, CO, NCH, N2H2, Oz. All of these nlole-
of bifurcated H30c compleues: (3) N2, Oz. (b) CzH4; (c) C2H2 (orthogonal views). Disand an~lcs xc for tile STO-3C species.
I:ig. 2. Structures OC, CO. NCII;
tmccs
cules formed bifurcated complexes exothermically, with the bonding hydrogen atoms being symmetrically disposed with respect to the atom donating the electrons and with hydrogen bond angles of about IO?. Criticality was not demonstrated, but for the struc603
Volume
108, number
Table 1 Single hydrogen
bond
CHEMICAL
6
complexes.
Energiesa).
H,OHi
PHYSICS
+ A -AL-,
[H,0HBA]+-A~2
A.
basis set
EA
Ecomples
NZ.
STO-3G 3-21G 4-31G 3-21G/6-31G’
- 107.500654 -108.300954 - 108.754220 -108.943878
-182.858894
C?_lIz.
C&d),
OC, CO. NCIl. N~l12. 1120.
c,
STO-3C 3-ZIG 4-3lG 3-21C/6-31C*c) STO-3G STO-3G STO-3G STO-3G STO-3G STO-3C 3-ZIG 4-31G 6-31G 3-21G/6-31G*
01, closed-shell: spwks I. STO-3C (linear) 5-21G 4-31G 6-31G 3-21G/6-31G* species I I. STO-3G (bent) 4-31c 02, open shrll: STO-3C species 1, (lincclrj 3-Z 1G ‘a-3lC spwia II, STO-3G (bent) 3-21G 3-21G/6-31G*
-75.85 6248 -76.395958
-77.073956 -111.225450 -111.225450 -91.675210 -108.556953 -74.965901 -75.9O863
b,
c,
-107.726111
PE1+2
-72.99
-184.973558 -185.241946
-49.19 -3159
-152.1791
-222.902402
-224.592378
-74.79 -67.06
-76.136520 \
365.15
221.27
-76.949129
-152.436300b) -186.592864 -186.596192b) -167.07364Vb) -183.961826 - 150.390629
-148.687178 -149.309028 -149.461723 -149.522407
-149.608412
AEl
-62.29
-151.215173bj\ -152.312729 -152.938018 -153.130742
1984
+ HBA+
-184.215909
-147.551572
-147.634171 -148.769085 - 149.392964
Hz0
EHBA+
-83.77 -97.08 -105.81 -178.53 -195.42 -24755
-77.389859
-111.475090
b,
c)
‘)
c)
27 July
LETTERS
-111.505272 -91.997831 -108.920872 -75.330439 -75.89 1228 -76.200604 -76.276336 -76.286036 -147.739155
-225.748262 -225.814263 -222.92 16 15 --115.523761 b)
-225.605590 -223.000328 -224.678961 -225.888003
-147.820494
I-J
a)
-147.891336”)
127.69 301.66 222.42 110.05 1.63 0.0
-183.51
0.0
-53.54
464.59
-26.79 -15.28 -103.98 -37.10
-31.56 -93.78
25 I_04
28 1.90
16.92
b) A rcroth order critir;ll point. ai E in h3rtrcc. AE in kJ/mol. c) Geometry basis sct/cncray basis set. d)Rcf. 1101. ‘)Rcf.[llj. ‘3 Closed-shell. linear. local minimum. 2) Closed-she!l, bond on$c 110.67’. local minimum. Iii Open shell. bond angle 104.53O. local minimum. Van Lcnthc and Ruttink 117J found the lowest stxe of HOT to bc 3 triplet, bond an$ 1 1 1 .O” .
turcs given ail the internal coordinate derivatives were small. (b) C,H2 and C2H,. A structure for the C,H4 bifurcatcd complex is given in ref. [IO] @TO-3G level). The C2Hz complex was investigated also with the 3-2 1G and 4-3 1G basis sets. Whereas the bonding hy-
GO4
drogens
with respect to the CH, they straddle the C-C bond in (1-10H-,C7H,~+. The (HOH-,C,H4)+ species was shown to be-a first order critic>1 point on the STO-3G surface. groups
are “staggered”
in (HOH7C2H4)‘,
Volume
108, number 6
CHEMICAL
PHYSICS
27 July 1984
LETTERS
Table 2 Sinplc hydrogen bond compleses.
Geometries a)_ l+OHB++A
-
[HZOHBAJ+-
H,O
+ HBA+
rbd)
0
0
“G e)
1.0767
177.63 180.00
178.78
0.928
180.00
179.96
180.00
88.76 89.99 90.00
176.73 179.69 180.00
0.947
89.99 175.5 1
177.81 178.89
0.860 0.873
1.1291 1.0457
178.13 177.46
177.88
0.858
179.07
0.772
0.9199
1.0508
131.00
175.38
0.522
h, 0.9894
0.9803
0.9903
125.89i.c)177.68
0512j)
1.2218 1.2375
1.2217 1.2419 1.1952
0.9857 0.9759
1.0287
175.17 179.57
179.13 179.54
0.926
1.1934
179.57
179.54
115.77 126.82
179.34 174.29
179.32
179.68
lj7.91
175.24
122.95
176.08
basis set
rl
r2
r3
STO-3G 3-21G
1.024 I 1.0086
1.55 18 1.6765
2.5758 2.685 1
1.1343 1.0806
1.1338 1.0828
0.9849 0.9744
4-31G
0.9873
1.7565
2.7437
1.0828
1.0847
0.9607
STO-3G 3-21G 4-3lG
1.0386 1.0117 0.9984
1.7029 1.9708 1.9856
2.7405 2.9824 2.9840
1.1807 1.1946
1.1685 1.1875
0.9854 0.9746
1.1845
0.9603
1.2135
C2H4 61, oc.
STO-3G STO-3G
1.0587 1.042 1
1.6404 1.3602
2.6986 2.4023
1.3297 1.1582
1.3061 1.1456
0.985 1 0.9833
1.1508 1.0016
CO, NCH.
STO-3G STO-3G
1.0519 1.0787
1.5527 1.3615
2.6042 2.4402
1.1392 1 ml484
1.1455 1.1530
0.9839 0.9824
l&Hz.
STO-3G
1.1625
1.2507
2-4112
1.2661
1.2668
HzO.
STO-3G
1.1474
1.1551
2.3020
0.9759
2.5058 2.6983
A, N2.
C2H2.
r4")
r4
r5 c)
1.1965
fl
f)
0.900
Oz. closed-shell: specks I. (linear)
STO-3G 3-21G 4-31G
1.0134 0.9897
1.4925 1.7086
6-31G
0.9706
1.8169
2.7874
1.1905
spccics Il. (bent)
STOJG 4.31G
1.0658 0.9846
1.3452 1.738 1
2.4110 2.7195
1.2262 1.1923
0.9740
1.7674
2.7414
1.1945
1.1963
0.9617
02,
0.9607 0.9835 0.9614
1.0416k)
0.793
open shell:
species 1. (linear)
4-31G
species II,
STO-3G
1.046 1
1.3897
2.4337
1.2914
1.2172
0.9828
(bent)
3-21G
1.0030
1.6600
2.6615
1.3027
1.2396
0.9754
3) rs in A; 8,o in degree. Defined in ligs. 1 and 3,. e) UG = [(r6 - rz)/rh] [(ryxO+rt )/rfI3O++ (‘6 --r2):67? fl Bridged ion. locnl minimum.
i, H-0-Hn r, 0-O-H:
a&e.
Open structure more srablc
j) The complex
is a bit zwmmctric.
1.030Sr)
c, Mean of hk’o values.
d) HB-A
OX61
distance in HR_A+_
A-
on STO-3G 3s recorded
surface. elsewhere
P) Ref. [lo]. h, O-H distance. k, 0- 0 -H = 110.68” (e.g. relies of ref. [ 13 1 ).
104.53=‘.
4. Discussion Sfability trends. The results are of interest with reference to the postulate of Buoma and Radon1 and others (ref. [ 1] and literature cited therein) that when two sets of reactants (AB + C) or (A + BC) interact to form a common stable complex (A...B__.C), the complex will generally resemble the set of reactants of lower energy. In table 2 are listed values of (cuG), a parameter defined by Press and Radom which compares the structural similarity of the complex to the reactants and products. This parameter ranges from 0 to 1.O, 1 .O indicating high resemblance to reactants and 0 high resemblance to products. A value of OS corresponds to a symmetrical complex, which in the present case is (H20HOH$.
The 4-3 1G calculations of ref. [ 1 ] concerned substituent effects on the linear cationic proton transfer reactions [X-F--H]++F--X’+[X--F...H...F-X’]++X--F + [H-F-X’]+, in which both X and X’ were varied. All of the present complexes more nearly resemble the reactants than the products. The correlation between oG and the endothermicity of proton transfer (fig_ 4) is not smooth, but is generally as found by Pross and Radom. The latter found a more satisfactory relationship when only one substituent of the complex was varief, as is the case in this study. Our correlation is no better than theirs, but the substituent changes are perhaps greater. Relative energies of single and bifurcated species_
Table 3 shows the calculated
energies and geometries 605
Table
3
Bifurcated
hydrogen
bond
compleses.
and geometries”).
Energies
Ecomptcs N 2.
STO-3G
- 182.842717
-30.54
3-21G
- 184.204695
-32.85
4-31G
-184.9657
3-21G/6-3 C?_Hz.
fiE3
tG* c,
11
HxO++
A +A~9
[HOHzA]’
r,b)
r*b)
t-3
0.9915 0.977 1
2.3066 2.4054
2.7323 2.7725
1.1338 1.0822
0.9907 0.9759
101.62
0.9630
2.4648
2.8268
1.0841
0.9617
102.02
0.9937 0.9803 0.9656
2.4260 2.5752
1.1719
2.5964
2.8649 2.9626 2.98064
1.1925 1.1949
0.9905 0.9759 0.9613
106.07 103.57 103.97
-30.75 -45.12
0.9955 0.9923
2.3967
2.8409
1.3141
2.105 1 2.3524 2.0853
2.5296 2.7961 2.5449
1.1525 1.1407 1.1513
0.9910 0.9908 0.9909 0.9908
106.26 103.61 106.16 105.93
0.9962 0.9958
2.07 17
2.5423
1.2682
0.9914
106.59
1.8379
2.29549
0.9832
0.9975
104.23
-151.198400 -152.304370 - 152.929585
3-2lG/6-31GrC)
-t53.121739
STO-3G STO-3G STO-3G STO-3C
-152.415495c)
-29.14
OC. CO, NCH.
-186568721 -186571506 -167.041454
-33.69 -4 1 .oo -94.00
N2112.
STO-3G
-183.912969
-67.15
H* 0.
STO-3C 4-31G
-150.337663 -152.154300
-108.49 -118.40
STO-3G
-222.891961
2.088
-224.589644 -225.5 18946
-26.12 -29.50
0.9932
3-21G 4-3 1G
0.9787 0.9643
2.2206 2.2995
2.5028 2.5715 2.6463
6-3 1G
-225.747076
-23.67
0.9628
2.3088
2.6548
3-ZIG/G-31GfC)
-225.815075
-36.65
0.9924
2.1273
-29.19
0.9782
3 -._7649
0.9635
2.3479
2.6968
oz.
0,.
closed
d,
ob)
rs
104.72
-185.237364
STO-3G 3-21G 4-31G
czt-14.
r4
0.9927 0.9948
D
sMl:
e,
t .2208
0.9906
102.78
1.2389 1.1924 I.1908
0.9760 0.9619 0.9606
9959 100.20
2.5395
1.269 1
0.9906
102.85
2.6158
1.2810
0.9763
99.82
1.1961
0.9619
100.59
I
100.24
opc:nsi1cll: STO-3G
-222.97857
3-7 1G
-224.671661
4-3tG 3-21G/G-31G*
c,
-225.602238 -225.889452
1
13.12
3) E in txwtrec, a.E in kJ/mot. rs in A, Q in degree. Geometries dclined in figs. 2 and 3h. b) Mean 01. INW valt~cs. c, Gwmerry basis set/cncrg basis x:1. c, A firs1 order d)Rcf. 1101. 0 0 -ii distance in OH2 moiety. 2) From ref. [ 1 I]; parriatty optimized Cp\, species.
critical
poinr.
~20~
,0rr1X)60,o0* 10
NZHZ, 05
09
OS
06
Hz0 o’s
aG Fig. -1. Structures
and stnbititics
of comptcucs.
AE r+z defined
in kabte
t .a~ drfincd
in table 2. STO-3G
level.
I
I
Voltunc
108, number
Table 4 Basis set effects
CHEMICAL
6
on hydrogen
bond
energies.
H;
STO-3C
3-ZIG
I-31G
177.61
173.18
86.19
SO.33
184.26
91.84
91.63
58.91
H30H20+
139.08
H300f. closed sbcll: species I (liner) species II (bent)
114.68 325.77
30.04
238.99
80.3 i
HsOOt. species
3-21G/6-31G*
bJ
13.01
-8.91
51-239
o,pcn shell: 36.82
II (bent) and single bydrogcn
bonds.
Enrr~ies
of the bifurcated species. All were unstable with respect to the single-hydrogen-bond species. at the STO-3G level. Extension of the basis set lessened the difference, however. and as shown in table4, for two of the oxygen species the 3-2 I G/6-3 1G* results showed the bifurcated structure to be the more stable for the oxygen complexes. This trend is in accord with the results reported [2] for bifurcated hydrogen bonds involving two oxygen atom donors. e.g. dimethyl phosphate and formate anions interacting with water. In the present case, however, the results relate to bifurcated bonds to a single atom or. for C7H7 and C3 H,, to a rr complex. The two bonds otthe bifurcatedspecies are significantly bent (4 of table 3). Qualitatively, the relatively great stability of the bifurcated HOHzOi might be espected because of the symmetry of the In:, HOMO of molecular oxygen. PI-O~OJ? trumfercwwss. It was reported in ref. [JO] that the STO-3G proton transfer potential energy curve for
STO-3C
6-31G
65.10
sprcics I (linc3r)
Table 5 Proton tmnsfcr.
1984
Basis set
HaON;
a) R and S refer to bifurcated
27 July
LETTERS
EB -Es ')
comptcs
HsOCa
PHYSICS
-15.90
in kJ/mol.
bJ Geometry
basis set/energy
basis set.
(H,OHC,H,)+ exhibited a single well. This was found true also for (HIOH&)+ and (H20HC7H,)i. Starting - with the optimal specks, the distance?-; was gradually lengthened, and at each distance an energy scan was conducted with the geometries of the HZ0 and substrate moieties held constant and the hydrogen bond constrained to linearity. The distance at which a second well began to appear was recorded, and the complex otherwise completely optimized at that rl and rj_ Table 5 records the results. For these three species, the height of rhe barrier correlates with AE7, the endothermicity of the dissociation reaction, or with Q’G: the complexes closely resemble the reactants, and the closer the resemblance the greater the barrier to proton transfer.
Acknowledgement This study was supported by a grant front Research Corporation and by the University Research Committee of the University of West Florida. One of us (WHJ)
Icvcl af
is indebted
to Dr.
Raynrond
A. Poirier
for
helpful
dis-
cussions_ c2114c)
7.70
3.1
13.5
C2J12
2.74
3.25
217
Nq
3.58
3.2
341
;I) Distances in A. energies in kJ/mol. b) Encrey difference bctwecn confiyration well appears, and optimal species. c, Rcf.110).
at wbicb
double
References [ I] A. Pross and L. Radom. J _Am. Cbcm. Sot. 103 ( 198 1) 6049. 121 G. Aln_rona. C. Gbio and P. Koilmxt. J. Am. Clwn~. Sot. 105 (1983) 5226.
607
Volume
108, number
6
CHEMICAL
131 M.R. Prtcrson and R.A. Poirier. hIONSTERCAUSS. Dcpxtment of Chemistry. University of’ Toronto. Toronto, Ontario h15S 1A 1, Canada. (4 1 WC. Davidon and L. Nazareth, Program DRVOCR, Applied hlathematics Division Tcclmical Memos 303 and 306, Argonne National Laboratory, Argonne. IN 60439 usx. 15 ] \V.C. Davidon, hlath. Pro_pram. 9 (1975) 1. jhj \\‘J. Hchre, R.F. Stcwurt and J.A. Poplc, J. Chcm. Phys. 51 (1969) 2657. 17 1 J S. Ilinkley. J .A. Poplc and W.J. I-lehre, J. Am. Chcm. Sot. 102 (1980) 939. 181 \\‘._I. Ilchrc. R. I~itcbficld and J.A. Popir. J. Chcm. Pbys. 56 (1972) ‘2.57.
GO8
PHYSICS
LETTERS
17 July
1984
19 1 PC. Hariharan and J.A. Poplc, Thcorct. Chim. Art;i 28 (1973) 213. [ 101 W.H. Jones, P.C. hlezcy and I.G. Csizmadh. J. Mol. Strucl. TIII~OCHEX~., to bc published. [ I 11 h1.D. Newton and S. Ehrunson. J. Am. Cbem. Sac. 93 (1971)4971. [ 121 J.li. van Lmtbc and l’.J.A. Rtlttink. Chcm. Phys. Lrttcrs 56 (1978) 20. [ 131 P.A. Kollman. in: Xlodcrn tlieorctical chctnistry. Vol. 4. Applications ofclcctronic structure theory. cd. 11.1:. Scltaefcr III (Plenum Press. New York. 1977) p. 109. 114 I 1’. Schuster. in: Tbc bydropen bond, 1. Tbcory. cds. I’. Schuster. C. Zundel and C. Srrndorfy (North-Holland. Amsterdam. 1976) p. 27.