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Energy surface calculations for the reaction HF + H+ ⇌ HFH+
:_V&me40,
nu&ber i : :
: :-
-.
1 CHEMICAL+YSICS LETTERS
15 May 1976
..
&RGY
S&ACE
&i&LATIONS
FOR THE REACTION HF f H? * HFH+’
H. VON HIRSCHHAUSEN, D.F. KTEN* and E. ZEECK** Stmnski-lnstitut fir ~hysikulisdw I 3eriia ZO, Getmany Received 23
und theoretische Chemie
der Technischen ihiuersit~t,
February i976
Vario~ GTO basis sets were investigated for their effectiveness in determining the SCF ener,v and geometry of the HFHi molecule. A double zeta set augmented with a pz function on each H atom was used to calculate the potentiaI energy surface for the collinear protomtion of HF. Limited configuration interaction calculations gave an energy of -100.27365 E, for an H-F separation of 1.819 00 and ;I bond angle of llB.l”, and an energy of protonation of 119.5 kcallmol. 1. Introduction
but evidence for a bent structure was found, which is in agreement with the rules of Walsh [6]. Theoretical
Hantzsch [l] proposed the fluoronium ion, HzFt, in the non-aqueous hydrofluoric add solvent system as the analog of H,O* in aqueous and NH$ in ammoniacal solutions to explain the appearance of complexes such as H2F’CIO;. Fredenhagtin [Z] held per&loric acid to be the only hydrogen ion donor strong enough to protonate HF directly by the reaction
studies, e.g. by Lischka [7] and Diercksen et al. [8], corroborate this finding and give a bond angle between 110” and 120°..It, also, seems likely that reaction (l), which proceeds so reluctantly in solution, can occur during the scattering of a proton from HF. At first we calculated the energy surface for the collinear protonation. In addition the change of the HF bond length and the angle made with an incoming proton were determined by energy minimization.
H+ + I-IF-+ HFH+. -.
(1)
Clifford et al. [3] later proved the existence of the fluoronium ion and studied its properties and reactivity. A second preparative method is that of allowing strong fluoride ion acceptors, such as BF3 or SbFS , to react directly with_ non-aqueous HF, abstracting Fions, and thus increasing the H’ ion concentration to the point where the equilibrium in reaction (1) is shifted to the right. The equilibria of these and similar reactions were studied by Hyman and Katz [4] using spectroscopic and other means. -Recently Couzi et al. [S] obtained infrared spectra of fluoronium ions prepared by the &secondmethod mentioned. The.exact bond angle was not determined, Resent address: LS III m Chemie der Universitit, 54 Regeqsbtkg; Gerinany. *T: Present addresk Fachbereich 4 der Ukversitit, 29 Oldehburg, Gervny. : 80’.
.--.
..:
-.__
2. Method of calculation In order to select a small but reasonably effective basis set for the calculation of the potential energy surface, the influence of the number and of the orientation of hydrogen p-functions on the energy and the bond angle of the HFIIf system w2s studied using four basis sets as shown in table 1. In the isosceles triangular arrangement (fig. 1) with C2, sy&et_T and the z-axis belonging to species b2, the ground state configuration is la1 2af bs 3aj bj. We introduced abbreviations for the linear combinations of orbitals, e.g. xc- = p,$H1) + pX(H2). Then y+ and z- belong to the symmetry species al, y- and zf to b2, and x+ to bl . The linear combination x- belongs to the unoccupied species a2. We started with a (9s, 5~14s) Huzinaga basis oi’
*ohime40,
-CtiE&AL
number 1
15 i&y 1976
PHYSICS LETTERS
.
Table 1 HFHf georhetries and SCF energies
Wdeg) A
1.803
0.010
120.4
B s
1.813
0.012
121-t t27.4
D 1.848 change by omitting all
0.023
125.8
1.825
Ejfunctions
MO
EdE,j -100.22954
2.98
g*
:100.22478 -100.21634
5.29
-1.6
-100.19475
13.54
0.045
5.4
1.8@4 1.819 1.844
21.82
-100.21320
1p5
0.015
. -100.20497
5.16
7.13
0.025
-1OOA8271
13’g6
7.55
0.040
19.12
on H
3 In kd/mol.
$2
Hl
Fig. 1. Coordinates for HFHf.
~$~~z~exp(--o~~) functions, which was contracted according to Dunning [9] to a double zeta (4,212) set (basis D). We added pX, pY, and pz functions with 0: = 1.0 to each H-atom to obtain a set of 10(q) f 6(b$ + 3(bl) = 19 symmetry functions (basis A). Using the IBMOL version of David [IO) the SCF energy was cafculated for a large number of internuclear separations. The energy mourn E;o = -100.22954 E, with the one-electron energies E = -2G7885, -2.1079, -13076, -1.1588, and -1.1262 was found at RI =R2 = R. = 1.803~~ and 9 = B. = 120-4”. For the linear case with D,, symmetry, the x-axis. is degenerate with fhe y-axis and the configuration is lo~220~2a~2n$. Hydrogen p functions befong to the occupied species a@-), ot(zf), and zr,(_@ , vc). In total the basis consists of 70: f 50: + 3% f 31ryU= 18 symzzetry functions. Optimization of the interatomic diskndes gives Elin= -100.21320 Ea withE = -26.7490,-2.0783, -1.3421 and -1 .I063 (double) for Rh = 1.804 ~0. Compared to the bent equilibrium conf&ur$ion the energy is 10.25 kcalfmol higher at virtualiy the same H-F bond length. Basis B is obtained by omitting the least sisnifcaut polarization function X* from batis A. When, in additioq,y" and y’ are neglected, basis C is obtained; The energies E. and ,I$,, , bond lengths R. and R,, and
bond angles 6 obtained ushig these various basis sets are given in table 1, as well as their changes A from one set to the next. It is to note that using on& the function pair zf and z- 62% of the E. and 50% of the Ro improvement for p functions was obtained. However, the bond angIe was increased because of the preferential choice of one bond direction and the stability of the bent relative to the linear molecule was diminished. Accordingly basis C gave even 73% of the improvement in Ek and 63% of the Rh improvement. A large basis set [7] gave 8, = I 16.0” without 1 I1.8” with consideration of electron correlation in the independent electron pair approximation (IEPA). It is thus seen that basis C is appropriate for calculations on the linear system, but is apparently less accurate than a double zeta set when the bond angle is to be determined. For the HF molecule (axis z) the bond Iengths Ro, energies Eo, and protonation energies Ep (without correction for the nuclear motion)‘calculated fiom’basis function sets corresponding to A, C and D are given in table 2. Table 2 Basis
Ro(roI
A C D
Eo@.,I
Epfkcalfmol)
1.722
-100.03789
120.2
1.744 1.760
-100.03025 -100.01698
116.7 Ill.5
[7] SCF
1.701
-100.0660
122.5
[7] IEPA experiment
1.756 x.733
.--loo.4005 -100.477
120.8 -
.._..
:
._.‘_
__-:
:
,_.
po*entiaiener_~-surface
~.:~iculati~ll~of the linehi riFEI* &ing ha+ C __ -... _.
foh
A
_
4. Configuration interaction Consideration of the electron pai- excitation accordTable 3 SCF energy and
atomic populations for%near HFH+
(&,),
RI = 1.82ao --EtE,)
R2bd
“Hl
nF
“H2
1.00
99.61106
0.411
3.466
1.123
1.50
100.16618
0.446
3.876
0.675
1.75
100.20262
0.460
9.036
0.504
1.82a)
lh.20388
0.464
9.072
0.464
1.90
100.20255
0.469
9.109
0.422
2.00
100.19796
0.474
9.151
0.375
100.15675
0.501
9.288
0.211
.3.00-
~100.11780
0.526
9.350
0.124
4.00
100.07392
0.572
9.387
0.041
5.00
100.05619
0.604
9.385
0.011
6.00
100.&769
0.622
9.376
0.002
100:04276
0.633
9.367
0.000
1do.02soq
-0.668.
9.332
0.00
j2.50
7.00
-,b)
--_.__
HFH+== HF+.H+.
6-m
Data-for a .typica.l cut (Rl fmed} through.the ener- gy surface for the linear HFH* ion are given in table 3. The-complete surface was prepared by combining such cuts_@d is displayed in fig. 2. The surface was calcti-iated point for point in intervals of 0.5 a0 increments of R in-the outer regiorzs and of 0.05 ~~ in the neighborhood of the-equilibrium~position. An ener,y minimum was found for the linear configuration with RI = Ra = 1.825 QO . It iS noteworthy that the surface does not show an energy barrier between the reactants and the products of the system. Population andysis data after Mulliken are given in the columns tiHr, nF, and nHa in table 3. The shift of the eIectron density toward II, and F as HZ is removed is evident, in agreement with the experimental ionization energies and electron affinities of hydrogen and fluorine. The value of n& becomes virtually zero as R2 approaches 7~70,showing that the removal of the proton iS essentially complete;
_:
:
-E
la.u.1
1 = 100.00 100 02 3 = 100.05 L 100.07 2 i
q
‘
..
-
0” -_ Gc
z ‘.
1
I
R, IO,)
* ‘
6
Fig- 2. Potential energy surface for linear HFH+. ing to ref. [l 1 J results in a reduction of the calculated energy of the most stable C2v configuration of 0.04411 E, G 27.7 kcai/moI to -100.27365 E,_ The F-H separation increases by 0.0 16 to 1.8 19 a0 , while the bond angle decreases by 2.3 to 118.1”. The corresponding energy of the HF molecule is -100.08306 E, for an atomic separation of 1.73 no, so that the protonation energy of 119.3 kcaI/mol is obtained. For the Iinear atomic configuration the same optimal F-H bond length of 1.819 a0 and an energy of -100.25590 E,, 11 .l kcal/mol higher than for the bent ion, are obtained. The HF molecule “feels” the approach of a proton to the fluorine atom as far away as the fourfold equilibrium separation, ca. 7.3 a,, as a 6 kcallmol stabilization at an H, FH; angle of 145”. At double the equilibrium R2 = 3.638 a0 the optimized RI is 1.769 a~The energy value of -100.13874 E, is v&u&y independent of the angIe in the range from 137’ to 145’ because the SCF contribution increases with the angle, whereas the CI contribution decreases. For R, < 2.5 a0 the optimal bond angle is identical with that of the equilibrium geometry, within the accuracy of the method. Examples of energies and separations are, with R2 given and RI optimized, shown in table 4. The results of various CI caiculations ‘seem to indi; cate that the SCF approximation gives a-_rasonable
Volume
CHEMiCALP&SlCS
40, number-l-
1
LETTERS-
iS May 1976
.-
Rkferences
Table 4
.
Mao?
RI(Q)
EYEa)
[ 11 A. Hantqch~ Chem. Ser. 60 (1927) Chem. 134 (1928)
-1.797
-100.21672
‘[ZJ H. Fredenhagen.
2.583
1.808
-100.25346
f3]
1.811
-iOO.268+%
---
qualitative description of the energy hypersurface reIative to R2 = *.
Mutowledgement The calcdations were carried out on the CD 6500 of the Rechenzentrum der TU Berlin. We thank the Deutsche Forschungsgemeinschaft for financial support.
1933; 2. Pi&k.
413.
2. Physik. Chem. A 146 (1930) 245. ., H.C. Beacbel and W-M. Jack, J. forg. Nucl. Chem. 5 (1957) 57. 14 J H-H. Hyman and J.J. Katz, in: Non-aqueoussolvent systerns, ed. T-C. Waddington (Academic Press, London, 1965). [S] M. Couti, J.-C. Cornut ad P.V. Huong. J. Chem. Phys. 56 (1972) 426. (61 R,J. Bueoker sod S-D. Peyerimhoff, Chem. Rev. 74 (1974) 127.
2.546 2.001
-.
A.F. Clifford,
(71 H. Lischka. Theoret. Chim. Acta 31 (1973) 39. [S] G.H.F. Diercksen, W- von Niessen and W-P. Kraemer, Theoret. Chisn. Acta 31 (1973) 205. [9f T. Dunning, J. Chen+ Phys. 53 (1970) 2823. [IO] D.-J. D&c!, fBMOL CDC 6600 Version, Patis (1971). 1111 H. von Hirschhausen and FL Wenzel, T&eoret. Chim. Acta 35 (1974) 293.
83
nu&ber i : :
: :-
-.
1 CHEMICAL+YSICS LETTERS
15 May 1976
..
&RGY
S&ACE
&i&LATIONS
FOR THE REACTION HF f H? * HFH+’
H. VON HIRSCHHAUSEN, D.F. KTEN* and E. ZEECK** Stmnski-lnstitut fir ~hysikulisdw I 3eriia ZO, Getmany Received 23
und theoretische Chemie
der Technischen ihiuersit~t,
February i976
Vario~ GTO basis sets were investigated for their effectiveness in determining the SCF ener,v and geometry of the HFHi molecule. A double zeta set augmented with a pz function on each H atom was used to calculate the potentiaI energy surface for the collinear protomtion of HF. Limited configuration interaction calculations gave an energy of -100.27365 E, for an H-F separation of 1.819 00 and ;I bond angle of llB.l”, and an energy of protonation of 119.5 kcallmol. 1. Introduction
but evidence for a bent structure was found, which is in agreement with the rules of Walsh [6]. Theoretical
Hantzsch [l] proposed the fluoronium ion, HzFt, in the non-aqueous hydrofluoric add solvent system as the analog of H,O* in aqueous and NH$ in ammoniacal solutions to explain the appearance of complexes such as H2F’CIO;. Fredenhagtin [Z] held per&loric acid to be the only hydrogen ion donor strong enough to protonate HF directly by the reaction
studies, e.g. by Lischka [7] and Diercksen et al. [8], corroborate this finding and give a bond angle between 110” and 120°..It, also, seems likely that reaction (l), which proceeds so reluctantly in solution, can occur during the scattering of a proton from HF. At first we calculated the energy surface for the collinear protonation. In addition the change of the HF bond length and the angle made with an incoming proton were determined by energy minimization.
H+ + I-IF-+ HFH+. -.
(1)
Clifford et al. [3] later proved the existence of the fluoronium ion and studied its properties and reactivity. A second preparative method is that of allowing strong fluoride ion acceptors, such as BF3 or SbFS , to react directly with_ non-aqueous HF, abstracting Fions, and thus increasing the H’ ion concentration to the point where the equilibrium in reaction (1) is shifted to the right. The equilibria of these and similar reactions were studied by Hyman and Katz [4] using spectroscopic and other means. -Recently Couzi et al. [S] obtained infrared spectra of fluoronium ions prepared by the &secondmethod mentioned. The.exact bond angle was not determined, Resent address: LS III m Chemie der Universitit, 54 Regeqsbtkg; Gerinany. *T: Present addresk Fachbereich 4 der Ukversitit, 29 Oldehburg, Gervny. : 80’.
.--.
..:
-.__
2. Method of calculation In order to select a small but reasonably effective basis set for the calculation of the potential energy surface, the influence of the number and of the orientation of hydrogen p-functions on the energy and the bond angle of the HFIIf system w2s studied using four basis sets as shown in table 1. In the isosceles triangular arrangement (fig. 1) with C2, sy&et_T and the z-axis belonging to species b2, the ground state configuration is la1 2af bs 3aj bj. We introduced abbreviations for the linear combinations of orbitals, e.g. xc- = p,$H1) + pX(H2). Then y+ and z- belong to the symmetry species al, y- and zf to b2, and x+ to bl . The linear combination x- belongs to the unoccupied species a2. We started with a (9s, 5~14s) Huzinaga basis oi’
*ohime40,
-CtiE&AL
number 1
15 i&y 1976
PHYSICS LETTERS
.
Table 1 HFHf georhetries and SCF energies
Wdeg) A
1.803
0.010
120.4
B s
1.813
0.012
121-t t27.4
D 1.848 change by omitting all
0.023
125.8
1.825
Ejfunctions
MO
EdE,j -100.22954
2.98
g*
:100.22478 -100.21634
5.29
-1.6
-100.19475
13.54
0.045
5.4
1.8@4 1.819 1.844
21.82
-100.21320
1p5
0.015
. -100.20497
5.16
7.13
0.025
-1OOA8271
13’g6
7.55
0.040
19.12
on H
3 In kd/mol.
$2
Hl
Fig. 1. Coordinates for HFHf.
~$~~z~exp(--o~~) functions, which was contracted according to Dunning [9] to a double zeta (4,212) set (basis D). We added pX, pY, and pz functions with 0: = 1.0 to each H-atom to obtain a set of 10(q) f 6(b$ + 3(bl) = 19 symmetry functions (basis A). Using the IBMOL version of David [IO) the SCF energy was cafculated for a large number of internuclear separations. The energy mourn E;o = -100.22954 E, with the one-electron energies E = -2G7885, -2.1079, -13076, -1.1588, and -1.1262 was found at RI =R2 = R. = 1.803~~ and 9 = B. = 120-4”. For the linear case with D,, symmetry, the x-axis. is degenerate with fhe y-axis and the configuration is lo~220~2a~2n$. Hydrogen p functions befong to the occupied species a@-), ot(zf), and zr,(_@ , vc). In total the basis consists of 70: f 50: + 3% f 31ryU= 18 symzzetry functions. Optimization of the interatomic diskndes gives Elin= -100.21320 Ea withE = -26.7490,-2.0783, -1.3421 and -1 .I063 (double) for Rh = 1.804 ~0. Compared to the bent equilibrium conf&ur$ion the energy is 10.25 kcalfmol higher at virtualiy the same H-F bond length. Basis B is obtained by omitting the least sisnifcaut polarization function X* from batis A. When, in additioq,y" and y’ are neglected, basis C is obtained; The energies E. and ,I$,, , bond lengths R. and R,, and
bond angles 6 obtained ushig these various basis sets are given in table 1, as well as their changes A from one set to the next. It is to note that using on& the function pair zf and z- 62% of the E. and 50% of the Ro improvement for p functions was obtained. However, the bond angIe was increased because of the preferential choice of one bond direction and the stability of the bent relative to the linear molecule was diminished. Accordingly basis C gave even 73% of the improvement in Ek and 63% of the Rh improvement. A large basis set [7] gave 8, = I 16.0” without 1 I1.8” with consideration of electron correlation in the independent electron pair approximation (IEPA). It is thus seen that basis C is appropriate for calculations on the linear system, but is apparently less accurate than a double zeta set when the bond angle is to be determined. For the HF molecule (axis z) the bond Iengths Ro, energies Eo, and protonation energies Ep (without correction for the nuclear motion)‘calculated fiom’basis function sets corresponding to A, C and D are given in table 2. Table 2 Basis
Ro(roI
A C D
Eo@.,I
Epfkcalfmol)
1.722
-100.03789
120.2
1.744 1.760
-100.03025 -100.01698
116.7 Ill.5
[7] SCF
1.701
-100.0660
122.5
[7] IEPA experiment
1.756 x.733
.--loo.4005 -100.477
120.8 -
.._..
:
._.‘_
__-:
:
,_.
po*entiaiener_~-surface
~.:~iculati~ll~of the linehi riFEI* &ing ha+ C __ -... _.
foh
A
_
4. Configuration interaction Consideration of the electron pai- excitation accordTable 3 SCF energy and
atomic populations for%near HFH+
(&,),
RI = 1.82ao --EtE,)
R2bd
“Hl
nF
“H2
1.00
99.61106
0.411
3.466
1.123
1.50
100.16618
0.446
3.876
0.675
1.75
100.20262
0.460
9.036
0.504
1.82a)
lh.20388
0.464
9.072
0.464
1.90
100.20255
0.469
9.109
0.422
2.00
100.19796
0.474
9.151
0.375
100.15675
0.501
9.288
0.211
.3.00-
~100.11780
0.526
9.350
0.124
4.00
100.07392
0.572
9.387
0.041
5.00
100.05619
0.604
9.385
0.011
6.00
100.&769
0.622
9.376
0.002
100:04276
0.633
9.367
0.000
1do.02soq
-0.668.
9.332
0.00
j2.50
7.00
-,b)
--_.__
HFH+== HF+.H+.
6-m
Data-for a .typica.l cut (Rl fmed} through.the ener- gy surface for the linear HFH* ion are given in table 3. The-complete surface was prepared by combining such cuts_@d is displayed in fig. 2. The surface was calcti-iated point for point in intervals of 0.5 a0 increments of R in-the outer regiorzs and of 0.05 ~~ in the neighborhood of the-equilibrium~position. An ener,y minimum was found for the linear configuration with RI = Ra = 1.825 QO . It iS noteworthy that the surface does not show an energy barrier between the reactants and the products of the system. Population andysis data after Mulliken are given in the columns tiHr, nF, and nHa in table 3. The shift of the eIectron density toward II, and F as HZ is removed is evident, in agreement with the experimental ionization energies and electron affinities of hydrogen and fluorine. The value of n& becomes virtually zero as R2 approaches 7~70,showing that the removal of the proton iS essentially complete;
_:
:
-E
la.u.1
1 = 100.00 100 02 3 = 100.05 L 100.07 2 i
q
‘
..
-
0” -_ Gc
z ‘.
1
I
R, IO,)
* ‘
6
Fig- 2. Potential energy surface for linear HFH+. ing to ref. [l 1 J results in a reduction of the calculated energy of the most stable C2v configuration of 0.04411 E, G 27.7 kcai/moI to -100.27365 E,_ The F-H separation increases by 0.0 16 to 1.8 19 a0 , while the bond angle decreases by 2.3 to 118.1”. The corresponding energy of the HF molecule is -100.08306 E, for an atomic separation of 1.73 no, so that the protonation energy of 119.3 kcaI/mol is obtained. For the Iinear atomic configuration the same optimal F-H bond length of 1.819 a0 and an energy of -100.25590 E,, 11 .l kcal/mol higher than for the bent ion, are obtained. The HF molecule “feels” the approach of a proton to the fluorine atom as far away as the fourfold equilibrium separation, ca. 7.3 a,, as a 6 kcallmol stabilization at an H, FH; angle of 145”. At double the equilibrium R2 = 3.638 a0 the optimized RI is 1.769 a~The energy value of -100.13874 E, is v&u&y independent of the angIe in the range from 137’ to 145’ because the SCF contribution increases with the angle, whereas the CI contribution decreases. For R, < 2.5 a0 the optimal bond angle is identical with that of the equilibrium geometry, within the accuracy of the method. Examples of energies and separations are, with R2 given and RI optimized, shown in table 4. The results of various CI caiculations ‘seem to indi; cate that the SCF approximation gives a-_rasonable
Volume
CHEMiCALP&SlCS
40, number-l-
1
LETTERS-
iS May 1976
.-
Rkferences
Table 4
.
Mao?
RI(Q)
EYEa)
[ 11 A. Hantqch~ Chem. Ser. 60 (1927) Chem. 134 (1928)
-1.797
-100.21672
‘[ZJ H. Fredenhagen.
2.583
1.808
-100.25346
f3]
1.811
-iOO.268+%
---
qualitative description of the energy hypersurface reIative to R2 = *.
Mutowledgement The calcdations were carried out on the CD 6500 of the Rechenzentrum der TU Berlin. We thank the Deutsche Forschungsgemeinschaft for financial support.
1933; 2. Pi&k.
413.
2. Physik. Chem. A 146 (1930) 245. ., H.C. Beacbel and W-M. Jack, J. forg. Nucl. Chem. 5 (1957) 57. 14 J H-H. Hyman and J.J. Katz, in: Non-aqueoussolvent systerns, ed. T-C. Waddington (Academic Press, London, 1965). [S] M. Couti, J.-C. Cornut ad P.V. Huong. J. Chem. Phys. 56 (1972) 426. (61 R,J. Bueoker sod S-D. Peyerimhoff, Chem. Rev. 74 (1974) 127.
2.546 2.001
-.
A.F. Clifford,
(71 H. Lischka. Theoret. Chim. Acta 31 (1973) 39. [S] G.H.F. Diercksen, W- von Niessen and W-P. Kraemer, Theoret. Chisn. Acta 31 (1973) 205. [9f T. Dunning, J. Chen+ Phys. 53 (1970) 2823. [IO] D.-J. D&c!, fBMOL CDC 6600 Version, Patis (1971). 1111 H. von Hirschhausen and FL Wenzel, T&eoret. Chim. Acta 35 (1974) 293.
83