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Hydrogen bonding in linear (LiH)2
Voluti~e
37,
number
i
CHEMICAL~PHYSICS
I Januwy
LETTERS
1976
,’
HYDROGEN
BONDING
RYCHLEWSKI* Quor~tu~~ Tlreor~. Project,
jacek
Received 3G September
IN LINEAR
(LiH),
and John k. SAPIN Deportment
of Plrysics, Wnir,ersit_v of Florida, Gaitzesvillr, fiYon.da,
USA
1975
Ab initio LCAO MO SCF calculations are reported on the linear form of LiH dimer. The prcperties Li-H-Li linkage xe discussed in the light of hydrogen bonding.
of the
2. Calculations
I_ Introduction In the past few years, -here has been a number of books [ 14] and review [5-71 .papers published which --deal with hydrogen bonding. Each author discusses the ineArg of the term hydrogen bond, and requires that en adduct meet certain criteria before it should be called a hydrogen bon&d system. All definitions include.all cases which are conventionally considered to be hydrogen bonded, and disagreement concerns only less straightforward cases. All definitions of hydrogen bonding se&l to h&;! two common points; they require a divalent bridging hydrogen atom in an association which we shall designate A-H---B, and they invoke an ener,oy criterion, generally that the addcct is more stable than the separated.species by at least some specified amount. Frequently other properties \t.hich are generally observed on hydrogen bond formation are included in the definition, such as the reiatively high electronegativities of A and R with respect to H, the Lewis base character of B, the decrease of the A-H stretching frequency and attendant intensity increase, fcrmation of a short A-B bond with respect to van der Wasls radii, an NMR downfield shift for the proton, loss of electron density on the bridging proton, proton,doncr and acceptor MO level shifts (61, and others. Here, we. wish to consider a system, linear LiH dimer; which meets the two comman critena of hydrogen bonding, but not many of tile &hers, and d&us-s the bonding of this adduct in light of its properties. 5 Permanent address; Department : University of Paznsri, Poland.
and structure
Calculations were carried out using the gaussian basis IBMOLS [8] program. The basis set used r’or hydrogen was an uncontracted (Ss, lp) set*’ while that used for lithium was an uncontracted (I&, 2p)p set. As only linear configurations were considered only polarization p, functions were used. Calculations were initially carried out on LiH monomer, and the minimum energy was found to be -7.982954 hartree at 3.090 bohr. This compares well with previous accurate results [11] which report *t f
The hydrogen
s
Table 1 Computed
properties
-_~---_
ref.
[9],
with
of Lill at the minimum
‘TOT 610
e20 p k
St
Chemistry,
-
pI orbital
ener,qy geometry
Experiment
?eq
an added
with added pz orbit&
Cdcul3led
-._-
1.595 A
1.635 X -7.982954
hartree hsrtree
-
-G.2984 hxtree 6.1394 D
-.
-2.4566
5.882 D
1.047 mdyn/4
hlulliken populations: of Theoretical
set from
with exponent 0.75. The lithium s set from ref. [lo], with exponents 0.157 and 0.02.
Li H
1.026 mdyn/.i 2.4149 1.5151
OVLP 0.3 108 -
-
Volume’37, number 1
CHEhiIC.Ai. Pk’SICS
I January
LETTERS
1976
I
L
.;m__i___fJ
c-
d
c
Fig. 1. Coordinate system
and
atonlic numbering
-7.98262 hnrtree at 3.086 bohr, and with the HartreeFock limit of -7.9867 hartree Ci2]. Ths computed properties of LiH at its minimum enerh~ configuration are presented in table 1. From the table, it appears that.the calculation describes the system well enough for the present purposes. Calculations were then carried out on the linear dimer (fig. 1). where the Li, --Liz disknce (R), the Table 2 Computed
properties
of linai
(LiH)2 ;it the minimum
geometry -----~-_
--.-
R
3.440
A
‘1
L.627
A
&O-I P %ta)
‘3Q E
-D.2508 ----
Table 3 ?.fuUiken population
.~
antiysis
~_
-16.00591 i hartree was obtained for R = 6.500 bohr, r1 = 3.075 bohr, and rz = :_,I 76 bohr, in good agreement with previous resolts?T. The energy difference between the dimer and two monomers gives a dimerization energy of 25.11 kcai/mole, making this a strongly bound system with respect to most hydrogen bonded systems (cf. ref., [I J , appendix B). Tl?e calculated properties of the linear dimer are presented in tabIe:Z, and the results of a Muiliken population analysis are presented in tab!e 3.
.,
----
a) For the bridging proton
(rI), and Li,-H, distance (r2) were varied. The minimum energy of
The L.--H-Li bond formed should certainly be considered as a hydrogen bonded system from energy and divalent hydro;en criteria, even though Li(‘x = 1.O) [ 13) has a considerably smaller eiectronegativity than does H(x = 2.1) [13] . This is not the only example of the violation of the rule that onlji atoms more electro-
-2.5179 -2.3644 -0.3912
610 620
Lit -H, distance all independently
3. Results and discussion
1.681 X -16.005911 tlartrce 13.9376 D 0.5161 mdyn/A
r2
_.~
energy
used far (LiHJ2.
scheme
7
H.
for linear (UH)2 zt the minimum energ
The lrue minimum energ configuration of the systzm is in fxt not linear but squzrre [ 111, which WE also find..
,oeornetry
~ Liz
.Hg
Lit
Hz -
-_
atomic
1.5901.
2.5352
1.5576
2.3171
population overlap population
_---
_,_-.-_L.
,. _’
.,
0.2155
__-_-___
0.0044
me----
0.2899
.:
181
Voiumu
37, nom&r
1
..
CI%hfICAt
PHYSICS
negative than hydrogen participate in hydrogen bonds, however. as ihe bomnes and bridged metal hydrids attest. !n f2ct, many OF the properties of the linkage 2re very reminiscent of other strong hydrogen bonds. Development of the protonic potential for H, shows an asymmetric single ivell, with a minimum at i .627 8, from Li, and 1.813 ,% from Li,. This contrasts with the symmetric LizHi system with equal LiH distances of 1.629 a [ 141 , just a bit shorter than in LiH itself. The charge migration on dimer Formation is evident from.perusal of the Mulliken pop&fions. For the sake of comparison we consider the dimer where I~ = r? = 3.09 bohr, the monomer minimum energy distance, aad R 7 6.500 bohr. Ln @is case we find the population changes on going from two monomers to the dimer to be -0.159, +0.016, fl.076, a.066 e- for Lil, H, , Liz, and Hz respectively. These shifts, as well as the decreased Li, --HI and increased H, -Liz overlap pop-
i January
LETTERS
1976
ul2tions are shown in the density difference map presented in fig. 2. The increase of electron density on the bridging proton is contrary to the normal expectation or’loss of density at the proton on hydrogen bond formation. It is further found that the bridging proton is net negative in this case (since )CLi
Acknowledgement J.R. is grateful for support provided by the UF Office of Academic Affairs during his visit. CoInputer support from the UF College of Arts and Sciences is grate. fully acknowledged.
References [ 11 G.C. Pimentel and A.L. McC’le.Uan, The hydrogen bond (Freeman, San Francisco, 1960). [2] WC. Hamilton and J.A. Ibers, Hydrogen bonding in solids (Benjamin, New York, 1966). [ 31 S.N. VinoFadov and R.H. LinneU, Hydrogen bonding (Van Nostrand, Princeton, 1971). [4] 5i.D . kesten 2nd L.J. Schmd, Hydroper. bonding (Dekker, New York, ,Fig. 2. Dimer n&us for Li-H--iLi-H
mdnomer electron at R = 6.500 bohr;
density difference map r, = rz = 3.09 bohr.
[S j S. B&to&
1974).
Advan: Quantum
161 P.A. Kollmar:
and L.C. Allen.
Chem. 3 (1967) Chem.
209. Rev. 72 (1972)
282.
Volume 37. number
I
CHEMICAL PHYSICS LETTERS
I71 KA . Ratner and J.R. &bin, in: Wave mechanics, the fust fifty yzars,‘eds. W.C. Price et al. (Butteworths, London, 1973). IBI E. Clementi and J. hiehl, IBM Resexch Publiution RJE89 (1971). 191 A. Rauk, L.C. Allen and E. Clementi, J. Chem. Phys. 52 (1970! 4133. [JOI L.R. K&n, J. Hay and I. Shavitt, J. Chcm. Phys. 61 (1974) 3530. [Ill P. Kollman, C.F. Bender 2nd 6. Rothenberg, J. Am. Chem. sot. 94 (1972) 8016.
1 January
1976
[12] P.E. Cade and WM. Huo. J. Chem. Phys. 47 (1967) 614; K.K. Docken and J. Hinze. i. Chem. Phys. 57 (1972) 4928. [13] L. Fzuliny, The nature of the chemical bond, 3rd Ed. (Cornell Univ. Press, Ithaca, 1960) p. 93. [14] N.K. Ray, J; Chem. Phys. 52 (1970) 463; G. Diercksen nnd H. Preuss, Intern. I. Quantum Chem. 1 (1967) 637; A. Wu and F.O. EUison, 5. Chem. Phys. 47 (1967) 1455. (151 J.R. Sabin.J. Am. Chem. Sot. 93 (1971) 3613.
37,
number
i
CHEMICAL~PHYSICS
I Januwy
LETTERS
1976
,’
HYDROGEN
BONDING
RYCHLEWSKI* Quor~tu~~ Tlreor~. Project,
jacek
Received 3G September
IN LINEAR
(LiH),
and John k. SAPIN Deportment
of Plrysics, Wnir,ersit_v of Florida, Gaitzesvillr, fiYon.da,
USA
1975
Ab initio LCAO MO SCF calculations are reported on the linear form of LiH dimer. The prcperties Li-H-Li linkage xe discussed in the light of hydrogen bonding.
of the
2. Calculations
I_ Introduction In the past few years, -here has been a number of books [ 14] and review [5-71 .papers published which --deal with hydrogen bonding. Each author discusses the ineArg of the term hydrogen bond, and requires that en adduct meet certain criteria before it should be called a hydrogen bon&d system. All definitions include.all cases which are conventionally considered to be hydrogen bonded, and disagreement concerns only less straightforward cases. All definitions of hydrogen bonding se&l to h&;! two common points; they require a divalent bridging hydrogen atom in an association which we shall designate A-H---B, and they invoke an ener,oy criterion, generally that the addcct is more stable than the separated.species by at least some specified amount. Frequently other properties \t.hich are generally observed on hydrogen bond formation are included in the definition, such as the reiatively high electronegativities of A and R with respect to H, the Lewis base character of B, the decrease of the A-H stretching frequency and attendant intensity increase, fcrmation of a short A-B bond with respect to van der Wasls radii, an NMR downfield shift for the proton, loss of electron density on the bridging proton, proton,doncr and acceptor MO level shifts (61, and others. Here, we. wish to consider a system, linear LiH dimer; which meets the two comman critena of hydrogen bonding, but not many of tile &hers, and d&us-s the bonding of this adduct in light of its properties. 5 Permanent address; Department : University of Paznsri, Poland.
and structure
Calculations were carried out using the gaussian basis IBMOLS [8] program. The basis set used r’or hydrogen was an uncontracted (Ss, lp) set*’ while that used for lithium was an uncontracted (I&, 2p)p set. As only linear configurations were considered only polarization p, functions were used. Calculations were initially carried out on LiH monomer, and the minimum energy was found to be -7.982954 hartree at 3.090 bohr. This compares well with previous accurate results [11] which report *t f
The hydrogen
s
Table 1 Computed
properties
-_~---_
ref.
[9],
with
of Lill at the minimum
‘TOT 610
e20 p k
St
Chemistry,
-
pI orbital
ener,qy geometry
Experiment
?eq
an added
with added pz orbit&
Cdcul3led
-._-
1.595 A
1.635 X -7.982954
hartree hsrtree
-
-G.2984 hxtree 6.1394 D
-.
-2.4566
5.882 D
1.047 mdyn/4
hlulliken populations: of Theoretical
set from
with exponent 0.75. The lithium s set from ref. [lo], with exponents 0.157 and 0.02.
Li H
1.026 mdyn/.i 2.4149 1.5151
OVLP 0.3 108 -
-
Volume’37, number 1
CHEhiIC.Ai. Pk’SICS
I January
LETTERS
1976
I
L
.;m__i___fJ
c-
d
c
Fig. 1. Coordinate system
and
atonlic numbering
-7.98262 hnrtree at 3.086 bohr, and with the HartreeFock limit of -7.9867 hartree Ci2]. Ths computed properties of LiH at its minimum enerh~ configuration are presented in table 1. From the table, it appears that.the calculation describes the system well enough for the present purposes. Calculations were then carried out on the linear dimer (fig. 1). where the Li, --Liz disknce (R), the Table 2 Computed
properties
of linai
(LiH)2 ;it the minimum
geometry -----~-_
--.-
R
3.440
A
‘1
L.627
A
&O-I P %ta)
‘3Q E
-D.2508 ----
Table 3 ?.fuUiken population
.~
antiysis
~_
-16.00591 i hartree was obtained for R = 6.500 bohr, r1 = 3.075 bohr, and rz = :_,I 76 bohr, in good agreement with previous resolts?T. The energy difference between the dimer and two monomers gives a dimerization energy of 25.11 kcai/mole, making this a strongly bound system with respect to most hydrogen bonded systems (cf. ref., [I J , appendix B). Tl?e calculated properties of the linear dimer are presented in tabIe:Z, and the results of a Muiliken population analysis are presented in tab!e 3.
.,
----
a) For the bridging proton
(rI), and Li,-H, distance (r2) were varied. The minimum energy of
The L.--H-Li bond formed should certainly be considered as a hydrogen bonded system from energy and divalent hydro;en criteria, even though Li(‘x = 1.O) [ 13) has a considerably smaller eiectronegativity than does H(x = 2.1) [13] . This is not the only example of the violation of the rule that onlji atoms more electro-
-2.5179 -2.3644 -0.3912
610 620
Lit -H, distance all independently
3. Results and discussion
1.681 X -16.005911 tlartrce 13.9376 D 0.5161 mdyn/A
r2
_.~
energy
used far (LiHJ2.
scheme
7
H.
for linear (UH)2 zt the minimum energ
The lrue minimum energ configuration of the systzm is in fxt not linear but squzrre [ 111, which WE also find..
,oeornetry
~ Liz
.Hg
Lit
Hz -
-_
atomic
1.5901.
2.5352
1.5576
2.3171
population overlap population
_---
_,_-.-_L.
,. _’
.,
0.2155
__-_-___
0.0044
me----
0.2899
.:
181
Voiumu
37, nom&r
1
..
CI%hfICAt
PHYSICS
negative than hydrogen participate in hydrogen bonds, however. as ihe bomnes and bridged metal hydrids attest. !n f2ct, many OF the properties of the linkage 2re very reminiscent of other strong hydrogen bonds. Development of the protonic potential for H, shows an asymmetric single ivell, with a minimum at i .627 8, from Li, and 1.813 ,% from Li,. This contrasts with the symmetric LizHi system with equal LiH distances of 1.629 a [ 141 , just a bit shorter than in LiH itself. The charge migration on dimer Formation is evident from.perusal of the Mulliken pop&fions. For the sake of comparison we consider the dimer where I~ = r? = 3.09 bohr, the monomer minimum energy distance, aad R 7 6.500 bohr. Ln @is case we find the population changes on going from two monomers to the dimer to be -0.159, +0.016, fl.076, a.066 e- for Lil, H, , Liz, and Hz respectively. These shifts, as well as the decreased Li, --HI and increased H, -Liz overlap pop-
i January
LETTERS
1976
ul2tions are shown in the density difference map presented in fig. 2. The increase of electron density on the bridging proton is contrary to the normal expectation or’loss of density at the proton on hydrogen bond formation. It is further found that the bridging proton is net negative in this case (since )CLi
Acknowledgement J.R. is grateful for support provided by the UF Office of Academic Affairs during his visit. CoInputer support from the UF College of Arts and Sciences is grate. fully acknowledged.
References [ 11 G.C. Pimentel and A.L. McC’le.Uan, The hydrogen bond (Freeman, San Francisco, 1960). [2] WC. Hamilton and J.A. Ibers, Hydrogen bonding in solids (Benjamin, New York, 1966). [ 31 S.N. VinoFadov and R.H. LinneU, Hydrogen bonding (Van Nostrand, Princeton, 1971). [4] 5i.D . kesten 2nd L.J. Schmd, Hydroper. bonding (Dekker, New York, ,Fig. 2. Dimer n&us for Li-H--iLi-H
mdnomer electron at R = 6.500 bohr;
density difference map r, = rz = 3.09 bohr.
[S j S. B&to&
1974).
Advan: Quantum
161 P.A. Kollmar:
and L.C. Allen.
Chem. 3 (1967) Chem.
209. Rev. 72 (1972)
282.
Volume 37. number
I
CHEMICAL PHYSICS LETTERS
I71 KA . Ratner and J.R. &bin, in: Wave mechanics, the fust fifty yzars,‘eds. W.C. Price et al. (Butteworths, London, 1973). IBI E. Clementi and J. hiehl, IBM Resexch Publiution RJE89 (1971). 191 A. Rauk, L.C. Allen and E. Clementi, J. Chem. Phys. 52 (1970! 4133. [JOI L.R. K&n, J. Hay and I. Shavitt, J. Chcm. Phys. 61 (1974) 3530. [Ill P. Kollman, C.F. Bender 2nd 6. Rothenberg, J. Am. Chem. sot. 94 (1972) 8016.
1 January
1976
[12] P.E. Cade and WM. Huo. J. Chem. Phys. 47 (1967) 614; K.K. Docken and J. Hinze. i. Chem. Phys. 57 (1972) 4928. [13] L. Fzuliny, The nature of the chemical bond, 3rd Ed. (Cornell Univ. Press, Ithaca, 1960) p. 93. [14] N.K. Ray, J; Chem. Phys. 52 (1970) 463; G. Diercksen nnd H. Preuss, Intern. I. Quantum Chem. 1 (1967) 637; A. Wu and F.O. EUison, 5. Chem. Phys. 47 (1967) 1455. (151 J.R. Sabin.J. Am. Chem. Sot. 93 (1971) 3613.