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Quantum chemical study of the adsorption of an H2O molecule on an uncharged mercury surface
Journal
of Electroanalytzcal
Chemzstry, 369 (1994) 227-231
227
Quantum chemical study of the adsorption of an H,O molecule on an uncharged mercury surface l, M. Probst **, and K Hemzinger
Renat R Nazmutdmov Max-Planck-Instztut (Received
fur Chemze (Otto-Hahn-Instztut),
10 May 1993, m revised
form 17 September
D-6500 Maznz (Germany) 1993)
Abstract Despite the fact that attempts were made to describe the mteractlon of a smgle H,O molecule with a mercury surface, usmg both semi-emplncal and ab mltlo quantum chemical calculations, reliable mlcroscoplc mformatlon on the Hg iH,O Interface IS stdl lackmg In this work, non-emplncal quantum chemical calculations were carried out to study water molecule adsorption on an uncharged mercury electrode The mercury surface was modelled by a cluster Hg,, with n = 6, 7 The effect of electromc correlation plays an important role An “on-top” position of the H,O molecule with the dipole moment pomtmg away from the surface reveals an adsorption energy mmlmum (AE,,,) of -38 5 kJ molF’ The dipole reorientation energy was estimated to be 218 kJ mol-’ Accordmg to our results, the dependence of AI?,,,, on the tilt angle has no hmlt Analysis of the chemical bmdmg between the cluster and the H,O molecule shows the electrostatic nature of the bmdmg The mean field approxlmatlon was applied to describe the mteractlon between the adsorbed H,O molecules m a monolayer The results were m agreement with experimental data
1. Introduction
Although Hg/electrolyte solution interfaces have been Investigated experimentally m detail for a long time, a mlcroscoplc picture of the structure of the electrical double layer 1s still lacking Even a reliable value for the adsorption energy of an H,O molecule (AE,,,) IS mlssmg-a quantity which 1s of importance for the description of a number of electrochemical phenomena On studying the adsorption of water vapour on a mercury surface, Kemball reported an experimental value for AE,,, of -71 kJ mol-’ [ll Another method to estimate the electrochemical AE,,, value (-46 to -59 kJ mol-‘1 phenomenologltally IS usmg the relationship [2] AE,,, + AEHg_-H + kT = AE, where AE,,_* bond between
(1)
1s the energy of the chemlsorptlon mercury and a hydrogen atom (ap-
Permanent address Kazan, Tatarstan ‘* Permanent address Chemle, Umversltat
Institute
l
of Chemical
Technology,
420015
Instltut fur Anorgamsche und Analytlsche Innsbruck, A-6020 Innsbruck, Austria
0022-0728/94/$7 00 SSDI 0022-0728(93)03151-E
proximately 146 kJ mol- ‘> [3], and A E, IS the actlvatlon energy for the hydrogen discharge (96 kJ mol-‘) [2] For the comparison of these AE,,, values with theoretical values it has to be kept m mmd that the contrlbutlons from H,O-H,O mteractlons are meluded here After it had been demonstrated that the imagecharge model IS not correct for small H,O-metal dlstances [4], the most suitable method for a theoretical mvestlgatlon of the adsorption of solvent molecules IS the cluster model for the metal surface [5-81 The adsorption of both a single H,O molecule [9] and water clusters (H,O), [lo] on mercury have been studled by semi-emplncal CND0/2 calculations Recently, Sellers and Sudhakar have reported for the first time a potential descrlbmg the interaction between an H,O molecule and a mercury surface, based on ab mltlo quantum chemical calculations 1111 However, the potential energy surface was constructed on a rather small number of H,O molecule onentatlons Their value for the adsorption energy (-54 8 kJ mol-‘1 was lower than all known theoretical estlmatlons obtained for transition metals [5-8,121, which are more hydrophdlc than mercury Therefore, the result 0
1994 - Elsevler
Sequoia
All rights reserved
R R Nazmutdmou
228
et al / Hz0 molecule adsorptIon on Hg
presented m ref 11 1s apparently overestimated, and mformatlon on the dipole reorientation energy, which 1s of importance for the theory of the electric double layer, 1s lackmg Moreover, the sequence of the equhbrmm Hg-0 distances found for the relative surface posltlons of the H,O molecule (on-top, bridge and hollow site) differs from that for the Pt IH,O interface iI31 Thus, it was of interest to continue the mvestlgatlon of H,O molecule adsorption on the mercury surface using the cluster model and ab mltlo methods of quantum chemistry
20 10 O-10-20 -
t 027
I
I
I
0 30
0 33
036
1
0 39
R( Hg-O)/nm
2. Details of the calculations The model surface cluster used to study the adsorption of an H,O molecule consisted of seven mercury atoms for the case where the oxygen atom 1s posltloned on top of a mercury atom, while only SIXmercury atoms were employed for a bridge and a hollow site position (Fig 1) Such a choice of the symmetry of the clusters 1s expected to eliminate partially fmlte size artifacts The nearest Hg-Hg distance corresponds to the first peak of the radial dlstrlbutlon function for liquid mercury at 0 3 nm [14] Neither a surface charge nor an external electric field were considered All the quantum chemical calculations were carried out at ab mltlo level with the program GAUSSIAN-90 [15] The mercury valence orbital 5d”6s26p0 conflguratlon was described by a (3s3p3d) Gaussian basis set of double zeta (DZ) quahty [16] The effects of the inner shell electrons were included m the effective core potential by Hay and Wadt [16] To describe the oxygen and hydrogen atoms m the H,O molecules, the well-known basis set 6-31G * * (DZ + polarlzatlon quality) was used [17] The calculated density of electronic states for the mercury clusters displayed surface features However, the electronic work function for the cluster Hg, was found to be 5 4 eV, which 1s close to the bulk value of 45 eV
Fig 1 Clusters (2) and bridge outward-dlrected
Fig 2 Restricted Hartree-Fock (RHF) energies for the cluster-H20 molecule mteractlon as a function of the between the mercury surface and the oxygen atom of molecule for four different posItIons and orientations 0, 8 ==0”, A, bridge site, 0 = O”, n , hollow site, 0 = O”, +, 8 ==180”
mercury distance an H,O top We, top site,
The adsorption energy was calculated as a function of the distance from the surface for on-top, bridge and hollow site posltlons, and different angles 8, where 8 IS defined m Fig 1 An additional calculation was performed, where the Hg-0 distance was fixed while 13 was varied from 0” to 90” The mtramolecular geometry of the H,O molecule was fured at R(O-H) = 0 09572 nm and LHOH = 104 52” It should be noted that the resulting dipole moment of 2 18 debye (D) 1s close to the experimental value of 1 82 D The results of the restrlcted Hartree-Fock (RHF) calculations for all three posltlons and 0 = O”, as well as for the on-top posltlon with 8 = 180”, are presented m Fig 2 This fmal arrangement leads to only a very shallow mmlmum To clarify the sensltlvlty of the system for different basis sets, we carried out several calculations with the Dunning-Huzmaga valence DZ basis set (D95V) for the H,O molecule [18] The total energy of the system Hg,-H,O,,, was found to have a mmlmum near 0 305 nm for 8 = 0” and the on-top site
modelhng the mercury surface for the calculation of the adsorption energy of an H,O molecule positioned on a top (l), hollow site (3) 0 describes the orlentatlon of the H,O molecule relatrve to the surface, and IS defined by the angle between the surface normal and the dipole moment vector of the H,O molecule
RR
Nazmutdmov et al / H,O molecule adsorptIon on Hg
229
-25 i
‘j25
0 30
0 35
0 40
0 45
-35 1 0
R ( Hg-0 )/nm Fig 3 Correlation energy per mercury atom as a fun&Ion of the distance between a mercury atom and the oxygen atom of an H,O molecule for a hollow site posItIon and three different orlentatlons n , e=O”, A, 0=90”, V, 8=180”
The adsorption energy was calculated to be -20 kJ mol-’ These values are close to those obtained with the 6-31G* * basis set We also found that, for the D95V basis set, the calculated potential for all posltlons 1s more repulsive for 8 = 180” In the followmg calculations, only the 6-31G** basis set was employed for the H,O molecule According to the results of early studies of the chemical bmdmg between an H,O molecule and atoms of the transition metals nickel and copper, the mtermolecular electron correlation plays a crucial role [19,20] Therefore, the results deplcted m Fig 2 are expected to be of a quahtatlve nature To take mto account the effect of electromc correlation, quantum
I 18
1 36
I 54
I 72
I 90
6 Fig 5 Moller-Plesset energies of the fourth order (MP4) for the mercury cluster-H20 molecule mteractlon as a function of the angle 0 for a futed Hg-0 distance of 0 32 nm 0, top site, q , hollow site
chemical calculations were carried out at the MP4 level (Moller-Plesset perturbation theory of the fourth order) for the model system Hg,-H,O, with n = 1, 2, 3 The correlation energy was estimated by L,(r)
=&E&r)
-&F%(r)
(2) are the total energies of
where E,,(r) and E,,,(r) the respective systems For a given distance m the range 0 26-O 44 nm, Ecorr(r) was found to be directly proportional to IZ It can be seen from Fig 3 that, for the three representative examples, Ecorr(r) decays exponentially with r This means that, together with a constant value for Ecorr/n, for the mfmltely extended mercury surface, E&r) converges rapidly Therefore, it can be concluded that the cluster size employed m the calculations was sufficient for mcludmg correctly the correlation effects It 1s then possible to correct the RHF results (Fig 2) by %lVIP4(~)=&m(r)
- ~K,&Z)/~
(3)
r=l
I
-40 1 0 23
/ 027
1 031
I 0 35
I 0 39
1
1
R ( Hg-0 )/nm Fig 4 Moller-Plesset energies of the fourth order (MP4) for the mercury cluster-H20 molecule mteractlon as a function of the distance between the mercury surface and the oxygen atom of an H,O molecule for five different posItIons and orlentatlons 0, top site, 0 = o”, A, bridge site, 0 = O”, n , hollow site, 13= O”, +, top site, e = 180”, v , hollow site, e = 180”
where N 1s the number of atoms of the model surface cluster All the calculations were carried out without counterpoise correction As was shown m ref 21, the basis set superposltlon error for the basis set 6-31G * * should be small 3. Results and discussion The final results are presented m Figs 4 and 5, and collected m Table 1 The H,O molecule 1s adsorbed on the mercury surface for all the orlentatlons mvestl-
230
RR Nazmutdmou et al / HZ0 moles ule adsorptron on Hg
gated The orientation where the dipole moment of the H,O molecule points away from the metal surface was found to be energetically more favourable for all posltlons For the on-top position, the difference between the adsorption energies of dipole moment orientations towards and away from the surface 1 e AE T 1, was 218 kJ mol- ’ (Table 1) This value 1s m good agreement with model theoretical estimates [22] and seml-emplrlcal calculations [9] The surface corrugation (Fig 4) disappears for 8 = 0” at R(Hg-0) > 0 33 nm Thus, the adsorbed H,O molecule 1s expected to have quite a high moblhty near the mercury surface beyond this distance The equlhbrmm distances increase m the sequences which 1s m contradlctlon with results reported elsewhere [ll] The adsorption energy for an on-top site position has a mmlmum of -38 5 kJ mol-’ (Table 1) and differs from that m ref 11 ( - 54 8 kJ mol- ‘1 which 1s closer to the CNDO predlctlon ( - 66 1 kJ mol- ‘)[9] It can be seen from Table 1, that the difference between the posltlons of the mmlma for 13= 0” and 19= 180” 1s 0 06 nm, which may result m a dependence of the thickness of the electrical double layer on the charge of the electrode It 1s important to note that the dependence of the system energy on the rotation angle has no hmlt (Fig 5) This fmdmg 1s also m contradlctlon with some of the results presented m ref 11, where an energy mmimum was found for hollow positions and 0 = 86” Energy differences AE T * between 0 =O” and 0 = 90 are found to be 8 1 and 10 9 kJ mol-’ for on-top and hollow site posltlons, respectively, if the Hg-0 dlstance 1s fixed so that E has a mmlmum for 0 = 0 Since the close-packed mercury surface has a hexagonal symmetry and the AE f -+ values are comparable with the energy of hydrogen bonds for H,O, one may expect the formation of ice-like structures at the mer-
distance R (Hg-01, TABLE 1 Adsorption energy AEads, eqmhbrmm charge a of the adsorbed H,O molecule and change of the cluster highest occupied molecular orblt energy AE,,,, resulting from chemlsorptlon for various posltlons and orlentatlons of the Hz0 molecule a
O(T) O(t) O(r) 180(J) 180 (J )
Site On-top Bridge Hollow On-top Hollow
kJ
- A&,,, / mol-’
NHg-O)/ nm
q(H,O)/ e
385 331 318 167 13 4
0 0 0 0 0
006 0 05 0 06 0 03 0 03
285 32 32 34.5 40
0 28
0 30
a 0 IS defined as the angle between the dipole moment H,O molecule and the surface normal vector
AC,,,,/
kJ mol-’ 16 22 23 - 13 - 16 vector
3 2 0 4 3 of the
0 32
R ( Hg-0 )/nm Fig 6 Dipole moment of the mercury cluster-H,0 as a function of the Hg-0 distance for an on-top
on-top < bridge = hollow site
fI/deg
0 26
molecule system posItIon and 0 = 0”
cury surface for the potential of zero charge The posslblhty of the existence of such a structure was established recently for the Pt(lll)/H,O interface on the basis of molecular dynamics (MD) slmulatlons [23] It can be seen from Table 1 that only a shght charge transfer to the metal 1s observed for all posltlons and orientations This seems to be twice as large for onentatlons where the H,O dipole moment 1s directed towards the surface rather than away from It It 1s demonstrated m Fig 6 that the dipole moment for the depends linearly on the Hg-0 system Hg,/H,O,,, distance Accordmg to Bagus et al [24], this result indicates a predommantly electrostatic component for the adsorption energy The energy change of the highest occupied molecular orbital (HOMO) of the cluster under the effect of the adsorption was found to reverse sign, while Its absolute value remains the same if the dipole onentatlon 1s changed from 8 = 0” to 0 = 180” (Table 1) This result confirms the conclusion about the electrostatic nature of the Hg-H,O,,, interaction However, the effect of the H,O molecule does not lead to a simple polarlzatlon of the metal As shown by the Mulhken population analysis of the system Hg,-H,O,,,, the metal electronic density 1s rearranged as a result of electrostatic repulsion from dZz, dX~_y~ and pZ orbltals, directed perpendicular to the metal surface, to empty px and p, orbltals with parallel orlentatlon It should be noted that the mam features of the chemical are similar to those of translbmdmg of Hg/H,O,,, tlon metal-H,0 molecule systems [251 The mteractlons between the H,O molecules m the compact part of the electrical double layer can be subdivided mto two parts The first part describes the electrostatic dipole mteractlons, whereas the second part depends on the number of hydrogen bonds there are between nearest nelghbours Then, the energy of
RR
Nazmutdmov
et al / H,O molecule adsorption on Hg
electrochemical adsorption of H,O molecules (AE,*,,) may be written as a simple sum E AE,&=AE$;+(n,-n,)$
(4)
where AE$i 1s the adsorption energy of a single H,O molecule corrected for dipole-dipole mteractlons, nb and IZ, are average numbers of hydrogen bonds m the bulk and at the metal surface, respectively, and EHzO IS the internal energy of liquid H 2O ( - 39 0 kJ mol- ’
La For further estimates it 1s convenient to consider the H,O molecules near the mercury surface as a closepacked monolayer H,O molecules, adsorbed m on-top positions, form the centres of such a lattice Followmg ref 27, we used the mean field approxlmatlon for the three-state model F=-
In(s)
kJ mol-’ This result 1s m excellent agreement with experimental data (-- 71 1 kJ mol-‘) [l] More detailed mformatlon on the structure of the Hg-H,O interface will be gamed from MD slmulatlons which are m progress Acknowledgment
Financial support from Deutscher Akademlscher Austauschdlenst 1s gratefully acknowledged References
(5)
P
where (s) characterizes dipoles, such that
the mean orientation
of the
H’x2---HL (s) =
(6)
H’x2+H’x+HL
10
with H’ = exp(-AE&/kT), x = exp(--pF/kT) and I = p2/R3 Here p 1s the dipole moment of the H,O molecule (1 82 D), R 1s the first neighbor distance between H,O molecules m the surface layer (0 3 nm) and IZ 1s the lattice sum For the calculation of n, the SIXnearest nelghbours and 12 molecules m the second shell were included Simple numerical calculations yield (s) = 0 178 In terms of the three-state model, the final expression for AE$z 1s given by ?(i AEdIP ads
=
(7) bw(
-
11 12 13 14 15 16 17 18 19
exp( - U,/kT)
=l
LIl/kT)
20 21
1
22
where iJl=AE~d,t~F, U2=AEazs and u3=dEkd,+ ELF With these values, A E$T was calculated to be -27 5 kJ mol-’ One can assume that, m the first approxlmatlon, it, 1s close to 2 7 [23], whereas nb 1s about 2 4 [28l Thus, we have obtained for the electrochemical adsorption energy AE,*,, (eqn (4)) a value of -32 2 kJ mol-‘, which agrees with the low hmlt of phenomenologlcal predlctlons (eqn (1)) However, the estimation of the energy of adsorption from a vacuum on the mercury surface (AEdlp + r~,(E~,~/n,,) leads to the value -713 ads
231
23 24
25 26 21 28
C Kemball, Proc R Sot , London, Ser A 190 (1947) 117 L I Krlshtahk, Electrode Reactions Mechanism of the Elementary Act, Nauka, Moscow, 1979 VA Bendersku, A G Krlvenko and AA Qvchmmkov, Rep Acad of USSR, 249 (1979) 629 E Spohr and K Hemzmger, Ber Buns Phys Chem, 92 (1988) 1358 J E Muller and J Harris, Phys Rev Lett , 53 (1984) 2493 M W Rlbarsky, W D Luedtke and U Landman, Phys Rev B, 32 (1985) 1430 H P Bonzel, G PIrug and J E Muller, Phys Rev Lett , 58 (1987) 2138 H Yang and J L Whltten, Surf SCI , 223 (1989) 131 An Kuznetsov, J Remhold and W Lorenz, J Electroanal Chem , 164 (1984) 167 An M Kuznetsov, RR Nazmutdmov and M S Shapmk, Electrochlm Acta, 34 (1989) 1821 H Sellers and R V Sudhakar, J Chem Phys , 97 (1992) 6644 J I Slepmann and M Sprlk, Surf Scl Lett , 279 (1992) L185 E Spohr, J Phys Chem, 93 (1989) 6171 L Boslo, R Cortes and C Segaud, J Chem Phys, 71 (1979) 3595 M J Frlsch, et al, GAUSSIAN 90, Gausslan Inc, Pittsburgh, PA, 1990 P J Hay and W R Wadt, J Chem Phys, 82 (1985) 270 W J Hehre, R DItchfield and J A Pople, J Chem Phys, 56 (1971) 2257 T H Dunning and P J Hay, m H F Schaefer III (Ed ), Modern Theoretical Chemistry, Vol 3, Plenum, New York J Sauer, H Haberlandt and G Pacchlom, J Phys Chem. 90 (1986) 3051 C W Bauschhcher, Chem Phys Lett , 142 (1987) 71 J M Leclercq, M Allavena and Y Bouteder, J Chem Phys , 78 (1983) 4606 M J R Gonzales, D Posadas and A J Arvla, J Phys Chem, 83 (1979) 1733 K Raghavan, K Foster, K Motakabbu and M Berkowitz, J Chem Phys , 93 (1991) 2110 P S Bagus, G Pacchlom and C J Nehn, m R Carbo (Ed ), Quantum Chemistry Basic Aspects, Actual Trends, Studies m Physlcal and Theoretlcal Chemistry, Vol 62, Elsevler, Amsterdam, 1989, p 475 C W Bauschhcher, J Chem Phys , 84 (1986) 260 W L Jorgensen, J Chem Phys , 77 (1982) 4157 W Schmlckler, J Electroanal Chem , 149 (1983) 15 K Hemzmger and G Pbhnkis, m H Kleeberg (Ed ), Interactlon of Water m Ionic and Nomomc Hydrates, Sprmger, Berlin, 1987, pp l-22
of Electroanalytzcal
Chemzstry, 369 (1994) 227-231
227
Quantum chemical study of the adsorption of an H,O molecule on an uncharged mercury surface l, M. Probst **, and K Hemzinger
Renat R Nazmutdmov Max-Planck-Instztut (Received
fur Chemze (Otto-Hahn-Instztut),
10 May 1993, m revised
form 17 September
D-6500 Maznz (Germany) 1993)
Abstract Despite the fact that attempts were made to describe the mteractlon of a smgle H,O molecule with a mercury surface, usmg both semi-emplncal and ab mltlo quantum chemical calculations, reliable mlcroscoplc mformatlon on the Hg iH,O Interface IS stdl lackmg In this work, non-emplncal quantum chemical calculations were carried out to study water molecule adsorption on an uncharged mercury electrode The mercury surface was modelled by a cluster Hg,, with n = 6, 7 The effect of electromc correlation plays an important role An “on-top” position of the H,O molecule with the dipole moment pomtmg away from the surface reveals an adsorption energy mmlmum (AE,,,) of -38 5 kJ molF’ The dipole reorientation energy was estimated to be 218 kJ mol-’ Accordmg to our results, the dependence of AI?,,,, on the tilt angle has no hmlt Analysis of the chemical bmdmg between the cluster and the H,O molecule shows the electrostatic nature of the bmdmg The mean field approxlmatlon was applied to describe the mteractlon between the adsorbed H,O molecules m a monolayer The results were m agreement with experimental data
1. Introduction
Although Hg/electrolyte solution interfaces have been Investigated experimentally m detail for a long time, a mlcroscoplc picture of the structure of the electrical double layer 1s still lacking Even a reliable value for the adsorption energy of an H,O molecule (AE,,,) IS mlssmg-a quantity which 1s of importance for the description of a number of electrochemical phenomena On studying the adsorption of water vapour on a mercury surface, Kemball reported an experimental value for AE,,, of -71 kJ mol-’ [ll Another method to estimate the electrochemical AE,,, value (-46 to -59 kJ mol-‘1 phenomenologltally IS usmg the relationship [2] AE,,, + AEHg_-H + kT = AE, where AE,,_* bond between
(1)
1s the energy of the chemlsorptlon mercury and a hydrogen atom (ap-
Permanent address Kazan, Tatarstan ‘* Permanent address Chemle, Umversltat
Institute
l
of Chemical
Technology,
420015
Instltut fur Anorgamsche und Analytlsche Innsbruck, A-6020 Innsbruck, Austria
0022-0728/94/$7 00 SSDI 0022-0728(93)03151-E
proximately 146 kJ mol- ‘> [3], and A E, IS the actlvatlon energy for the hydrogen discharge (96 kJ mol-‘) [2] For the comparison of these AE,,, values with theoretical values it has to be kept m mmd that the contrlbutlons from H,O-H,O mteractlons are meluded here After it had been demonstrated that the imagecharge model IS not correct for small H,O-metal dlstances [4], the most suitable method for a theoretical mvestlgatlon of the adsorption of solvent molecules IS the cluster model for the metal surface [5-81 The adsorption of both a single H,O molecule [9] and water clusters (H,O), [lo] on mercury have been studled by semi-emplncal CND0/2 calculations Recently, Sellers and Sudhakar have reported for the first time a potential descrlbmg the interaction between an H,O molecule and a mercury surface, based on ab mltlo quantum chemical calculations 1111 However, the potential energy surface was constructed on a rather small number of H,O molecule onentatlons Their value for the adsorption energy (-54 8 kJ mol-‘1 was lower than all known theoretical estlmatlons obtained for transition metals [5-8,121, which are more hydrophdlc than mercury Therefore, the result 0
1994 - Elsevler
Sequoia
All rights reserved
R R Nazmutdmou
228
et al / Hz0 molecule adsorptIon on Hg
presented m ref 11 1s apparently overestimated, and mformatlon on the dipole reorientation energy, which 1s of importance for the theory of the electric double layer, 1s lackmg Moreover, the sequence of the equhbrmm Hg-0 distances found for the relative surface posltlons of the H,O molecule (on-top, bridge and hollow site) differs from that for the Pt IH,O interface iI31 Thus, it was of interest to continue the mvestlgatlon of H,O molecule adsorption on the mercury surface using the cluster model and ab mltlo methods of quantum chemistry
20 10 O-10-20 -
t 027
I
I
I
0 30
0 33
036
1
0 39
R( Hg-O)/nm
2. Details of the calculations The model surface cluster used to study the adsorption of an H,O molecule consisted of seven mercury atoms for the case where the oxygen atom 1s posltloned on top of a mercury atom, while only SIXmercury atoms were employed for a bridge and a hollow site position (Fig 1) Such a choice of the symmetry of the clusters 1s expected to eliminate partially fmlte size artifacts The nearest Hg-Hg distance corresponds to the first peak of the radial dlstrlbutlon function for liquid mercury at 0 3 nm [14] Neither a surface charge nor an external electric field were considered All the quantum chemical calculations were carried out at ab mltlo level with the program GAUSSIAN-90 [15] The mercury valence orbital 5d”6s26p0 conflguratlon was described by a (3s3p3d) Gaussian basis set of double zeta (DZ) quahty [16] The effects of the inner shell electrons were included m the effective core potential by Hay and Wadt [16] To describe the oxygen and hydrogen atoms m the H,O molecules, the well-known basis set 6-31G * * (DZ + polarlzatlon quality) was used [17] The calculated density of electronic states for the mercury clusters displayed surface features However, the electronic work function for the cluster Hg, was found to be 5 4 eV, which 1s close to the bulk value of 45 eV
Fig 1 Clusters (2) and bridge outward-dlrected
Fig 2 Restricted Hartree-Fock (RHF) energies for the cluster-H20 molecule mteractlon as a function of the between the mercury surface and the oxygen atom of molecule for four different posItIons and orientations 0, 8 ==0”, A, bridge site, 0 = O”, n , hollow site, 0 = O”, +, 8 ==180”
mercury distance an H,O top We, top site,
The adsorption energy was calculated as a function of the distance from the surface for on-top, bridge and hollow site posltlons, and different angles 8, where 8 IS defined m Fig 1 An additional calculation was performed, where the Hg-0 distance was fixed while 13 was varied from 0” to 90” The mtramolecular geometry of the H,O molecule was fured at R(O-H) = 0 09572 nm and LHOH = 104 52” It should be noted that the resulting dipole moment of 2 18 debye (D) 1s close to the experimental value of 1 82 D The results of the restrlcted Hartree-Fock (RHF) calculations for all three posltlons and 0 = O”, as well as for the on-top posltlon with 8 = 180”, are presented m Fig 2 This fmal arrangement leads to only a very shallow mmlmum To clarify the sensltlvlty of the system for different basis sets, we carried out several calculations with the Dunning-Huzmaga valence DZ basis set (D95V) for the H,O molecule [18] The total energy of the system Hg,-H,O,,, was found to have a mmlmum near 0 305 nm for 8 = 0” and the on-top site
modelhng the mercury surface for the calculation of the adsorption energy of an H,O molecule positioned on a top (l), hollow site (3) 0 describes the orlentatlon of the H,O molecule relatrve to the surface, and IS defined by the angle between the surface normal and the dipole moment vector of the H,O molecule
RR
Nazmutdmov et al / H,O molecule adsorptIon on Hg
229
-25 i
‘j25
0 30
0 35
0 40
0 45
-35 1 0
R ( Hg-0 )/nm Fig 3 Correlation energy per mercury atom as a fun&Ion of the distance between a mercury atom and the oxygen atom of an H,O molecule for a hollow site posItIon and three different orlentatlons n , e=O”, A, 0=90”, V, 8=180”
The adsorption energy was calculated to be -20 kJ mol-’ These values are close to those obtained with the 6-31G* * basis set We also found that, for the D95V basis set, the calculated potential for all posltlons 1s more repulsive for 8 = 180” In the followmg calculations, only the 6-31G** basis set was employed for the H,O molecule According to the results of early studies of the chemical bmdmg between an H,O molecule and atoms of the transition metals nickel and copper, the mtermolecular electron correlation plays a crucial role [19,20] Therefore, the results deplcted m Fig 2 are expected to be of a quahtatlve nature To take mto account the effect of electromc correlation, quantum
I 18
1 36
I 54
I 72
I 90
6 Fig 5 Moller-Plesset energies of the fourth order (MP4) for the mercury cluster-H20 molecule mteractlon as a function of the angle 0 for a futed Hg-0 distance of 0 32 nm 0, top site, q , hollow site
chemical calculations were carried out at the MP4 level (Moller-Plesset perturbation theory of the fourth order) for the model system Hg,-H,O, with n = 1, 2, 3 The correlation energy was estimated by L,(r)
=&E&r)
-&F%(r)
(2) are the total energies of
where E,,(r) and E,,,(r) the respective systems For a given distance m the range 0 26-O 44 nm, Ecorr(r) was found to be directly proportional to IZ It can be seen from Fig 3 that, for the three representative examples, Ecorr(r) decays exponentially with r This means that, together with a constant value for Ecorr/n, for the mfmltely extended mercury surface, E&r) converges rapidly Therefore, it can be concluded that the cluster size employed m the calculations was sufficient for mcludmg correctly the correlation effects It 1s then possible to correct the RHF results (Fig 2) by %lVIP4(~)=&m(r)
- ~K,&Z)/~
(3)
r=l
I
-40 1 0 23
/ 027
1 031
I 0 35
I 0 39
1
1
R ( Hg-0 )/nm Fig 4 Moller-Plesset energies of the fourth order (MP4) for the mercury cluster-H20 molecule mteractlon as a function of the distance between the mercury surface and the oxygen atom of an H,O molecule for five different posItIons and orlentatlons 0, top site, 0 = o”, A, bridge site, 0 = O”, n , hollow site, 13= O”, +, top site, e = 180”, v , hollow site, e = 180”
where N 1s the number of atoms of the model surface cluster All the calculations were carried out without counterpoise correction As was shown m ref 21, the basis set superposltlon error for the basis set 6-31G * * should be small 3. Results and discussion The final results are presented m Figs 4 and 5, and collected m Table 1 The H,O molecule 1s adsorbed on the mercury surface for all the orlentatlons mvestl-
230
RR Nazmutdmou et al / HZ0 moles ule adsorptron on Hg
gated The orientation where the dipole moment of the H,O molecule points away from the metal surface was found to be energetically more favourable for all posltlons For the on-top position, the difference between the adsorption energies of dipole moment orientations towards and away from the surface 1 e AE T 1, was 218 kJ mol- ’ (Table 1) This value 1s m good agreement with model theoretical estimates [22] and seml-emplrlcal calculations [9] The surface corrugation (Fig 4) disappears for 8 = 0” at R(Hg-0) > 0 33 nm Thus, the adsorbed H,O molecule 1s expected to have quite a high moblhty near the mercury surface beyond this distance The equlhbrmm distances increase m the sequences which 1s m contradlctlon with results reported elsewhere [ll] The adsorption energy for an on-top site position has a mmlmum of -38 5 kJ mol-’ (Table 1) and differs from that m ref 11 ( - 54 8 kJ mol- ‘1 which 1s closer to the CNDO predlctlon ( - 66 1 kJ mol- ‘)[9] It can be seen from Table 1, that the difference between the posltlons of the mmlma for 13= 0” and 19= 180” 1s 0 06 nm, which may result m a dependence of the thickness of the electrical double layer on the charge of the electrode It 1s important to note that the dependence of the system energy on the rotation angle has no hmlt (Fig 5) This fmdmg 1s also m contradlctlon with some of the results presented m ref 11, where an energy mmimum was found for hollow positions and 0 = 86” Energy differences AE T * between 0 =O” and 0 = 90 are found to be 8 1 and 10 9 kJ mol-’ for on-top and hollow site posltlons, respectively, if the Hg-0 dlstance 1s fixed so that E has a mmlmum for 0 = 0 Since the close-packed mercury surface has a hexagonal symmetry and the AE f -+ values are comparable with the energy of hydrogen bonds for H,O, one may expect the formation of ice-like structures at the mer-
distance R (Hg-01, TABLE 1 Adsorption energy AEads, eqmhbrmm charge a of the adsorbed H,O molecule and change of the cluster highest occupied molecular orblt energy AE,,,, resulting from chemlsorptlon for various posltlons and orlentatlons of the Hz0 molecule a
O(T) O(t) O(r) 180(J) 180 (J )
Site On-top Bridge Hollow On-top Hollow
kJ
- A&,,, / mol-’
NHg-O)/ nm
q(H,O)/ e
385 331 318 167 13 4
0 0 0 0 0
006 0 05 0 06 0 03 0 03
285 32 32 34.5 40
0 28
0 30
a 0 IS defined as the angle between the dipole moment H,O molecule and the surface normal vector
AC,,,,/
kJ mol-’ 16 22 23 - 13 - 16 vector
3 2 0 4 3 of the
0 32
R ( Hg-0 )/nm Fig 6 Dipole moment of the mercury cluster-H,0 as a function of the Hg-0 distance for an on-top
on-top < bridge = hollow site
fI/deg
0 26
molecule system posItIon and 0 = 0”
cury surface for the potential of zero charge The posslblhty of the existence of such a structure was established recently for the Pt(lll)/H,O interface on the basis of molecular dynamics (MD) slmulatlons [23] It can be seen from Table 1 that only a shght charge transfer to the metal 1s observed for all posltlons and orientations This seems to be twice as large for onentatlons where the H,O dipole moment 1s directed towards the surface rather than away from It It 1s demonstrated m Fig 6 that the dipole moment for the depends linearly on the Hg-0 system Hg,/H,O,,, distance Accordmg to Bagus et al [24], this result indicates a predommantly electrostatic component for the adsorption energy The energy change of the highest occupied molecular orbital (HOMO) of the cluster under the effect of the adsorption was found to reverse sign, while Its absolute value remains the same if the dipole onentatlon 1s changed from 8 = 0” to 0 = 180” (Table 1) This result confirms the conclusion about the electrostatic nature of the Hg-H,O,,, interaction However, the effect of the H,O molecule does not lead to a simple polarlzatlon of the metal As shown by the Mulhken population analysis of the system Hg,-H,O,,,, the metal electronic density 1s rearranged as a result of electrostatic repulsion from dZz, dX~_y~ and pZ orbltals, directed perpendicular to the metal surface, to empty px and p, orbltals with parallel orlentatlon It should be noted that the mam features of the chemical are similar to those of translbmdmg of Hg/H,O,,, tlon metal-H,0 molecule systems [251 The mteractlons between the H,O molecules m the compact part of the electrical double layer can be subdivided mto two parts The first part describes the electrostatic dipole mteractlons, whereas the second part depends on the number of hydrogen bonds there are between nearest nelghbours Then, the energy of
RR
Nazmutdmov
et al / H,O molecule adsorption on Hg
electrochemical adsorption of H,O molecules (AE,*,,) may be written as a simple sum E AE,&=AE$;+(n,-n,)$
(4)
where AE$i 1s the adsorption energy of a single H,O molecule corrected for dipole-dipole mteractlons, nb and IZ, are average numbers of hydrogen bonds m the bulk and at the metal surface, respectively, and EHzO IS the internal energy of liquid H 2O ( - 39 0 kJ mol- ’
La For further estimates it 1s convenient to consider the H,O molecules near the mercury surface as a closepacked monolayer H,O molecules, adsorbed m on-top positions, form the centres of such a lattice Followmg ref 27, we used the mean field approxlmatlon for the three-state model F=-
In(s)
kJ mol-’ This result 1s m excellent agreement with experimental data (-- 71 1 kJ mol-‘) [l] More detailed mformatlon on the structure of the Hg-H,O interface will be gamed from MD slmulatlons which are m progress Acknowledgment
Financial support from Deutscher Akademlscher Austauschdlenst 1s gratefully acknowledged References
(5)
P
where (s) characterizes dipoles, such that
the mean orientation
of the
H’x2---HL (s) =
(6)
H’x2+H’x+HL
10
with H’ = exp(-AE&/kT), x = exp(--pF/kT) and I = p2/R3 Here p 1s the dipole moment of the H,O molecule (1 82 D), R 1s the first neighbor distance between H,O molecules m the surface layer (0 3 nm) and IZ 1s the lattice sum For the calculation of n, the SIXnearest nelghbours and 12 molecules m the second shell were included Simple numerical calculations yield (s) = 0 178 In terms of the three-state model, the final expression for AE$z 1s given by ?(i AEdIP ads
=
(7) bw(
-
11 12 13 14 15 16 17 18 19
exp( - U,/kT)
=l
LIl/kT)
20 21
1
22
where iJl=AE~d,t~F, U2=AEazs and u3=dEkd,+ ELF With these values, A E$T was calculated to be -27 5 kJ mol-’ One can assume that, m the first approxlmatlon, it, 1s close to 2 7 [23], whereas nb 1s about 2 4 [28l Thus, we have obtained for the electrochemical adsorption energy AE,*,, (eqn (4)) a value of -32 2 kJ mol-‘, which agrees with the low hmlt of phenomenologlcal predlctlons (eqn (1)) However, the estimation of the energy of adsorption from a vacuum on the mercury surface (AEdlp + r~,(E~,~/n,,) leads to the value -713 ads
231
23 24
25 26 21 28
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