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Empirical equations for the bond energies and vibrational frequencies at chemisorptive bonds on surfaces
CHEhtlCAL
Volume 9 I, number 4
17 September
PHYSICS LFXTERS
EMPIRICAL EQUATIONS FOR THE BOND ENERGIES AND VIBRATIONAL OF CHEMlSORPlIVE chin-An
BONDS
ON SURFACES
1982
FREQUENCIES
*
WANG
IBhl T.J. Watson Researclr Center. Yorktonn
Heights. New York lOS98,
USA
Received26 May 1982
Empirical equations dewed for bond encrgcs and force constants of gaseous molecules arc apphed to chenusorptivc bonds on surfaces. For two adsorbed atoms from the same famdy of the pnodrc hblc, A and B, the chemsorptk bond E (EA~/EB,)‘I’, where EA, and EB ;LR:the energics, E, to the same metal, hf. GUI be approxunated by J?A_hf/EB_ht bond energies of &atomic molecules A* and Bz, respcctivcly. The correspondmg vrbrational frequcncics.Y,can L approvr mated by&&$-~, IT(mB/mA)(h2/&3$‘Z. mA and mg ue the masses of atoms A and B, respectively;FAN and of IQ2 are the force constants of molecules A2 and B2, respcctwcly. These rclatlons arc apphcd to the chcmisorption halogens on metals and shovxd good agreement with expenmcn:.
Bond energy and vlbratlonal frequency are two of the most Important properties in the study of chemisorption on surfaces. Extensive expenmental and theoretical efforts have been devoted to understanding such properties [ 1,2]. From the expenence on gas-phase &atomic and larger molecules it is very useful to estabhsh empmcal correlatrons among molecules involving smular chemical bonds, which have been of great value to the stuhes of thelmodynarmc and structural properties of these molecules [3]. Unhke the gas-phase molecules, however, few empuical equations have been proposed for the chemisorptlve bonds on surfaces. It IS therefore the purpose of this work to establish such empuical relations for the chemisorptive bonds from the available data and to prerhct for those where experimental data are lackmg. In this letter we show that the empIrIca equations which have been derived for the bond energies and force constants of gaseous molecules GM be equally useful for correlating the chemisorptive bonds on surfaces. In the present approach, the chemisorptive bond between an adsorbed atom, A, and a metal, M, is correlated with a sm-tilar chemisorptlve bond between * Sponsored IIIpart by the US kmy Research Office. 0 009.2614/82/0000~000/$02.75
0 1982 North-Holland
an adatom 9, which belongs to the same fanuly of A m the penodic table, and the same metal M. Such a corrclatlon allows the properties of bonds A-M and B-M to be related to those of diatomic molecules A2 and B2, analogous to the correlations estabbshed for the gaseous molecules [3]. For the gaseous molecules AX and BX, where X can be either atomic or molecular in form, we have derived empIrical equatlons for the bond energles,E, force constanIs,F, and bond lengths, R, as [3] E,&EBx
Z=(EA~IEB,)“~
9
RAX - RBX z ~(RA~ - RB,) a
(1)
(3)
These equations were appbed to dialkahs, &halogens and alkah halides and showed excellent agreement with experiment [3]. The only exception is the fluorine-containing
molecules where the systematic
denation
indicates
observed
a new set of empnical
values of EF2, FF~ and RF~ to be used in eqs. (l)(3). Good agreement has also been obtamed for many other dratomic and larger molecules [4]. Eqs. (1) and (2) are shown to provide a physical meaning for the expenmental observations between the bond enewes 277
(Er,/ECt
EB-hl: ht z (E,Q/EB~)~”
.
(4)
A simrlar approximation IS taken for the force constant to calculate the vrbrattonal frequenctes, V, of the chemtsorptrve bonds A-M and B-M. The general equatron between force constant and vtbrational frequency for a &atomic molecules is [S] 2nv = (F/jr)1/2, p bemg the reduced mass. For the bond A-M to be treated as “dtatomrc”, p becomes essentrally mA , the mass of atom A. From eq. (2), we obtam z (~~rB/~~A>(F~,/F~,)‘~~ .
u$,-ht/ut-ht
The calculated wbrational frequency for 1 on Ag IS in excellent agreement with experiment. The value
for Br on Ag, however, devrates from the observed frequency by 21 cm-l. The reason for such a discrepancy Is unclear. It is mteresttng to compare our values with the theoretical calculations recently reported on the adsorption of halogens on Ag [I91 which are also shown m table 2. The latter calculatron shows good agreement with experiment for Cl on Ag and I on Ag, but a devlatron of 20 cm-1 for the case of Br on Ag, similar to that obtained m this work. The calculated vlbratronal frequency for F on Ag is 437 cm-l, compared wrth our value of 424 cm-l. Although the dtscrepancy between our calculated vtbrational frequency of Br on Ag wth experiment
(9
Eqd. (4) and (5) are now apphed to the adsorptron of halogen atoms on metal surfaces. The btndmg energtes of F, Cl and Br on (100) and (111) MOare found to be 4.6-4.65,4.11-4.15 and 3.65-3.70 eV, respectively [9,10]. Srmdar binding energies have also been reported for both (100) and (111) Nb surfaces [I 1] and for the adsorptron of Cl on (100) and (I 11) W [12-141. We use the expcrrmental bondmgenergy of Cl on MO to calculate the others wrth the followmg parameters: (Erz/E~12)1/2 = 1.17, (EQ/EB,,)~/~ = Table 1 Blndmg
cnergm
*
(in cV) for the adsorption
calculated a) obscrvcd b)
of
F, Cl, Br and 1 on
hlo surfaces
r
Cl
4.8 I-4.86 4.6-4.65
4.1 l-4.15 4.1 l-4.15
a) h?SCntWorku~IgEA-h#B_ht * (#?A2/EB2)1’2. b)Refs. [g,lo]. c) The obwvcd value of Cl on hlo IS used for the present calculations. 278
1982
1.12, and (Ec~,/E~,)I/~ = 1.27. Except for the )t/2 value whtch was established emprrically from adali halides [3], the other values are taken from the tabulatton of Gaydon [l.S]. The results are shown in table 1. It is seen that the bmding energres calculated from eq. (4) agree very well with expenment for both Cl on MOand Br on MO, an encouraging result for the empuical equation proposed. We have also calculated the binding energy of I on MO whose experimental value is not available at present. The same calculations should also be useful to the adsorption of halogens on Nb and W where the observed bmdmg energtes are smular to those on MO. For the calculation of vtbrattonal frequenaes of halogens on the Ag surface, the observed frequencres are 240 cm-l for Cl [16], 170 cm-l for Br [17] and 110 cm-t for 1 [ 171. We use the observed frequency of Cl on Ag to calculate the others wrth the followrng parameters. an emptncal value of (FE2/Fa2)fIz = I .67 from alkah hahdes [3], and (FQ/F~~~)~/~ = 1.16 and (F~Ja/Fta)t/~ = 1.39 from the tabulation of Jones [18]. The results are shown in table 2.
and for constants of oxtdes and sulfides [S], and have been successfully apphed by other workers to various systems [6,7]. To apply the above equahons to the chemrsorpttve bonds A-M and B-M, we assume that both the bondmg geometry and the number of metal surface atoms mvolvcd m these bonds are similar, which are probably most vahd when srmrlar adatoms, such as A and B descrtbed here, are compared. In addition, bmdmg energes at the same coverage of adatoms on the metal surface should be compared. The metal, M, can thus be treated as one entity, simdar to X used in cqs. (l)-(3). Such an approximation therefore allows a stmdar cquatron for the bond energrcs EA_*, and
EA-ht/EB-
17 Scptcmbcr
CHEMICAL PHYSICS LETTERS
Volume 91. number 4
c)
Br
I
3.67-3.7 I 3.65-3.70
3.24-3.27
Volume
CHEMICAL
91, number 4
PHYSICS
Vibralonal frequcnacs (m cm-‘) Br and I on A@ surfaces
for the adsorptlon
] I] 1.Toyoshuna nr
I
calculated
424
240 b)
149
108
(prcscnt work) a) calculated [ 191
437
241
150
240
170
113 110
obscrvcd [l&17]
112. a) Usmg tic cqustmn u~_h&_hl = (mB/m.\)(FAZ/FBz) b)The observed value of Cl on Ag IS used for the present CIIculatlons. rcmams
unclear,
avaIlable
the close agreement
data and with
with
rous calculatron
indicates
the usefulness
pirical
described
m ths work.
approach
In summary, equations
we have shown
established
also be mochfied
for a reliable
Further
the emplrlcal
the values from
estimate
of the bond
expenmental
expenment is therefore properties
obtamed illustrated
of bond from
on surfaces
can also bc
as has recently
been
for the chemisorption of CO on NI( 111)
[ITO].Apphcation systems
standmg
strength
such an approach,
of these empirical
should
equatrons
to the
also be useful to our under-
of the chemisorpfive
bonds on surfaces.
30 (1972) 251. [l I] IL ranhan and i121 B. Bxdcrmann
C. Baucr, Phys. Letters 54A (19751 313.
and t1.W. Wxmuth, Procadmgs oi the 7th Intcrnatronal Vacuum Congress and 3rd lnlcrnatronal on Sohd Surlaccs, Vlcnna (1979) p. 1091.
1131 G.G. Prlcc, K.L. Rawimgs and B.J. Hopkms, Surfxc
(1979) 379. I-. Bonczck, T. hgcl
SCL 85
114
wd
E. Baucr, SU~~XC
SCL 97
( 1980) 595.
1151 AC. Gaydon. DrssoaaIron cncrguzs and spears of dlalomlc
data are lackmg.
physxal insight mto the nature and magnitude
of changes
[9] G. Bolbach and J.C. Balas, Surface SCL 111 (1981) 575. R Klcm and J.D. McKinley, Surhcc SCL
[lo] M.D. Sheer,
Confcrencc
theoretical
approach
Rev. Ser. Cng.
(1979). 13 1 C.-A. Chang, Hugh Temp. SCI. 6 (1974) 276. 141 C.-A. Chang, unpublished. [S] R.H. Haugc and J.L. Margmvc, HI& Temp. SCL 4 (1972) 170. [6] T.C. DcVorc and HI. rranzcn, High Temp. Ser. 7 (1975) 220. [ 7 I T.C. DcVorc and T.N. C&her, J. Chcm. Phys. 70 (1979) 3497. [S] G. Henbcrg. Spcctm of dntomlc molecules, 2nd Cd. (Van Nostrand, Prmccton, 1950).
cpn
to the chenusorptlvc
Such an empirical where
of the em-
The results agree with
and wth
calculations. on surfaces
that
rigo-
for the gaseous molecules
and applied
on surfaces.
m most uses
the other
all the values of a more
and C.A. Somogar. Cal.
19 (1979) 105. [Z] G.A. SomorJa and M.A. van Hove, Struct. Bondmg 38
CI
other
1982
of I-, Cl,
I-
useful
17 Scptcmbcr
References
Table 2
bonds
LETTERS
molcculcs,
3rd Ed. (Chapman and IIalJ, London,
1968). [16l J.A. Crcyhton, CM Albrccht, R.E. llcslcr and J.A.D. Matthew, Chcm. Phys. Lcllcrs 55 (1978) 55. 1171 h1.M.C. Pcmblc, as quoted rn ref. 1191. (181 L.H. Joncs (Inorganrc vibnt~onal spectroscopy, Vol. I (Dckkcr,
New York,
1971).
1191 H. Nrcols and R.M. I!cxtcr,
I. Chcm. Phyr. 24 (1981) 2059. [20] C.-A. Chang, Surface SCL 95 (1980) L239.
279
Volume 9 I, number 4
17 September
PHYSICS LFXTERS
EMPIRICAL EQUATIONS FOR THE BOND ENERGIES AND VIBRATIONAL OF CHEMlSORPlIVE chin-An
BONDS
ON SURFACES
1982
FREQUENCIES
*
WANG
IBhl T.J. Watson Researclr Center. Yorktonn
Heights. New York lOS98,
USA
Received26 May 1982
Empirical equations dewed for bond encrgcs and force constants of gaseous molecules arc apphed to chenusorptivc bonds on surfaces. For two adsorbed atoms from the same famdy of the pnodrc hblc, A and B, the chemsorptk bond E (EA~/EB,)‘I’, where EA, and EB ;LR:the energics, E, to the same metal, hf. GUI be approxunated by J?A_hf/EB_ht bond energies of &atomic molecules A* and Bz, respcctivcly. The correspondmg vrbrational frequcncics.Y,can L approvr mated by&&$-~, IT(mB/mA)(h2/&3$‘Z. mA and mg ue the masses of atoms A and B, respectively;FAN and of IQ2 are the force constants of molecules A2 and B2, respcctwcly. These rclatlons arc apphcd to the chcmisorption halogens on metals and shovxd good agreement with expenmcn:.
Bond energy and vlbratlonal frequency are two of the most Important properties in the study of chemisorption on surfaces. Extensive expenmental and theoretical efforts have been devoted to understanding such properties [ 1,2]. From the expenence on gas-phase &atomic and larger molecules it is very useful to estabhsh empmcal correlatrons among molecules involving smular chemical bonds, which have been of great value to the stuhes of thelmodynarmc and structural properties of these molecules [3]. Unhke the gas-phase molecules, however, few empuical equations have been proposed for the chemisorptlve bonds on surfaces. It IS therefore the purpose of this work to establish such empuical relations for the chemisorptive bonds from the available data and to prerhct for those where experimental data are lackmg. In this letter we show that the empIrIca equations which have been derived for the bond energies and force constants of gaseous molecules GM be equally useful for correlating the chemisorptive bonds on surfaces. In the present approach, the chemisorptive bond between an adsorbed atom, A, and a metal, M, is correlated with a sm-tilar chemisorptlve bond between * Sponsored IIIpart by the US kmy Research Office. 0 009.2614/82/0000~000/$02.75
0 1982 North-Holland
an adatom 9, which belongs to the same fanuly of A m the penodic table, and the same metal M. Such a corrclatlon allows the properties of bonds A-M and B-M to be related to those of diatomic molecules A2 and B2, analogous to the correlations estabbshed for the gaseous molecules [3]. For the gaseous molecules AX and BX, where X can be either atomic or molecular in form, we have derived empIrical equatlons for the bond energles,E, force constanIs,F, and bond lengths, R, as [3] E,&EBx
Z=(EA~IEB,)“~
9
RAX - RBX z ~(RA~ - RB,) a
(1)
(3)
These equations were appbed to dialkahs, &halogens and alkah halides and showed excellent agreement with experiment [3]. The only exception is the fluorine-containing
molecules where the systematic
denation
indicates
observed
a new set of empnical
values of EF2, FF~ and RF~ to be used in eqs. (l)(3). Good agreement has also been obtamed for many other dratomic and larger molecules [4]. Eqs. (1) and (2) are shown to provide a physical meaning for the expenmental observations between the bond enewes 277
(Er,/ECt
EB-hl: ht z (E,Q/EB~)~”
.
(4)
A simrlar approximation IS taken for the force constant to calculate the vrbrattonal frequenctes, V, of the chemtsorptrve bonds A-M and B-M. The general equatron between force constant and vtbrational frequency for a &atomic molecules is [S] 2nv = (F/jr)1/2, p bemg the reduced mass. For the bond A-M to be treated as “dtatomrc”, p becomes essentrally mA , the mass of atom A. From eq. (2), we obtam z (~~rB/~~A>(F~,/F~,)‘~~ .
u$,-ht/ut-ht
The calculated wbrational frequency for 1 on Ag IS in excellent agreement with experiment. The value
for Br on Ag, however, devrates from the observed frequency by 21 cm-l. The reason for such a discrepancy Is unclear. It is mteresttng to compare our values with the theoretical calculations recently reported on the adsorption of halogens on Ag [I91 which are also shown m table 2. The latter calculatron shows good agreement with experiment for Cl on Ag and I on Ag, but a devlatron of 20 cm-1 for the case of Br on Ag, similar to that obtained m this work. The calculated vlbratronal frequency for F on Ag is 437 cm-l, compared wrth our value of 424 cm-l. Although the dtscrepancy between our calculated vtbrational frequency of Br on Ag wth experiment
(9
Eqd. (4) and (5) are now apphed to the adsorptron of halogen atoms on metal surfaces. The btndmg energtes of F, Cl and Br on (100) and (111) MOare found to be 4.6-4.65,4.11-4.15 and 3.65-3.70 eV, respectively [9,10]. Srmdar binding energies have also been reported for both (100) and (111) Nb surfaces [I 1] and for the adsorptron of Cl on (100) and (I 11) W [12-141. We use the expcrrmental bondmgenergy of Cl on MO to calculate the others wrth the followmg parameters: (Erz/E~12)1/2 = 1.17, (EQ/EB,,)~/~ = Table 1 Blndmg
cnergm
*
(in cV) for the adsorption
calculated a) obscrvcd b)
of
F, Cl, Br and 1 on
hlo surfaces
r
Cl
4.8 I-4.86 4.6-4.65
4.1 l-4.15 4.1 l-4.15
a) h?SCntWorku~IgEA-h#B_ht * (#?A2/EB2)1’2. b)Refs. [g,lo]. c) The obwvcd value of Cl on hlo IS used for the present calculations. 278
1982
1.12, and (Ec~,/E~,)I/~ = 1.27. Except for the )t/2 value whtch was established emprrically from adali halides [3], the other values are taken from the tabulatton of Gaydon [l.S]. The results are shown in table 1. It is seen that the bmding energres calculated from eq. (4) agree very well with expenment for both Cl on MOand Br on MO, an encouraging result for the empuical equation proposed. We have also calculated the binding energy of I on MO whose experimental value is not available at present. The same calculations should also be useful to the adsorption of halogens on Nb and W where the observed bmdmg energtes are smular to those on MO. For the calculation of vtbrattonal frequenaes of halogens on the Ag surface, the observed frequencres are 240 cm-l for Cl [16], 170 cm-l for Br [17] and 110 cm-t for 1 [ 171. We use the observed frequency of Cl on Ag to calculate the others wrth the followrng parameters. an emptncal value of (FE2/Fa2)fIz = I .67 from alkah hahdes [3], and (FQ/F~~~)~/~ = 1.16 and (F~Ja/Fta)t/~ = 1.39 from the tabulation of Jones [18]. The results are shown in table 2.
and for constants of oxtdes and sulfides [S], and have been successfully apphed by other workers to various systems [6,7]. To apply the above equahons to the chemrsorpttve bonds A-M and B-M, we assume that both the bondmg geometry and the number of metal surface atoms mvolvcd m these bonds are similar, which are probably most vahd when srmrlar adatoms, such as A and B descrtbed here, are compared. In addition, bmdmg energes at the same coverage of adatoms on the metal surface should be compared. The metal, M, can thus be treated as one entity, simdar to X used in cqs. (l)-(3). Such an approximation therefore allows a stmdar cquatron for the bond energrcs EA_*, and
EA-ht/EB-
17 Scptcmbcr
CHEMICAL PHYSICS LETTERS
Volume 91. number 4
c)
Br
I
3.67-3.7 I 3.65-3.70
3.24-3.27
Volume
CHEMICAL
91, number 4
PHYSICS
Vibralonal frequcnacs (m cm-‘) Br and I on A@ surfaces
for the adsorptlon
] I] 1.Toyoshuna nr
I
calculated
424
240 b)
149
108
(prcscnt work) a) calculated [ 191
437
241
150
240
170
113 110
obscrvcd [l&17]
112. a) Usmg tic cqustmn u~_h&_hl = (mB/m.\)(FAZ/FBz) b)The observed value of Cl on Ag IS used for the present CIIculatlons. rcmams
unclear,
avaIlable
the close agreement
data and with
with
rous calculatron
indicates
the usefulness
pirical
described
m ths work.
approach
In summary, equations
we have shown
established
also be mochfied
for a reliable
Further
the emplrlcal
the values from
estimate
of the bond
expenmental
expenment is therefore properties
obtamed illustrated
of bond from
on surfaces
can also bc
as has recently
been
for the chemisorption of CO on NI( 111)
[ITO].Apphcation systems
standmg
strength
such an approach,
of these empirical
should
equatrons
to the
also be useful to our under-
of the chemisorpfive
bonds on surfaces.
30 (1972) 251. [l I] IL ranhan and i121 B. Bxdcrmann
C. Baucr, Phys. Letters 54A (19751 313.
and t1.W. Wxmuth, Procadmgs oi the 7th Intcrnatronal Vacuum Congress and 3rd lnlcrnatronal on Sohd Surlaccs, Vlcnna (1979) p. 1091.
1131 G.G. Prlcc, K.L. Rawimgs and B.J. Hopkms, Surfxc
(1979) 379. I-. Bonczck, T. hgcl
SCL 85
114
wd
E. Baucr, SU~~XC
SCL 97
( 1980) 595.
1151 AC. Gaydon. DrssoaaIron cncrguzs and spears of dlalomlc
data are lackmg.
physxal insight mto the nature and magnitude
of changes
[9] G. Bolbach and J.C. Balas, Surface SCL 111 (1981) 575. R Klcm and J.D. McKinley, Surhcc SCL
[lo] M.D. Sheer,
Confcrencc
theoretical
approach
Rev. Ser. Cng.
(1979). 13 1 C.-A. Chang, Hugh Temp. SCI. 6 (1974) 276. 141 C.-A. Chang, unpublished. [S] R.H. Haugc and J.L. Margmvc, HI& Temp. SCL 4 (1972) 170. [6] T.C. DcVorc and HI. rranzcn, High Temp. Ser. 7 (1975) 220. [ 7 I T.C. DcVorc and T.N. C&her, J. Chcm. Phys. 70 (1979) 3497. [S] G. Henbcrg. Spcctm of dntomlc molecules, 2nd Cd. (Van Nostrand, Prmccton, 1950).
cpn
to the chenusorptlvc
Such an empirical where
of the em-
The results agree with
and wth
calculations. on surfaces
that
rigo-
for the gaseous molecules
and applied
on surfaces.
m most uses
the other
all the values of a more
and C.A. Somogar. Cal.
19 (1979) 105. [Z] G.A. SomorJa and M.A. van Hove, Struct. Bondmg 38
CI
other
1982
of I-, Cl,
I-
useful
17 Scptcmbcr
References
Table 2
bonds
LETTERS
molcculcs,
3rd Ed. (Chapman and IIalJ, London,
1968). [16l J.A. Crcyhton, CM Albrccht, R.E. llcslcr and J.A.D. Matthew, Chcm. Phys. Lcllcrs 55 (1978) 55. 1171 h1.M.C. Pcmblc, as quoted rn ref. 1191. (181 L.H. Joncs (Inorganrc vibnt~onal spectroscopy, Vol. I (Dckkcr,
New York,
1971).
1191 H. Nrcols and R.M. I!cxtcr,
I. Chcm. Phyr. 24 (1981) 2059. [20] C.-A. Chang, Surface SCL 95 (1980) L239.
279