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The existence of [NO−2;e+] and [NO−3;e+] systems
Volume
72, number
t
CHEMICAL
THE EXISTENCE
Rscewed
and Paul E. CADE
of Clzemtsr~.
15 January
15 May 1980
LEmRS
OF [NO; ;e” ] AND [NO; ;e* J SYSTEMS *
Abbas FARAZDEL** Deportment
PHYSICS
Amherst. Massachusetts 01003. USA
ozlwerszty of Massachusetts.
1980, m final form 25 February
1980
The [NOg;e+] and [NOi;e+‘f systems are evammed via Hartree-Fock-Rootban calculatrons. The posit-on affinities obtamed are 3.43 eV (NO;) and 3.19 eV (NOi). A “cycle” argument suge;ests that [NO; ;e”] is stable wtb respect to NO3 f Ps. but [NO; ,e*i appears unstable.
The electronic structure of the [NO; ;e”] and [NO; ; e+] systems are examined by approximate restricted Hartree-Fock-Roothaan calculatrons wnh the arm of consrdering the stabrhty of these positron/polyatomic molecule systems. We are not conccrned here with scattering, or resonance, states of e” wrth NOT and NO: or Ps with NO2 and NOS. The basrc idea IS to deterrmne tf [NO;;e*] are stable relatrve to NO, + Ps (n = 2,3). The [NO-;e+] system is excluded because NO has such a small electron affinity (e-024 eV) there seems no chance that [NO- ,e”] IS stable relatrve to NO + Ps The relative stabrhty of [NO, ; e”] relative to NO, t Ps cannot be answered conclusively from Hartree-Fock theory due to neglect of correlation effects, expected to be sjgni~can~y drfferent in the [WO; ,e’] and NO, systems. Thus a cycie (below) IS employed whrch meludes the experunental electron affmity (EA) of NO,, the known binding energy of Ps (Eps = 6.80 eV) and the calculated posrtron affinity, PA, to give the desired binding energy, BE (or Ps affinity), for the process, i.e. NO,+Ps
s
_I -EpS NO,+ei+e-%NO;+e+
[NO,.e+] t PA (1)
Since a negative ion aiways binds a positron (PA > Oj, the stabrhty of [NO,’ ;e’] pertams to the dissociation process. The basic equation from the cycle is BE = EA + PA - 6.80 (eV), = EA + (PA)RF + (PA),,
(2aj - 6.80,
(2bj
where we Introduce rn (2b), PA =E,,(NO,-)
-~_~(lNO,-;e+]j,
= IE”$‘JDi)
- EHP( [NO;;
+ fEm(NO;l = (WHF
(3aj eel 13
-f&,(WO;;eCl)~,
W) (3cj
+ VA),-
A positive PA means [NO; ; e*] is lower m energy than NO; + e”. Here ( PA)HF refers to the HartreeFock positron energy and (PA),, refers to the COTrelatron correction to the positron affiiity. Strictly speaking, PA defmed by eq. (3a) is the vertrcal positron detachment energy which may differ substantially from the adiabatic (thermodynamic) positron afftity. The difference arises from structural (geomet~) changes associated with positron attachment, I.e. eq. (34 should be rewritten as PA=E~(NO,-)-_e(CNO,-;e+])
* Research supported tn part b> NatIonal Science Foundation Grant NSF CHE 77-08542. ** Present address: Department of Chemistry, National Universlty, Teheran, Iran.
+ 4fi x i
{w,(NO;)
- $([NO;;efj)),
w
13’1
where the drfferences m zero-pomt energres of NO; and (NO,;d] are mtroduced and the energres of the systems refer to the equrhbnum structure of each. if the geometry of NO; is srgrzzfic~~tly modrfied by positron attachment, then the force field and fundamental frequencres, wi, will change and the correctron term may be notrceable. More rmportanrly, however, IS that ngnificant geometry changes wrll shift the potentral surfaces relative to one another and hence the difference in the first two terms, each taken at its equrlrbrnm~ geometry, will be changed relative to the case when the geometry of both systems are taken as that of the mttral system, e g. [NO; ; e* J _Schrader and Wang [ 11 suggest srgnifrcant mfluence of the structural detads in the capture of a posrtron or Ps by NO; and NO; or NO1 and NO,, respectrvely Our prehmmary studres do not confirm their suggestions, but this matter is drscussed fully in the complete study of these systems mcluding the angular correlatron curves Needless to say, the adrabatrc versus vertical Ps affimty afso needs consideration m any further study. It is easy to beheve the (PAjmrr 1s a posrtrve quantity smce one expects l~co,(tNO~;e~]
)I > IE,JNO;)I.
so that very likely (PAj,tr- B PA. In the present we use the srmpler eXpresston BE = EA + (PA),,,
15 May 1980
CHEMICM. PHYSICS IJXl-ERS
Volume 77, number 1
- 6 80,
(51 note
(6)
with an “unbalanced” treatment of the two systems mvolved. Hartree-Fock vertical iornzation potent&s are generally S-105 m error rf a fully relaxed L??,+F result is used. Sometimes Koopmans’ theory iomzatron potent&s are better as reorganizatton and correlation effects may tend to cancel one another. EIectron affiitres, on the other hand, are notoriously bad at the Hartree-Fock Ievel. In an earlier work, Cade and Farazdel [3] have argued that the accuracy of positron affmtties IS comparable to romzatron potentials on the basis of consrderatton of parallel PAS of hahde rons and IPs of alkalr atoms, e.g. conjugate [Cl-;e+] and IK*;e-] systems(abo see re!ated work by Kurtz and Jordan f4) ). In addrtron, proton affinities are also usually reliable even at the Hartree-Fock level. Hence, we submit that, until contrary evidence appears. our calculated posrtron affinities are accurate to w&in S-IO% If thus is true and iF(PA&,F < PA, rt might be suggested that (PAjcorr is roughly lo-ZO%, at most. oF(PA)~P. These very quahtatrve estimates may be useful in our stabrhty arguments. On the contrary, drrect calculation of the l&affinity, BE, IS perrlous from only Hartree-Fock results. The new mformatron presented here are positron affinrties of the NO; (II = 2,3) systems. These calcuIattons are Hartree-Fock-Roothaan results employing Cartesian gaussian functions to represent the electronic and posrtronic orbitals, i.e.
mstead ofeq. (2b) so the resultmg BEs should tend to be underestimates A posrttve BE, calculated by eq (6), IS strong evidence for B stable [NO; ,ef] system even though tzu correlatron 1s incIuded in these HFR calculations. It must be pomted out there 1s no proof that the correlation energy of a many-partrcle
must increase 1~1th the number of particles although thrs IS a sensible expectatton. fn particular, the additron of an electron or a posrtron can conceivably affect the total correlation energy of the ion system so that (PAjHr- < PA, although rt seems most unhkely without special qualifications Benioff [2] has given an apparent example where the electron affimty of NO, appears to decrease (by half) when correlatron effects are mtroduced. Thts 1s a puzzling result, counter to most normal experrence, and rt seems more hkely that any reductron of PA (or E4) upon inclusion of correlatron IS due to artrfacts associated 132
(7) and
(8) where 01is summed over expanuon centers (here only on the N, 0 nuclei) and p and r run successively over basis functions on the ath center. The electron and positron basis sets are drfferent to allow for efficient calculatron and flextble dlstmctron between &(r) and G+(t,). A common basrs set is,of course, a less ffexrble altematwe. In both cases, Cartesian gausstans are employed here x,(r),
xp
3
xaybzcexpC--o-%
with fa f b + c) = const.
families
used. The actual
69
basis sets used and complete results wtll be pubhshed subsequently with angular correlatton curves and interpretive aspects. Essenttally, we have rehed on conventional methods to construct the electronic basis
functions and an extensive study [S] to generate posrtronic basis functions from positron/atom systems. For the results summarized here, the Snyder-Basch basis set [6] * is used for elections centered on N and 0 and a set consistmg of one s- and three d-type gaussrans for N and 0 for the pontron, for a total of 87 total variatronal basis functions_ These calculatrons yield the results for NOT, NO,, and [NO, ;e”] , [NO; ; e-1 summarized in table 1. As noted et and EHF are vutuahy identical and give PA = 3.43 (NOT) and 3.19 eV (NO;) which are used to consider the stabihty of [NOT ; e’] and [NOT ; e”] as summarized in fig. 1. In fig. 1, the shaded area around the NO, levels reflects uncertainty in the expenmental EA for the NO, systems and this shading reflects III the projected level of the [NO; ; e”] systems. Frnally, smce (PA)HF is hkely to be a lower lmnt to PA, the shaded regions around [NO; ;e+] due to * In these studres we do not seek to establish fundamental basis sets to use for the electrons, but instead use a welldefined DZ-level basts set. Alternattve DZ basts sets for the electrons gtve very stmdar results. See ref. [S] . Table 1 Summary of energy results for NOI;/[NOi;e+j Hartrce)
systems (m
a)
NO;
[NOz;e*) NO; [NO% e*l
-E-r
-em
b)
204.00674 204.13314 278.81178 278 92921
0 14418 0.33636 0.22747 0 40024
-e+ c)
0.12652 0.11749
a) These calculattons are for NO: and [NOr;d] wrth coordinates N(O.O.O),0, a (= 1 9743175,1.2481122.0) whrch is consistent
with f&-O)
15 May 1980
CHEMICAL PHYSICS LETTERS
Volume 72, number 1
= 2.332 bohr and L (ONO) =
115.4”. based on the structure of the NOT ion. The cat-
culattons for NO; and [NOz;e+] are for the planar geometry N(O,O,O), 0, a (-1.150855, f l-9933393.0), O3 (2 30171.0,O) Ghrch conforms to R(N-0) = 2.3017 bohr
and L (ON01 = 120”. b) em IS the orbrtal energy of the least bound occupied elec tron orbrtal. c) e, is the orbrtal energy of the most bound positron orbital (occupied) There were several (S-6) bound (vutual) pantron orbttals.
T-l-
-
N@,+z-+c-
N3_+Fs
-
NI)_+Ps
Rg. I. Stab&@ of [NO$;e*l and [NO;;e+l systems. Alfenergy values rn eV. The electron affmittes. EA. are shown with estrmated error bars (4%); these error bars are projected into “tentatrve” error bars for fNO,.e+f levels with the fatter shtfted downward assuming (PA)iF d (PA),,,,. We conjecture the error bars for [NO&e+] are useful to speculate on the effect of corrections to stabihty questtons!
A( EA) should probably be lower than as shown. As concerns the electron affiiitres of NO, and N03, the experimental values have shown significant dtfferences. For NO,, Mathur et al. [7] give a value of 3.68 f 0.2 eV, Ferguson et al. [8] report 39 f 0.2 eV, and most recently Davrdson et al. ]9] use 3.91 5 0.24 eV. Earlier values bracketed EA(NO,), Le. 2.68 eV < EA G 4.34 eV. The value near 32 eV seems consistent with most earlier work (including even a lattice calculation). It is generally known that EA(N03) > EA(NO,), but there are several recent experimental results for EA(N02). In chronologkd order, Nalley et al. [ 10) summarize values for EA(N02) prior to 1973 and give a value of 2.5 t 0. I eV, Richardson et al. [ 111 follow closely with a value of =2.8 eV, and then Herbst et al. [ 121 report 2.36 f 0.10 eV. The spread in the electron affiities is not large, AEA(N03) = O-2-0.3 eV and AEA(NOZ) = 0.2 eV, but this spread may be significant in the present study. We are here ignoring any differences between vertical and adiabatic electron affinities strictly speaking we should employ adiabatic EAs (as well as adiabatic PAS). These results show convincingly that [NO;;e+] is a stable system relative to NO; f e+ and NO, f Ps (although other dissociation channels are possible). 133
Volume
72, number
1
CHCMICAL
PHYSICS
Ir appears that the uncertamty in the experimentd EA for NO3 cannot reverse this srtuatton - 1-e. vertical versus adiabatic EAs or geometry changes with posttron detachment. The bmdmg energy, BE. for [NO, .e’] IS > 0 3 eV. Schrader and Wang [ I] have prevrously constdered the stabrhty of PsNO9 [NOT ;e+] ~13 an approwmate CSDO molecular orbital approacir and they report a substantrally larger value (2.83 eV). Whtle the present results seem to conclusrvely establish the [NO; ;ef ] IS a thermodynamrcally stable gas phase entity, It IS hkely that the binding energy can be as much as 1 eV larger than our minimum of 0.3 eV - the larger value of Schrader and Wang may, however, be unreasonably high. Parallel results do not show [NO,;e+] to be stable relattve to NO2 + Ps. This does not mean it is necessanly proved unstable, tt merely means that (PA),,, must overcome the deficit of -0.9 eV. This IS not unpossrble, but does suggest that If [NOi;e+], or PsNO?. IS stable the bmding energy IS small. If our rough estimate that (PA),,, < 0.2PA then correlation could only add an addttronal0 7 eV whrch IS madequate to stabrlize [NO,;e’] _Only structural changes offer any other posstbrhtres to stabthLe thrs system. Schrader and Wang [I] report a value of 1.95 eV as the binding energy of Ps to N02. In summary, we suggest [NO, ;e+] IS stable relattve to NO3 + Ps by at least 0 3 eV and probably more, and cannot definttely say that [NO, ; e”] IS stable rel~twe to NO2 + Ps. These results may be a useful guide m constdenng aqueous solutions of NOT and NOT and thetr propenstty to capture a positron and form a stable entrty (not stable, however, to positron annihilatron). but stgnificant solvation effects cannot be Ignored [ 131. Fmally, due concern IS necessary to explore any structural dependency on these results Further study on these systems IS in progress addresstng these and interpretive problems. One should not overlook the possrbihty that mtrate ions added to a solution to serve as an electroil scavenger may also
134
LETTERS
15
May 1980
scavenge for positrons and contribute a characteristic feature to hfetimes and angular correlattons*. We have been supported m part by a grant from the National Scrence Foundatton (NSF-CHE-7708542). Generous support has also been provided by the Umversity Computmg Center, University of Massachusetts.
l
Thu has been pomtcd
out III expenmental work by J Ch. AbbC et al and 0. hfiigensen tn recent and forthcommg publtcations (prtvate communtcatron)
References D hl Schrader and C.M. Wang, J Phys. Chem 80 (1976) 2507 P A Bcmoff. J Chem Phys 68 (1978) 3405, Theoret Chum Acta 48 (1978) 337 P E Cade and A. Farazdel. J Chcm Phys 66 (1977)
2598 H A Kurtz and K D Jordan, J Phys B 12 (1979) L473. J. Chem. Phys 72 (1980) 493 P E Cade and A Farazdel, The Electrontc Structure of Posttron/hlolecule Systems. I. General Formulatron and Basks Set Development for Molecular Systems, to be submrtted for pubhcatron L C Snyder and H Basch, hlolecular wnvefunctrons and properttes (Wiley, New York, 1972) table 1, pp 22-27. B P Mathur, E W Rothe, S.Y Tang, K MahoJan and G P Reck, J Chem. Phys 64 (1976) 1247. E E Ferguson, D.B Dunkm and F d Fchsenfeld. J. Chem. Phys. 57 (1972) 1459 J A Davrdson, F C Fehsenfeld and CJ Howard, Intern. J Chem Kinettcs 9 (1977) 17. [ 101 S 1. NaBey, R N Compton, H C. Schwender and V E Anderson, J Chem Phys. 59 (197314125 1111 J H. Rrchaadson, L hl Stephenson and J 1 Brauman, Chem Phys. Letters 25 (1974) 318. J Chem 112 E Herbst. T A Patterson and W C. Lineberger, Phys. 61 (1974) 1300. t13 1 P-E. Cade and C -hl. Kao, Solvated Positron Chemtstry; Effects of Solvatron on [F-;e*] Systems in Tetrahedral and Octahedral Solvent Sttes, to be submitted for pubhcation
72, number
t
CHEMICAL
THE EXISTENCE
Rscewed
and Paul E. CADE
of Clzemtsr~.
15 January
15 May 1980
LEmRS
OF [NO; ;e” ] AND [NO; ;e* J SYSTEMS *
Abbas FARAZDEL** Deportment
PHYSICS
Amherst. Massachusetts 01003. USA
ozlwerszty of Massachusetts.
1980, m final form 25 February
1980
The [NOg;e+] and [NOi;e+‘f systems are evammed via Hartree-Fock-Rootban calculatrons. The posit-on affinities obtamed are 3.43 eV (NO;) and 3.19 eV (NOi). A “cycle” argument suge;ests that [NO; ;e”] is stable wtb respect to NO3 f Ps. but [NO; ,e*i appears unstable.
The electronic structure of the [NO; ;e”] and [NO; ; e+] systems are examined by approximate restricted Hartree-Fock-Roothaan calculatrons wnh the arm of consrdering the stabrhty of these positron/polyatomic molecule systems. We are not conccrned here with scattering, or resonance, states of e” wrth NOT and NO: or Ps with NO2 and NOS. The basrc idea IS to deterrmne tf [NO;;e*] are stable relatrve to NO, + Ps (n = 2,3). The [NO-;e+] system is excluded because NO has such a small electron affinity (e-024 eV) there seems no chance that [NO- ,e”] IS stable relatrve to NO + Ps The relative stabrhty of [NO, ; e”] relative to NO, t Ps cannot be answered conclusively from Hartree-Fock theory due to neglect of correlation effects, expected to be sjgni~can~y drfferent in the [WO; ,e’] and NO, systems. Thus a cycie (below) IS employed whrch meludes the experunental electron affmity (EA) of NO,, the known binding energy of Ps (Eps = 6.80 eV) and the calculated posrtron affinity, PA, to give the desired binding energy, BE (or Ps affinity), for the process, i.e. NO,+Ps
s
_I -EpS NO,+ei+e-%NO;+e+
[NO,.e+] t PA (1)
Since a negative ion aiways binds a positron (PA > Oj, the stabrhty of [NO,’ ;e’] pertams to the dissociation process. The basic equation from the cycle is BE = EA + PA - 6.80 (eV), = EA + (PA)RF + (PA),,
(2aj - 6.80,
(2bj
where we Introduce rn (2b), PA =E,,(NO,-)
-~_~(lNO,-;e+]j,
= IE”$‘JDi)
- EHP( [NO;;
+ fEm(NO;l = (WHF
(3aj eel 13
-f&,(WO;;eCl)~,
W) (3cj
+ VA),-
A positive PA means [NO; ; e*] is lower m energy than NO; + e”. Here ( PA)HF refers to the HartreeFock positron energy and (PA),, refers to the COTrelatron correction to the positron affiiity. Strictly speaking, PA defmed by eq. (3a) is the vertrcal positron detachment energy which may differ substantially from the adiabatic (thermodynamic) positron afftity. The difference arises from structural (geomet~) changes associated with positron attachment, I.e. eq. (34 should be rewritten as PA=E~(NO,-)-_e(CNO,-;e+])
* Research supported tn part b> NatIonal Science Foundation Grant NSF CHE 77-08542. ** Present address: Department of Chemistry, National Universlty, Teheran, Iran.
+ 4fi x i
{w,(NO;)
- $([NO;;efj)),
w
13’1
where the drfferences m zero-pomt energres of NO; and (NO,;d] are mtroduced and the energres of the systems refer to the equrhbnum structure of each. if the geometry of NO; is srgrzzfic~~tly modrfied by positron attachment, then the force field and fundamental frequencres, wi, will change and the correctron term may be notrceable. More rmportanrly, however, IS that ngnificant geometry changes wrll shift the potentral surfaces relative to one another and hence the difference in the first two terms, each taken at its equrlrbrnm~ geometry, will be changed relative to the case when the geometry of both systems are taken as that of the mttral system, e g. [NO; ; e* J _Schrader and Wang [ 11 suggest srgnifrcant mfluence of the structural detads in the capture of a posrtron or Ps by NO; and NO; or NO1 and NO,, respectrvely Our prehmmary studres do not confirm their suggestions, but this matter is drscussed fully in the complete study of these systems mcluding the angular correlatron curves Needless to say, the adrabatrc versus vertical Ps affimty afso needs consideration m any further study. It is easy to beheve the (PAjmrr 1s a posrtrve quantity smce one expects l~co,(tNO~;e~]
)I > IE,JNO;)I.
so that very likely (PAj,tr- B PA. In the present we use the srmpler eXpresston BE = EA + (PA),,,
15 May 1980
CHEMICM. PHYSICS IJXl-ERS
Volume 77, number 1
- 6 80,
(51 note
(6)
with an “unbalanced” treatment of the two systems mvolved. Hartree-Fock vertical iornzation potent&s are generally S-105 m error rf a fully relaxed L??,+F result is used. Sometimes Koopmans’ theory iomzatron potent&s are better as reorganizatton and correlation effects may tend to cancel one another. EIectron affiitres, on the other hand, are notoriously bad at the Hartree-Fock Ievel. In an earlier work, Cade and Farazdel [3] have argued that the accuracy of positron affmtties IS comparable to romzatron potentials on the basis of consrderatton of parallel PAS of hahde rons and IPs of alkalr atoms, e.g. conjugate [Cl-;e+] and IK*;e-] systems(abo see re!ated work by Kurtz and Jordan f4) ). In addrtron, proton affinities are also usually reliable even at the Hartree-Fock level. Hence, we submit that, until contrary evidence appears. our calculated posrtron affinities are accurate to w&in S-IO% If thus is true and iF(PA&,F < PA, rt might be suggested that (PAjcorr is roughly lo-ZO%, at most. oF(PA)~P. These very quahtatrve estimates may be useful in our stabrhty arguments. On the contrary, drrect calculation of the l&affinity, BE, IS perrlous from only Hartree-Fock results. The new mformatron presented here are positron affinrties of the NO; (II = 2,3) systems. These calcuIattons are Hartree-Fock-Roothaan results employing Cartesian gaussian functions to represent the electronic and posrtronic orbitals, i.e.
mstead ofeq. (2b) so the resultmg BEs should tend to be underestimates A posrttve BE, calculated by eq (6), IS strong evidence for B stable [NO; ,ef] system even though tzu correlatron 1s incIuded in these HFR calculations. It must be pomted out there 1s no proof that the correlation energy of a many-partrcle
must increase 1~1th the number of particles although thrs IS a sensible expectatton. fn particular, the additron of an electron or a posrtron can conceivably affect the total correlation energy of the ion system so that (PAjHr- < PA, although rt seems most unhkely without special qualifications Benioff [2] has given an apparent example where the electron affimty of NO, appears to decrease (by half) when correlatron effects are mtroduced. Thts 1s a puzzling result, counter to most normal experrence, and rt seems more hkely that any reductron of PA (or E4) upon inclusion of correlatron IS due to artrfacts associated 132
(7) and
(8) where 01is summed over expanuon centers (here only on the N, 0 nuclei) and p and r run successively over basis functions on the ath center. The electron and positron basis sets are drfferent to allow for efficient calculatron and flextble dlstmctron between &(r) and G+(t,). A common basrs set is,of course, a less ffexrble altematwe. In both cases, Cartesian gausstans are employed here x,(r),
xp
3
xaybzcexpC--o-%
with fa f b + c) = const.
families
used. The actual
69
basis sets used and complete results wtll be pubhshed subsequently with angular correlatton curves and interpretive aspects. Essenttally, we have rehed on conventional methods to construct the electronic basis
functions and an extensive study [S] to generate posrtronic basis functions from positron/atom systems. For the results summarized here, the Snyder-Basch basis set [6] * is used for elections centered on N and 0 and a set consistmg of one s- and three d-type gaussrans for N and 0 for the pontron, for a total of 87 total variatronal basis functions_ These calculatrons yield the results for NOT, NO,, and [NO, ;e”] , [NO; ; e-1 summarized in table 1. As noted et and EHF are vutuahy identical and give PA = 3.43 (NOT) and 3.19 eV (NO;) which are used to consider the stabihty of [NOT ; e’] and [NOT ; e”] as summarized in fig. 1. In fig. 1, the shaded area around the NO, levels reflects uncertainty in the expenmental EA for the NO, systems and this shading reflects III the projected level of the [NO; ; e”] systems. Frnally, smce (PA)HF is hkely to be a lower lmnt to PA, the shaded regions around [NO; ;e+] due to * In these studres we do not seek to establish fundamental basis sets to use for the electrons, but instead use a welldefined DZ-level basts set. Alternattve DZ basts sets for the electrons gtve very stmdar results. See ref. [S] . Table 1 Summary of energy results for NOI;/[NOi;e+j Hartrce)
systems (m
a)
NO;
[NOz;e*) NO; [NO% e*l
-E-r
-em
b)
204.00674 204.13314 278.81178 278 92921
0 14418 0.33636 0.22747 0 40024
-e+ c)
0.12652 0.11749
a) These calculattons are for NO: and [NOr;d] wrth coordinates N(O.O.O),0, a (= 1 9743175,1.2481122.0) whrch is consistent
with f&-O)
15 May 1980
CHEMICAL PHYSICS LETTERS
Volume 72, number 1
= 2.332 bohr and L (ONO) =
115.4”. based on the structure of the NOT ion. The cat-
culattons for NO; and [NOz;e+] are for the planar geometry N(O,O,O), 0, a (-1.150855, f l-9933393.0), O3 (2 30171.0,O) Ghrch conforms to R(N-0) = 2.3017 bohr
and L (ON01 = 120”. b) em IS the orbrtal energy of the least bound occupied elec tron orbrtal. c) e, is the orbrtal energy of the most bound positron orbital (occupied) There were several (S-6) bound (vutual) pantron orbttals.
T-l-
-
N@,+z-+c-
N3_+Fs
-
NI)_+Ps
Rg. I. Stab&@ of [NO$;e*l and [NO;;e+l systems. Alfenergy values rn eV. The electron affmittes. EA. are shown with estrmated error bars (4%); these error bars are projected into “tentatrve” error bars for fNO,.e+f levels with the fatter shtfted downward assuming (PA)iF d (PA),,,,. We conjecture the error bars for [NO&e+] are useful to speculate on the effect of corrections to stabihty questtons!
A( EA) should probably be lower than as shown. As concerns the electron affiiitres of NO, and N03, the experimental values have shown significant dtfferences. For NO,, Mathur et al. [7] give a value of 3.68 f 0.2 eV, Ferguson et al. [8] report 39 f 0.2 eV, and most recently Davrdson et al. ]9] use 3.91 5 0.24 eV. Earlier values bracketed EA(NO,), Le. 2.68 eV < EA G 4.34 eV. The value near 32 eV seems consistent with most earlier work (including even a lattice calculation). It is generally known that EA(N03) > EA(NO,), but there are several recent experimental results for EA(N02). In chronologkd order, Nalley et al. [ 10) summarize values for EA(N02) prior to 1973 and give a value of 2.5 t 0. I eV, Richardson et al. [ 111 follow closely with a value of =2.8 eV, and then Herbst et al. [ 121 report 2.36 f 0.10 eV. The spread in the electron affiities is not large, AEA(N03) = O-2-0.3 eV and AEA(NOZ) = 0.2 eV, but this spread may be significant in the present study. We are here ignoring any differences between vertical and adiabatic electron affinities strictly speaking we should employ adiabatic EAs (as well as adiabatic PAS). These results show convincingly that [NO;;e+] is a stable system relative to NO; f e+ and NO, f Ps (although other dissociation channels are possible). 133
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CHCMICAL
PHYSICS
Ir appears that the uncertamty in the experimentd EA for NO3 cannot reverse this srtuatton - 1-e. vertical versus adiabatic EAs or geometry changes with posttron detachment. The bmdmg energy, BE. for [NO, .e’] IS > 0 3 eV. Schrader and Wang [ I] have prevrously constdered the stabrhty of PsNO9 [NOT ;e+] ~13 an approwmate CSDO molecular orbital approacir and they report a substantrally larger value (2.83 eV). Whtle the present results seem to conclusrvely establish the [NO; ;ef ] IS a thermodynamrcally stable gas phase entity, It IS hkely that the binding energy can be as much as 1 eV larger than our minimum of 0.3 eV - the larger value of Schrader and Wang may, however, be unreasonably high. Parallel results do not show [NO,;e+] to be stable relattve to NO2 + Ps. This does not mean it is necessanly proved unstable, tt merely means that (PA),,, must overcome the deficit of -0.9 eV. This IS not unpossrble, but does suggest that If [NOi;e+], or PsNO?. IS stable the bmding energy IS small. If our rough estimate that (PA),,, < 0.2PA then correlation could only add an addttronal0 7 eV whrch IS madequate to stabrlize [NO,;e’] _Only structural changes offer any other posstbrhtres to stabthLe thrs system. Schrader and Wang [I] report a value of 1.95 eV as the binding energy of Ps to N02. In summary, we suggest [NO, ;e+] IS stable relattve to NO3 + Ps by at least 0 3 eV and probably more, and cannot definttely say that [NO, ; e”] IS stable rel~twe to NO2 + Ps. These results may be a useful guide m constdenng aqueous solutions of NOT and NOT and thetr propenstty to capture a positron and form a stable entrty (not stable, however, to positron annihilatron). but stgnificant solvation effects cannot be Ignored [ 131. Fmally, due concern IS necessary to explore any structural dependency on these results Further study on these systems IS in progress addresstng these and interpretive problems. One should not overlook the possrbihty that mtrate ions added to a solution to serve as an electroil scavenger may also
134
LETTERS
15
May 1980
scavenge for positrons and contribute a characteristic feature to hfetimes and angular correlattons*. We have been supported m part by a grant from the National Scrence Foundatton (NSF-CHE-7708542). Generous support has also been provided by the Umversity Computmg Center, University of Massachusetts.
l
Thu has been pomtcd
out III expenmental work by J Ch. AbbC et al and 0. hfiigensen tn recent and forthcommg publtcations (prtvate communtcatron)
References D hl Schrader and C.M. Wang, J Phys. Chem 80 (1976) 2507 P A Bcmoff. J Chem Phys 68 (1978) 3405, Theoret Chum Acta 48 (1978) 337 P E Cade and A. Farazdel. J Chcm Phys 66 (1977)
2598 H A Kurtz and K D Jordan, J Phys B 12 (1979) L473. J. Chem. Phys 72 (1980) 493 P E Cade and A Farazdel, The Electrontc Structure of Posttron/hlolecule Systems. I. General Formulatron and Basks Set Development for Molecular Systems, to be submrtted for pubhcatron L C Snyder and H Basch, hlolecular wnvefunctrons and properttes (Wiley, New York, 1972) table 1, pp 22-27. B P Mathur, E W Rothe, S.Y Tang, K MahoJan and G P Reck, J Chem. Phys 64 (1976) 1247. E E Ferguson, D.B Dunkm and F d Fchsenfeld. J. Chem. Phys. 57 (1972) 1459 J A Davrdson, F C Fehsenfeld and CJ Howard, Intern. J Chem Kinettcs 9 (1977) 17. [ 101 S 1. NaBey, R N Compton, H C. Schwender and V E Anderson, J Chem Phys. 59 (197314125 1111 J H. Rrchaadson, L hl Stephenson and J 1 Brauman, Chem Phys. Letters 25 (1974) 318. J Chem 112 E Herbst. T A Patterson and W C. Lineberger, Phys. 61 (1974) 1300. t13 1 P-E. Cade and C -hl. Kao, Solvated Positron Chemtstry; Effects of Solvatron on [F-;e*] Systems in Tetrahedral and Octahedral Solvent Sttes, to be submitted for pubhcation