6418
J. Phys. Chem. 1991, 95, 6418-6420
Electronic Structure of the Thermodynamically Stable Dlcation ScN2+ and Related
Molecules Kathryn L. Kunzet and James F. Harrison* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824- I322 (Received: June 3, 1991; In Final Form: July 10, 1991)
All diatomic dications AB2+, in which the second ionization energy of A is less than the first ionization energy of B, will dissociate to A2++ B and will, therefore. be thermodynamically stable. We discuss the electronic structure of ScN2+as an example of a molecule in this class.
Introduction
";1 1
Because the second ionization energy' of Sc (1 2.89 eV) is smaller than the first ionization energy of N (14.54 eV), ScN2+ and is, therefore, dissociates to the products S C ~ + ( ~ DN(4S) ) thermodynamically stable. Of course, any diatomic AB2+, where the second ionization energy of A is less than the first of B, will be thermodynamically stable? and ScN2+will be used to illustrate those aspects of electronic structure that we believe common to all molecules of this class. This condition is easily satisfied if A is a transition- or alkalineearth-metal element and B a main-group element, and we collect in Table I those diatomic dications containing a first-row transition-metal element that have this property' and in Table I1 thare diatomics containing an alkaline-earth-metal element. A similar collection could be constructed for the latter transition series, and Y and La are as rich as Sc. In the following, we will describe the electronic structure of ScN" as deduced from ab initio calculations. The basis set used for Sc and N and the electronic structure codes have been described3 previously.
+
Electronic Structure P"rk When S I ~ + ( ~approaches D) N('s), one can form triplets or quintets of E-,II, and A symmetries if the d electron on Sc2+is in a du, d r , or d&orbital. For the quintet states, there state is is one spin coupling, and the wave function for the 9generically 1?2-)
-
(core)2du pz px py aaaa
where the z axis is the internuclear line. This function describes the lon -range electrostatic interaction between N in its 's state and S& in the 2D state. In contrast, the triplet states contain a covalent spin coupling as well as an electrostatic coupling. The electrostatic component of the 32-state is (core)2 du pz px py [3@aaa- a(@aa+ a@a
14.0
.-C v
1
2.03
\1
ScN++
TRIPLET STATES
t c" E W
z
W
-10.0 -16.0
LL."
, 3.0
7.0
+
Figure 1. Potential energy curves calculated at the MCSCF + 1 2 level and 3A), which dissociate to the for the three triplet states (?Z-,
ground-state products Sc2+('D) + N ( 5 ) .
TABLE I: Diatomic Dimtioar Containlog a First Transition Sches Element Tbat WUI Be T~WIIW~YIU~~UIIY Stable
metal sc Ti V Cr, Fe, Co Mn Ni, Cu
+ cya@)]
main-group elements H, He, N, 0, F, CI, Ne, Ar, Kr He, N, 0, F, Ne, Ar, Kr He, N, F, Ne, Ar He, F, Ne He, F, Ne, Ar He, Ne
while the covalent component is (core)2(du pz
+ pz da) px py (a@ - @a)cya
We may represent these two couplings symbolically as
TABLE 11: Dirtomlc Dicrtioar ConbMog 80 Auuliac-Eutb-Metal Element Tbat Wlll Re Tbcrmod~lMicrllvStable metal main-nrouo elements Be He, Ne ~~~~~
1 electrostatic > = I S
/
s = 112 and
Deceased.
S = 312
C
~
~
Mg
Ca Sr Ba
~
He, F, Ne, Ar H, He, N, 0, F, Ne, CI, Ar, Kr H, He, C, N, 0, F, Ne, CI, Ar, Br, Kr H, He, C, N. 0, F, Ne, P,S,CI, Ar, Br, Kr
where the electrostatic component is obtained by coupling the Sc unpaired electron into the intact N quartet spin system, and the (1) Moore, C.E. Aromic Energy Lcucls; National Standard Reference Data Series; National Bureau of Standards: Washington. - D.C.. 1971; Vols. I, 11, and Ill. Circular 35. (2) Bauschlicher, C. W.; Langhoff, S. R. J . Phys. Chrm. 1991,95,2278. (3) Kunze, K.L.; Harrison, J. F. J . Am. Chcm. Soc. 1990, 112, 3812.
0022-3654/9 1/2095-64 18$02.50/0 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 6419
Letters
20.0-
-
14.0-
I
8.0-
I .-C v
2.01 -4.0/
W
z
W
-10.0 -16.0 ' 0 . 22 -
7.0
3.0
RSc -N(o.u.) Flgm 2, Potential energy curve8 calculated at the MCSCF + 1 + 2 level for the three quintet states (%-, Jll, and which dissociate to the ground-state products S C ~ + ( ~ + D )N(%).
covalent component obtains from singlet coupling one electron on Sc to one electron on N. In this notation, all quintets are Iquintet) = [electrostatic) and all triplets are Itriplet) = lelectrostatic)
Sc and the 2px, 2py, and 2pz orbitals on N will be active. Consequently, the %-, %, and 5A states are each represented by one configuration state function (CSF), the '2- and 'll by five CSFs, and the 'A by three CSFs. Subsequent to the MCSCF calculation, we performed a CI calculation in which all single and double excitationswere allowed from the MCSCF reference space. In the CI calculations, the N 2s orbital was active. The total energy, bond length, and vibrational frequency, along with the number of CSFs in the MCSCF and CI calculations, are reported in Table 111. The energies of the CI functions are shown in Figures 1-3. At large Sc-N separations, the energies of the triplet states (Figure 1) vary as 'A < 'll < 'Z-.This is the expected order if the interaction is electrostaticand the differential in energy is due to the coulombic repulsion between the Sc d orbital and the spherically symmetric N atom. As RscNdecreases, the 'A energy increases rapidly while the 'II and '6states continue to decrease. This is because in both the 311and 32-states, one is able to form a bond (the covalent coupling between 3ds and 2pr, and 3du and 2pu, respectively) and thereby offset the Pauli repulsion, whereas the 'A has no such option (the 3d6 orbital is orthogonal to all valence orbitals on N). It is interesting that the 311and 'Z7 states have very similar bond lengths and bond energies, suggesting that the single ?r or u bonds are equally effective in stabilizing the molecule. Although these two states seem to be forming a covalent bond, there is very little charge transfer at equilibrium. The population analysis for the valence orbitals in the 32-state at equilibrium is
+ XJcovalent)
Wave Function Construction. We will keep the Is, 2s, 2p, 3s, and 3p orbitals on Sc and the 1s and 2s orbitals on N doubly occupied in our MCSCF calculations, while the 3di orbitals on
sc++
N
Figure 3.
TABLE Ilk Total Energb,
Bond L.engths, Vibrational Frequencies, and the Number of Configuration State Functions (CSFs) Involved in the MCSCF and MCSCF + 1 + 2 Cdculrtiona on %N2+ MCSCF CI
state 32'A
CSF 5 5 3
srl
1 1
5A
1
'n
Jz-
E, au -8 13.49998 -8 13.50208 -813.50257 -8 13.494 05 -813.50046 -813.50326
4
3
kcal/mol 10.6 12.1 12.4 6.9 11.1
12.9
Re, A 2.524 2.448 2.535 2.794 2.576 2.5 17
cm-' 217 233 247 171 243 253
w,
CSF 18439 18430 17292 6854 6665 6493
E, au -813.611 76 -813.611 76 -813.61088 -813.60300 -813.609 14 -813.61 149
De, kcal/mol 12.3 12.5 12.0 6.9 10.9 12.3
Re, A 2.323 2.391 2.570 2.825 2.605 2.552
cm-' 178 202 234 168 234 239
w,
6420 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991
minimum will not be deep enough to replace the solvated species as the ground state. The potential energy curve around Re for the ‘E+state of ScN2+that traces its lineage to the ’F state of Sc+ and the ’P state of N+ is shown in Figure 4. Most remarkably, this state is bound relative to its asymptote. A population analysis of the associated MCSCF function reveals that Sc in situ is doubly charged, and N is essentially neutral. We believe this is a consequence of the low-lying asymptotic state S C ~ + ( ~+DN(2D), ) which is -0.7 eV above the Sc+(’D) N+(”P) asymptote.
95.0
50.0
+
35.0
Conclusions
20.04
Sc++pD)+ N(%)
- 10.0 -25.0 3.0
5.0
7.0
9.0
RSc - N(a.u*) N y 4. Comparison of the 32-state and the ]2+that separates to the Sc OD) + N+CP) products.
The quintets are shown in Figure 2. Since in these states the spin couplings preclude the formation of a covalent bond, the minimum energies are determined by the Pauli repulsion of the Sc2+d electron and the valence electrons on N , and the order < 511< 52-is maintained for all RScN.studied.Note that the 5A state, along with the ’Gand 311states, IS a contender for the global ground state of ScN2+. The increased stability of the versus the 5Gand the )lI versus the 511is seen in Figure 3. Since neither the ’A nor can form a covalent bond, they have very similar potential energy curves as shown in Figure 3. These results suggest that at equilibrium, ScN2+is essentially a dication of Sc solvated by an N atom. The basic reasons for this behavior are the low energy of the sc2+ + N asymptote relative to Sc+ N+ and the weakness of the ScN bond. The low energy of the Sc2++ N asymptote ensures that the solvated state is the lowest at large internuclear separations. The weakness of the ScN bond ensures that when the two cations Sc+ and N+ are high enough on the Coulombic repulsion curve to bond, the resulting
’&
+
Letters
There are many diatomic dications containing a transition- or alkaline-earth-metal element and a main-group element that are thermodynamically stable. The bonding in the low-lying states of these ions is expected to be primarily electrostatic, and consequently, the electronic spectrum involving these states should involve transitions to other electrostatic states. These higher states should be those of the main group element in the electric field of the neighboring dication or that of the dication slightly perturbed by its neutral neighbor. Interestingly, we have seen‘ similar behavior in CrNZ+. Even though at long range the Cr+ + N+ state is the lowest, the solvated state quickly becomes the ground state as the two cations repel one another. When a covalent bond eventually forms between Cr+ and N+, the resulting well is not deep enough to displace the solvated species as the ground state. Once again, the in situ structure is a doubly charged transition metal solvated by an N atom. Similar behavior is expected for many other dications, such as CaBr2+or SrP2+or TiH”, in which the symmetricallycharged asymptote is only slightly lower than the asymmetric asymptote.
Acknowledgment. We are indebted to the Argonne National Laboratory Theoretical Chemistry Group for providing the coLUMBUSelectronic structure codes used in this study. We thank Professor George Schatz for a helpful discussion on the possibility of electrostatic bonding in dications involving the alkaline-earth metals. This work was supported in part by the National Science Foundation (Grant No. CHE 8519752). (4) The Electronic Structure of the Dications ScNz+,TiN2+,VN2+,and CrNz+. Kunze, K. L., Harrison, J. F., in preparation.
