J. Phys. Chem. 1986,90, 3313-3319 associated with both matrix-isolated sF6 and SF, adsorbed on the surface of the cluster. The results suggest that for small Ar clusters an adsorbed SF6 molecule causes reconstruction of the cluster leading to an SF6 molecule surround by Ar atoms. However, as the cluster size is increased, stable surface sites are observed. This method is very appealing in that it provides a way of carrying out surface spectroscopy on molecular crystals. The problems associated with characterizing the surface of the cluster, to which the molecule is adsorbed, still need to be addressed. Finally, a word of caution is in order. Although there are obviously several areas where low-resolution spectra can be used to obtain useful information, it is the author's opinion that little can be learned from rotational band contour fits to low-resolution spectra unless considerable (although not necessarily completely resolved) rotational structure is present. Since the structure and rotational temperature of these species are not well-known, it is our experience that a fit of this type is not unique. For the case of Ne-C2H4 and Ar-C2H4considerable inhomogeneous structure has been observed by Casassa et al.69 and Liu et ales4 In both cases, convincing rotational contour fits have been reported. As pointed out by Boom et al.,98the far-infrared spectrum of van der Waals molecule probes, in a very direct way, the details of the intermolecular potential surface. Unfortunately, these early studies were not conclusive enough to allow an assignment of the spectium to be made. As indicated previously, two groups have developed techniques for observing far-infared transitions in van der Waals molecules formed under free jet conditions and with
3313
much higher resolution. At Harvard, Klemperer and c o - ~ o r k e r s ~ ~ used a far-infrared laser and stark tuning in conjunction with a molecular beam electric resonance apparatus to observe transitions in Ar-HCl associated with the van der Waals vibration. The same transitions have also been observed by Saykally and co-workersIm at Berkeley using intracavity laser absorption spectroscopy. Since a van der Waals bond tends to be very anharmonic, there is hope that overtone transitions will also be amenable to study so that the shape of the intermolecular potential can be mapped out in detail. Note Added in Proof. Baldwin and Watts (private communication) have recently observed fine structure in the 950-cm-I band of (C2H4)2 using a waveguide C 0 2 laser in conjunction with mass spectrometric and bolometric detection. Although these features have not been spectroscopically assigned, they do appear to place a lower limit of 10 ns on the lifetime of the dimer. How these results can be reconciled with the two laser saturation experiments is still unclear. With each new experiment, however, there seems to be more evidence for longer predissociation lifetimes, and therefore resolvable rotational structure, and less evidence for uniformly short predissociation lifetimes. Acknowledgment. The author thanks Professors G. Scoles, T. E. Gough, and W. R. Gentry for helpful comments on earlier versions of this manuscript.
SPECTROSCOPY AND STRUCTURE The Electronic and Geometric Structures of the Chromium Cations CrF', CrO', CrN', and CrC' James F. Harrison Department of Chemistry, Michigan State University, East Lansing, Michigan 48824-1 322 (Received: October 24, 1985; In Final Form: March 17, 1986)
The electronic and geometric structures of the title compounds have been studied by using MCSCF and CI techniques. In the following we note the term symbol of the predicted ground state, the calculated bond length (A), and De (kcal/mol): CrC+ (42-,1.74, 33); CrN' (%, 1.60,49); CrO' (411,1.63, 57); C r P (52+,1.76,73). The low-lying excited states of CrF' (511) and CrO' (42-)are estimated to be 14 and 6 kcal/mol, respectively, above the ground state of the molecule. The Mulliken population analysis suggests that the ligands all carry an excess negative charge ranging from 0.2 in CrC' to 0.7 in CrF+. While the bonding in CrN', CrO', and C r P involves various two-electron bonds between the Cr 3d orbitals and the ligand 2p orbitals, the bonding in CrC' involves a traditional double bond in the a system and a delocalized one-electron bond in the u system.
Introduction The experimental study of gas-phase, bimolecular reactions of transition-metal ions with organic and inorganic molecules is an active area of chemistry.' While the ion cyclotron resonance experiments of Foster and Beaucham$ pointed out the potential (1) Recent publications of the group currently active in this area include: (a) Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, 106,4403. (b) Peake, D. A.; Gross,M. L.; Ridge, D. P.J . Am. Chem. SOC. 1984,106,4307. (c) Jacobson, D. B.; Frieser, B. D. J. Am. Chem. Soc. 1984, 106, 4623. (d) Huang, S.K.;Allison, J. Organometallics 1983,2, 883. (e) Tolbert, N.; Beauchamp, J. L. J . Am. Chem. Soc. 1984, 106, 8117. (2) Foster, M. S.;Beauchamp, J. L. J . Am. Chem. SOC.1971, 93, 4924; 1975, 97, 4808; 1975, 97, 4814.
of such studies the more recent guided ion beam studies of Beauchamp, Armentrout, and co-workers3 are particularly noteworthy. The analysis of these experiments has resulted in accurate values for the bond energies3 of many species of the type M-R+ (M is a transition element and R is an atom or molecule) and is resulting in unprecedented insight into the gas-phase reaction mechanisms of transition-metal ions with various molecules. Unfortunately these experiments provide little structural (either (3) See for example: (a) Armentrout, P. B.; Beauchamp, J. L. J . Am. Chem. Soc. 1980,102, 1736. (b) Armentrout, P. B.; Halle, L. F.; Beauchamp, J. L. J . Chem. Phys. 1982, 76, 2449. (c) Armentrout, P. B.;Halle, L. F.; Beauchamp, J. L. J. Am. Chem. SOC.1981, 103, 6501.
0022-3654/86/2090-3313%01.50/0 0 1986 American Chemical Society
3314 The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 TABLE I: Correlation between the Molecular State of Cr-X+ and the Asymptotic State of X state of ligand orbital occupn molecular state ligand (X)
C
Harrison TABLE 11: Atomic Energies (in au) Used in This Work atom state SCF. au SCF+1+2,' au Cr+ 6S -1 043.113 54 -1043.15458 F 2P -99.409 17 -99.50510 -74.87052 0 'P -74.81043 N 4s -54.40033 -54.42388 -37.75953 C 'P -37.70463' "All SCF+l+2 calculations use one reference configuration. In addition, for Cr+only the 3d electrons are correlated; for F, 0, and N only the 2p electrons are correlated; for C the 2s and 2p electrons are correlated. 'The C SCF energy corresponds to a two-configuration SCF calculation in which the near-degeneracy on carbon was included.
like a carbonyl approaching a transition-metal ion. On the other hand, if 0 approaches in the m = f l state, (on the 411curve) we can also form a double bond but this time we have one u and one K component. Our goal in this work is to determine the bond energy of these various molecular states and characterize their electron distribution.
electronic or geometric) information. The purpose of this note and others in this series4 is to use a b initio electronic structure theory to provide insights into the electronic and geometric structures of representative transition-metal-containing cations. We believe these insights, when coupled with the experimental ICR and guided ion beam data, will enhance our understanding of these increasingly important species. The specific systems studied in this note are the diatomics CrF+, CrO+, CrN+, and CrC'. Even though there are few experimental data3q5for these molecules we feel it is essential to understand the bonding and energetics in series such as these so as to build a theoretical data base for future work.
Preliminaries The ground state of Cr+ is of 6S symmetry and arises from the configuration (argon core) 3d5 or simply 3d5. The first excited state is of 6D symmetry, lies 35.1 kcal/mol above the ground state: and arises from the configuration 4s3d4. The vbrious molecular states which result from the interaction of the ground-state Cr+ with the ground state of the atoms C, N , 0, and F are collected in Table I. The spin multiplicities shown are the lowest possible and are those appropriate for the formation of the largest number of chemical bonds (singlet coupled pairs). For example, the 32state of CrN+ corresponds to C w N + , i.e., a formal triple bond between N and Cr with both unpaired electrons on Cr. The 'I;state corresponds to Cr-N', Le., a single bond between Cr and N with four unpaired electrons on Cr and two on N. We assume these high-spin states have a higher energy and do not consider them further. Note also the interesting spatial options available, for example, to 0. If 0 approaches in the m = 0 state (on the 42-curve) it can form a double bond (in the ?r system), but since the Cr 3d, orbital is occupied it cannot form a conventional electron pair bond in the u system. Indeed, it looks very much (4) (a) Alvarado-Swaisgood, A. E.; Allison, J.; Harrison, J. F. J . Phys. Chem. 1985, 89, 2517. (b) Alvarado-Swaisgd, A. E.; Harrison, J. F. J . Phys. Chem. 1985, 89, 5198. (5) (a) Kent, R. A.; Margrave, J. L. J. Am. Chem. SOC.1966, 87, 3582. (b) Resch, G. D.; White, R. M.; Svec, H. J. Int. J . Mass Spectrom. Ion Phys. 1969, 3, 339. (6) Moore, C. E. "Atomic Energy Levels";NSRDS-NBS Circ. 35, 1971, VOl. 2.
Computational Details a. Basis Sets, Computer Codes, ... The basis sets for Cr and C used in this study have been described p r e v i o ~ s l y .The ~ ~ N, 0,and F basis sets are the 11s 7p Duijneveldt' functions contracted to 4s,3p following Raffenetti* and augmented with a single d polarization function with exponent 0.8,0.85, andQ.9 (respectively) as recommended by Dunning and Hay.9 For convenience we collect in Table I1 the SCF and SCF+1+2 energies for Cr', F, 0,and N. For Cr+ only the 3d electrons are correlated while for F, 0, and N only the 2p are correlated. The carbon S C F energy reported in Table I1 corresponds to a 2 configuration SCF function in which the near-degeneracy'O effect is considered. The carbon SCF+1+2 energy corresponds to all singles and doubles from the carbon 2s and 2p electrons when the single S C F reference configuration and the orbitals for the two-configuration S C F calculations are used. This was done to be consistent with the CrC+ molecular calculations. All calculations were done on a FPS-IM jointly supported by the Michigan State University Chemistry Department and the Office of the Provost by using the Argonne National Laboratory collections of QUEST-164 codes. In particular, the integrals were calculated by using the program ARGOS written by Pitzer," the S C F and MCSCF calculations used the GVBW program by Bair', and the UEXP program and related utility codes written by Shepard.I3 The configuration interaction calculations were done with the program UCI (and its related utility codes) written by Lischka, Shepard, Brown, and Shavitt.14 b. Wave Function Construction. Consider first, the CrF+ molecule. The asymptotic form of the %+ wave function is [u(Cr)u(F) + u(F)~(Cr)]2p~3d,~3d,~3d~+3d~ where the singly occupied d orbitals have ct spin. In this and in subsequent discussions we will suppress the Ar core on Cr and the ls22s2orbitals on F. These are, of course, included in the calculation. As the two atoms approach one another the character of the u bonding orbitals evolves from the pure atomic 3du,2p, to that appropriate for the molecular environment. A wave function of this form in which the orbitals are optimized and which separates to the proper SCF atoms consists (in C,, symmetry) of seven-configuration state functions (CSF's),13 and results in the (7) Duijneveldt, F. B. IBM Technical Research Report No. RJ-945; IBM Research Laboratory, San Jose, CA, 1971. (8) Raffenetti, R. C. J, Chem. Phys. 1973, 58, 4452. (9) Dunning, Jr., T. J.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer 111, H. F., Ed.; Plenum: New York, 1976; Vol. 2. (10) Clementi, E.; Veillard, A. J . Chem. Phys. 1966, 44, 3050. (1 1) The ARGOS integral program was developed by R. M. Pitzer (Ohio State University). (12) The GVB164 program was written by y. Bair (Argonne National Laboratory). ( 1 3) A description of the UEXP program is given in: Shepard,R.; Simons, J.; Shavitt, I. J . Chem. Phys. 1982, 76, 543. (14) Lischka, H.; Shepard, R.; Brown, F. B.; Shavitt, I. In?. J . Quantum Chem. Symp. 1981, I S , 91.
The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 3315
Structure of Chromium Cations +IO
-
=
L
9.0 10.0 R K r -F Nau)
2.0
-10
-20
all single and double excitations from the 7-CSF MCSCF reference space and consists of 72482 CSFs. The CI labeled SDCI* contains the configurations present in the SDCI except that no excitations are permitted from the Cr+ 3dA+and 3dL orbitals, resulting in 48 975 CSF's. The POLCI's contains the configurations present in the SDCI with the restriction that no more than one electron may be in the virtual orbital space in any CSF. The POLCI contains 5540 CSFs. Note that the potential curves reported in Figures 1-4 are all relative to the molecular energy calculated at a separation of 20 au and although the SDCI results in the lowest total energy, the difference between R = 20 and R a t equilibrium is larger for the POLCI. For convenience the relevant total energies calculated for C r P , as well as CrO', CrN+, and CrC+ are collected in Table 111. The wave function for the 511state is constructed in a similar way. The asymptotic form is
-30
[ry(Wry(F)
-40
Cr Ft - 50
- 60 h
0"
411y
-?O
+
[u(Cr)u(O) u(O)u(Cr)] X [ry(Cr)ry(O) + .ny(0)~,(Cr)12PE3d,3d~~3dL
The MCSCF function of this form which allows all spin couplings and which separates to the S C F atom consists of 34 SCF's and results in the potential energy curve labeled MCSCF in Figure 2. The SDCI, SDCI*, and POLCI functions were constructed as described for CrF+. Note that this means that the SDCI* correlates both the u and r orbitals involved in the bond as well as the 2p, and 3d,, electrons. The wave function for the 42-state of CrO+ was constructed in a similar way and required 68 CSF's at the MCSCF level, 120932 at the SDCI* level and 16 196 C S F s at the POLCI level. When N(4S) approaches Cr+ (%) only 2- states are possible and the low-spin (triple-bonded) state has 32-symmetry and is represented by
- 80
- 90
-100
32-
-110 -pocCl
SDCI (
(5n)(CLOSED TRIANGLES)
P+)(OPEN CIRCLES)
SDCI*(~PVSOLID CIRCLES)
120
- I30
-140
where, at large separation ry(Cr) is the 3d, orbital and ry(F) is the 2p,. The MCSCF function used in this case allows the molecule to separate to the proper S C F atoms and permits all occupancies and spin couplings to the three electrons in the 2p, and 3d, as well as the three in the 2p,,3d,. This requires 28 C S F s in C, symmetry. Since this state was higher in energy than the ?Z+ the only CI constructed was the POLCI which included 8494 CSFs. The wave-function construction for CrO' and CrN' proceeds in a similar fashion. When O(3P) approaches Cr+(%) both 2and II states are possible. The ll state admits a two-electron bond between the Cr 3d, and 0 2p, orbitals and if one allows for a bond between the 3d, and the 2py the molecular state has 411ysymmetry and is represented schematically by the function
-
r
2
Y
+ ~y(F)~y(Cr)12P~3d,2P~~d~~3d*+3d,,3d,
U
Figure 1. Binding energy of C r P in the IE' and 511states as a function of internuclear separation for various levels of calculation.
potential energy curve labeled MCSCF in Figure 1. Using the molecular orbitals generated in this MCSCF function we constructed several configuration interaction (CI) wave functions and in each CI no excitations were permitted from the argon core of Cr and the ls,2s orbitals on F. The CI labeled SDCI includes
-
+
+
[u(Cr)u(N) u(N)a(Cr)] [ry(Cr)ry(N)+ r y ( N ) ry(Cr11 [ * X ( C ~ ) ~ X+(rx(N)r.x(Cr) ~) 13dA+3dL
A MCSCF function of this type which allows all spin couplings separates to the proper S C F atoms consists of 126 CSF's and results in the MCSCF potential energy curve shown in Figure 3. The SDCI* and POLCI results were determined as described for CrF'. In the field of the Cr+ ion the 3P carbon atom has 32-or 311 symmetry, which when coupled to the 6S state of Cr+ gives rise to the low spin 42-and 411 molecular states. MCSCF wave functions which permit CrC+ in these states to dissociate to Cr+ at the SCF level and C(3P) correlated at the near-degeneracy level and allow all spin couplings among the active orbitals were constructed for both states. In particular the 42-MCSCF function consists of all CSF's possible (342 in C, symmetry) when one allows three electrons in the u system (2s, 2p,, and 3d,), two electrons in each of r, and ry (2p,, 3d,,) and (2py, 3d J, with the 3dA, and 3dL singly occupied. The 'IIY MCSCF Lnction consists of all C S F s possible (168 in C,,symmetry) when one allows four electrons in the u (15) Hay,
P. J.; Dunning, Jr., T. H.J. Chem. Phys. 1976, 64, 5077.
3316 The Journal of Physical Chemistry, Vol. 90, No. 15, 1986
Harrison
TABLE III: Molecular Energies (in au) Used in This Work MCSCF
POLCI
SDCI*
SDCI
molecule
state
R,
R = 20 au
R,
R = 20 au
R,
R = 20 au
R,
R = 20 au
CrF' CrO+ CrN' CrC'
%"
-1 142.6060 -1117.9683 -1097.5667 -1080.8492
-1 142.5226 -1117.9239 -1097.5139 -1080.8180
-1 142.6629 -1118.0284 -1097.5999
-1 142.5237 -1117.9252 -1097.5139
-1 142.7558 -1118.0907 -1097.6272 -1080.938 1
-1142.6330 -1117.9988 -1097.5526 -1 080.8861
-1 142.7741 -1118.1147 -1097.6553
-1 142.6571 -1118,0233 -1097.5777
4n 'Z-
42-
'Or
+I0
-
I 1 1 1 I 0 20 1 . 0 4.0 5.0 6.0 ICSCF( 1-1
70 8.0 9.0 1.0 I
/
1
I
l
l
R(Cr-NXau)
-10
- 20
-30
CrN'
- 40 - 50 ( 3 1 - ) ( 0 P E NCIRCLES)
- 60
-70
r
POLCI (4n)
-100
-
- 80
i JI"
POLCI ( 3 1 7
I
J
Figure 2. Binding energy of CrO' in the 411and 42-states as a function of internuclear separation for various levels of calculation.
- 9c
system (2s, 2p, 3d, and 2p), two electrons in the ?r orbitals (2p, 3d), and one each in the 3dA+,3d,, and 3d, orbitals. Note that all spin couplings, including the spectator orbitals, are included. The SDCI configuration lists generated- from these MCSCF reference spaces were too large for our computational facilities. Consequently, the SDCI* function for 411 was generated from the 84-CSF list obtained by allowing two electrons in each of the pairs (2s, 2py), (3d,, 2p,), and (2px, 3d,,) while keeping the 3d,, 3d,, and 3d, singly occupied. The SDCI* functions for 48- was generated from the 68 CSF configuration list obtained by keeping three electrons in the pair (2s, 3d,), two each in the 2p,, 3d,, and
Figure 3. Binding energy of CrN+ in the '2- state as a function of internuclear separation for various levels of calculation.
2pyzand one each in the 3d,, 3d,. While this 68-CSF list would allow the 42-state to separate to the S C F atoms the orbitals used for the SDCI* calculation (on both the 42-and 411 states) were those obtained from the larger MCSCF functions. This ensures that the CI calculations treat the near-degeneracy on carbon properly. c. Observations on Size Consistency. From Tables I1 and 111 we see that every calculation reported is size-consistent1' to within
The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 3317
Structure of Chromium Cations t6
2.00
1.8 1.7 -
1.9
1st I.4
1.3 1.2 1.1
z
1.0
0
Q 0.9 J
3
a 0.a 0 a 0.7
0.6 0.5
Figure 4. Bin1-...g energy ( CrCt in the 42-and 411 states as a .-netion
0.4
of internuclear separation ir various levels of calculation.
a millihartree or two. This is apparent for the MCSCF, SDCI, and POLCI calculations from the tabulated energies. That the SDCI* is also size-consistent is easily seen by noting that this particular level of C I differs from the SDCI only in that it keeps the spectator Cr+ orbitals (dL and d a singly occupied and thus correlates only three of the five Cr+ d electrons. If one calculates the SDCI on Cr+ keeping these two electrons at the SCF level and thus correlates the remaining three electrons one obtains the energy -1043.12905 au. When this is used as the asymptotic Cr+ energy we see that the molecular SDCI* calculations are indeed (essentially) size-consistent. Note that the difference between this Cr+ energy and the SCF+1+2 reported in Table I1 is 25.4 mhartrees which is very close to the difference between the asymptotic SDCI and SDCI* energies reported in Table 111. Presumably, this approximate size consistency obtains because the single and double excitation CI, relative to the MCSCF reference space, includes triple and quadrupole excitations relative to the S C F function. These observations suggest strongly that the larger bond energies calculated with the POLCI technique are artifacts resulting from a differential bias toward the in situ atomic correlation energy. It seems likely that the De)s calculated from the SDCI are lower bounds and will increase with calculations which include a more extensive level of correlation.
Discussion Ground State. The ground states are calculated to be CrC+(4Z-); CrN+( Z-) ; CrO+(47r); Cr F+( Z ) +
For the last three molecules these states correspond to the ligand approaching Cr+ with a singly occupied p, orbital while for CrC+ (16) Mulliken, R. S.J . Ckem. Phys. 1955, 23, 1833, 1841, 2338, 2343. For a critique see: Nocll, J. 0. Inorg. Chem. 1982, 21, 1 1 . (17) Bartlett, R. J. Annu. Reu. Phys. Ckem. 1981, 32, 359 and references therein.
I O1
t
W I
I
I
I
I
1
I
l
I
I
I
2
3
4
5
6
7
8
9
10
R (Cr-X ) ( a d Figure 5. Electron population of the a-bonding natural orbitals of CrFt (%), CrO' (411),and CrN' (%-) obtained from the MCSCF functions described in the text and partitioned into their 3d, and 2p, components.
TABLE I V Bond Lengths (in %.)of Predicted Ground States of Cr-X+ for Various Levels of Calculation
molecule CrCt(42-) CrN+(%) ~ ~ 0 7 4 1 1 )
CrF'(?Z+)
MCSCF 1.712 1.590 1.641 1.765
POLCI 1.604 1.623 1.753
SDCI* 1.735
SDCI
1.610 1.637 1.763
1.602 1.630 1.755
the 42-corresponds to the C atom approaching with an "empty" p, orbital. The u bond between Cr+ and N, 0, and F involves the 3d, on Cr+ and the 2p, on the main-group element, and the electron population of these orbitals as a function of internuclear separation is shown in Figure 5 . While the limitations of the Mulliken population analysis16precludes detailed arguments based on these numbers it is clear that the extent of electron transfer in the u systems is consistent with the electronegativity of the ligand, being largest for F and smallest for N. A similar analysis of the electron transfer between the bonding orbitals of the T system reveals that the population of each of the N 2p, orbitals increases from 1.O to 1.07 while the population of the 0 2p, orbital increases from 1.0 to 1.19. These calculations suggest that we have an excess of 0.2,0.5,and 0.7 electrons on N, 0, and F, respectively. These
3318 The Journal of Physical Chemistry, Vol. 90, No. 15, 1986
Harrison
TABLE V De (in kcal/mol) of Predicted Ground States of Cr-X+ for Various Levels of Calculation
1.4
-
MCSCF 19.6 33.1 28.4 52.1
POLCI
SDCI*
SDCI
53.8 64.4 87.0
32.5 46.7 57.4 76.7
48.5 57.1 73.2
shift of electrons from C 2s to 2p, (hybridization) with a concomitant shift of electrons from the Cr 3d, to the developing sp hybrid on carbon. At equilibrium the singly occupied u orbital is 42% Cr 3d, and 45% carbon 2p, and 13% carbon 2s. The doubly occupied u valence orbital is dominated by the carbon 2s atomic orbital (83%) with the remaining 17% being predominantly in orbitals centered on Cr. The A system is slightly polarized toward the Cr with the Cr A orbitals hosting 2.07 electrons as opposed to carbon's 1.93. Qualitatively, the bonding in CrC+(4Z-) consists of a delocalized one-electron u bond and an essentially covalent A bond. In balance the carbon atom has approximately 0.2 excess electrons. Schematically we have
I I
I I
12-
molecule CrC+(42-) CrN+('Z-) cr0+(4n) Cr F+( 2')
I
0.4
3d +2p ="J A Y
02
Oo
I
2
3
4
5
6
7
8
9
1
0
R (Cr-CIau Figure 6. Electron population of selected atomic orbitals from the bonding natural orbitals of the 324 CSF MCSCF wave function for the 42-state of CrC+.
three states have the schematic electron distribution (Lewis structure) 2 2px
dal-
*- \,
C
1g
4
2 28
+2px
X
The bond lengths, bond energies, and vibrational frequencies are collected in Tables IV-VI. While the calculated bond lengths are not very sensitive to the level of calculation, the D;s certainly are. As one goes from CrC+ to CrF' the De increases for all computational levels beyond the MCSCF. Since the molecules CrC+, CrN+, and CrO' all have formal multiple bonds this trend in the DC)s reflects the importance of the ionic component in the bond. We anticipate similar results for the main-group elements C1, S, P, and Si interacting with Cr'. Excited Stares. The 42-state of CrO+ and the slIstate of C r F are characterized by the ligand having a formally doubly occupied 2p, orbital. CrO+ can form two A bonds while CrF can form only one. These states are represented schematically as
:p; / /
.\-A
C r
0:
2s
*+/ '
In Figure 6 we show the evolution of the electron population in the C s and p, and Cr' d, orbitals as a function of internuclear separation. As the two atoms approach one another there is a
A population analysis of the MCSCF functions at the calculated equilibrium separation suggests that the 2p, pair delocalizes somewhat (-0.2 e) into Cr orbitals (3d,, 4s, and 4p,) while the Cr d, electrons involved in the formal A bonds delocalize onto the ligand (backbond) to a much larger extent. In CrF+ the A bond
The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 3319
Structure of Chromium Cations TABLE VI: Vibrational Frequency (0,cm-I) of Predicted Ground States of Cr-X+ for Various Levels of Calculation molecule
MCSCF
POLCI
CrC+(4Z-) CrN+(%) cro+(4n) CrF+(%+)
719 893 822 758
898 907 770
TABLE VII: Bond Excited States molecule CrC+(4n) CrO+(4Z-) CrF+(Sll)
Lengths (in
SDCI* 726 902 899 763
SDCI 891 915 769
A) and De (in kcal/mol) for Selected
MCSCF 2.44117.9 1.655124.0 1.786138.2
POLCI
SDCI* 2.0591 13.4
CrF
69,' 71b 74,b 53: 77c
'Reference 5a. bReference 5b. cReference 3c.
is 80% on F and 20% on Cr while in CrO+ both Cr d, orbitals transfer 0.3 e to the 0 2p, orbitals. The population analysis suggests that, in both molecules, the C r loses -0.4 electrons to the ligand. Note that, although these states are not predicted to be the ground states, they are remarkably strongly bound. We estimate that the fluoride is 14 kcal/mol above the ground ?3+ while the oxide is only 6 kcal/mol above the ground 411. Note that this oxide ordering is the reverse of that predicted by Bauschlicher, Nelen, and Bagus'" for the neutral CrO where the (a 7r hole) was 14.5 kcal/mol lower than the %+. Interestingly, the 411state of CrC+ is significantly less bound than the 42- (by 19 kcal/mol a t the SDCI* level), and has a much larger bond length. In addition, a population analysis suggests that the u and a bonds are essentially covalent. The predicted bond lengths and De(s for these excited states are collected in Table VII. Comparison with Experiment. We collect in Table VI11 the literature estimates for the bond energies of CrF+ and CrO+. There are no data for CrN+ and CrC+. The Armentrout et al. value3c of 77 f 5 kcal/mol for CrO+ agrees with one of the two values suggested by Flesch et al.5b Taking the experimental value to be -76 kcal/mol we see that our calculated SDCI value of 57 kcal/mol is in reasonable agreement. The situation for CrF+ is a bit different. The available experimental values are essentially identical and suggest a 00 of -70 kcal/mol. From Table V we
-
(18) Bauschlicher, Jr., C. W.; Nelen, C. J.; Bagus, P. S.J . Chem. Phys. 1985, 82, 3265.
I
IP(CrF)
w
-
Cr
+ F
t
t + CrF
1.650f58.5 1.773172.6
TABLE VIII: Experimental Energies for Selected Chromium Cations molecule 00,kcal/mol CrP CrO+
see that this is smaller than the estimates obtained from all three levels of C I used in this study. In particular it is smaller than the SDCI value of 73 kcal/mol. Since it is not likely that this C I overestimates the bond energy we suspect the experimental value may be too low. For example, from the thermochemical cycle
> C r + F
we obtain the relation Do(CrF+) = Do(CrF)
+ IP(Cr) - IP(CrF)
Clearly if the measured IP of C r F is too large the resulting Do(CrF+) would be too small. It seems likely that the ground state of C r F will be quite ionic C:F-
r
or :{r.
AI
.i
:E
3 doubly occupied 2 p o r b i t a l s
L 5 unpaired d electrons
and the 2p electrons on F rather diffuse. When C r F is ionized it is likely that the electron will come from either a u or 7 orbital on F. If the ejected electron comes from a u orbital the resulting ion will be of ?Z+ symmetry, which is the predicted ground state of CrF+. If, however, the ejected electron is from the more spatially extended nonbonding F 2p, orbital the resulting state will be the excited 511. In our calculations this state is -14 kcal/mol above the ground ?Z+ state but we expect the experimental separation to be larger because differential correlation effects will favor the %+state. If in fact this separation is -20 kcal/mol and if the scenario as described obtains, then the dissociation energy of CrF+ would be -90 kcal/mol and our calculated SDCI value would be appropriately low. Additional experimental (e.g., a guided ion beam study of for C r P ) and more accurate theoretical estimates of the bond energies in these molecules would be useful. Acknowledgment. We thank Professor J. Allison for helpful discussions and the Theoretical Chemistry Group at Argonne National Laboratory for providing the QUEST-164 system. Registry No. CrF+, 2091 1-34-6; CrO', 56371-63-2; CrN', 8301797-4; CrC', 102436-40-8.
