J. Phys. Chem. 1994,98, 6967-6971
6967
Rydberg-like Ground States of H[ 11 11-Cryptate and H2[ 1111-Cryptate: An ab Initio Study R. C. Boehm,*vt**vfR. J. Rencsok,+***# J. F. Harrison,+*#and T. A. Kaplan**i Department of Chemistry, Department of Physics and Astronomy, and Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824 Received: January 14, 1994; In Final Form: March 4, 1994"
The electronic structures of [ 11 11-cryptand, H+[ 11 11-cryptate, H [ 11 I]-cryptate, Hz2+[11 11-cryptate, and H2[11l]-cryptate {cl11, H + c l l l , H c l 11, Hz2+c111, and Hzcll I} have been determined previously using a self-consistent-field method (HF) featuring a split-valence basis (6-31G) augmented with diffuse functions (L). In this report we focus on the unusual electronic structure of the Rydberg-like states of H [ 11 11-cryptate and H2[ 11 11-cryptate. These correspond to the C3 minimum of the singly complexed cryptate and a C3h minimum (labeled in-in) of the twice protonated cryptate. Density difference plots are used to illustrate that the ground electronic state of H c l l l and the low-lying excited state of Hzcll 1 (in-in) are highly diffuse in character. Further, the trace of the polarizability tensor of ground-state H c l 11 is 3 times larger than that of a geometrically larger, higher-energy isomer with an encapsulated, intact H atom. The Fermi contact term a t the internal hydrogen of the low-energy, C3 isomer of H [ l 1 11-cryptate (0.0005 au) is dramatically reduced compared to free hydrogen (0.30 au).
Introduction
clll
Cryptands and crown ethers are two known classes of materials which can serve as basis molecules for electride and alkalide The alkalides are ionic salts of the form ((M+))M-, where the parentheses represent saturated covalent molecules that shield the cation. The electridesare believed to take a similar stoichiometry: ((M+))e- with the electron assuming the role of the anion. These can be either insulating or conducting. The insulating electrides are Mott-type insulators where the least bound, localized electrons are believed to reside in the interstitial cavities of ((M+)) crystals (hereafter called traps) that are connected to each other in space by narrow channels. In the conducting class of electrides these channels are In this paper we report the electronic structure of several states of the isolated cryptands Hcl 11 and Hzcl 11. Although neither of these has been shown to form an electride, we believe their electronic structure will be pertinent to that of known solid electrides. The rest of this paper is structured as follows. In the results section we introduce a host of visual and numeric data for the Hcl 11 and H2clll systems based on our calculationsand analysis, as well as a narrow range of discussion and conclusions which are directly relevant to the data. The discussion section contains a summary of what we have learned from all of these investigations, relates it to previous studies, and presents conclusions that are relevant to the known electride systems. The main points of this paper are introduced here: (1) Isolated Hcl 11 and Hzcl 1 1 molecules form Rydberg-like ground states (as found4.5 for Li(9-crown-3)2), which we believe is a unifying characteristic of electride basis molecules. (2) The main weight of the Rydberglike electron distribution in these molecules is external to, and situated at the end(s) of the molecule. (3) We find that the HOMO distribution is highly polarizable, which supports our previous assertion4J that the idea of trap-localized electrons in theelectrides is reasonable. (4) The Fermi contact density at the chelated center(s), as well as the hypervalent (nitrogen) center@), is very small, and the total integrated spin density within the cryptand is extremely small (as found495 for Li(9C3)~). A summary of our analysis is presented in the conclusion section, Department of Chemistry. Department of Physics and Astronomy. I Center for Fundamental Materials Research. @Abstractpublished in Aduunce ACS Absfrucfs, April 15, 1994.
0022-3654/94/2098-6967$04.50/0
&71 I
\ H22+~lll
H+clll/
\
Hzclll
Hclll
cpo 0.69 )
l'O')clll+H
0.13j-
fmm-
1 ' 6 1 3 L 1 1
Figure 1. Relative energies diagram (in electronvolts). The reference state is {2H++ 2e- + cll 1). The letter R refers to "Rydberg-likestate", and the letter v refers to "valence-like (or regular) state". All of the tick marks are drawn to scale except for those corresponding to the double proton affinity of cl 1 1. and an explanation of the methods we used to obtain our results is presented as an appendix.
Results There are two isomers of c l 11 (C3and C3h)which are essentially degenerate at the H F level.6 The electronic properties of the C, isomer of c l 1 1 are included here as a reference for each of the cryptates because this isomer is most closely related to the groundstate structures of H+cl 11 and Hcl 11. In Figure 1 we show two energy diagrams representing the single and dual protonation processes along with thecorresponding reductions of the respective cations. The total energy of the C3 minimum of c l 1 1 is set equal to zero, and the total electron density of c l 11 is calculated at a geometry that matches the crypt portion of H + c l l l . The equilibrium structure of H+cl 11 contains one nitrogen atom that is clearly skewed inward, while the other nitrogen resides approximately in the same plane as its three nearest carbon 0 1994 American Chemical Society
6968
Boehm et al.
The Journal of Physical Chemistry, Vol. 98, No. 28, 1994 TABLE 1: Cage Boundary Distances I 5 species isomer Roo143 RNNI~ (.&)*6
a)
I
clll
I
.
0 0
40
23
i3
m
20
0 0
1
2
3
4
5
R, Distance From Internal Proton (aJ
R, Distance From Internal Roton (a,) Figure 2. (a) Electron density of H+cl11, sphericallyaveraged about the internal proton. (b) Electron density of H+cl 1 1 minus that of cl 1 1, spherically averaged about the internal proton. r is the spherically
averaged density (whether differential or total) times 47rRZ. The population P = Jfr dr.
neighbors6 (see Table 1). Protonation induces a 15% decrease in the dimensions of the crypt cage (which we define as a trigonal bipyramid with N atoms or 0 atoms a t each corner), and this final volume is too small to hold a hydrogenic 1s electron within its interior. The internal proton is found to be 1.02 A away from the inwardly skewed nitrogen and is bound by 11.8 eV relative to c l 11 plus a free proton. After examining the nature of the proton binding to the nitrogen, we found the following. There is a total charge of about l e located within 0.60 A, and 2e within 0.80 A, of the encapsulated proton (see Figure 2a), and there is little change in the total charge density (about 0. l e within 1 bohr, as seen in Figure 2b) in the region around the final equilibrium position of the proton before and after protonation. Lastly, we find that the sum of those diagonal density matrix elements that correspond to hydrogen 1s-like basis functions on the encapsulated proton (two such elements) is 0.25. These results taken together indicate that, upon protonation, the encapsulated proton essentially sits in a nitrogen sp3 lone pair orbital and that very little charge transfer from the crypt to the proton has occurred. That the proton acquires very little H ( 1s) character was surprising, but the data are clear in this respect. When we studied the diprotonated system, we found that the complexation of two internal protons induces a 20% reduction with respect to c l 11 in the volume of the crypt cage, so the final volume is again too small to hold a hydrogenic electron, or a H21+ electron. The equilibrium structure of H22+c111 is clearly
H+clll
in-in
in-out out-out in-out*
2.045 2.230 1.489 2.243
Rno
RnN
2.187 1.989 2.328 1.668 2.182 2.335
1.489 2.328 2.286 1.023 2.182 Hclll in-in 2.252 2.252 1.484 2.335 out-out 1.484 1.017 1.771 2.239 in-ut’ 2.166 HzZ+cl11 in-in* 1.844 1.942 2.067 1.008 1.008 Hzcl 1 1 in-in* 1.842 1.942 2.065 H2clll out-out 2.307 2.275 2.333 1.925 L1 All distances correspondto HF/6-3 1GLlocal stationary points. * The equilibrium structures of the starred isomers are employed in this work. puckered inward at each nitrogen? and each internal proton is attached to a nitrogen atom a t a distance of 1.01 A. The second proton is bound by 8.2 eV relative to H+cl 11 plus a free proton, nearly as large as the first proton affinity. Also, when one applies the same analysis to the second proton as we did for the first proton, to determine the nature of the binding, we find that a similar conclusion is reached, namely, that the protons are simply sitting in essentially undisturbed nitrogen sp3 lone pair orbitals. Although these results by themselves are interesting, and we will speak further of this in the discussion section, our main interest is with respect to the properties of the neutral species, as given below. The Once Chelated Isomer, H c l l l . The crux of this report is concerned with the properties of the neutral cryptates, H c l 11 and H2clll (in-in), but before we proceed with this discussion we must define a few terms. The terms “inside”, “on”, and “outside” describe the location of the odd electron of H c l 11. “Inside” implies that normal 6-3 1G orbitals, centered on the internal hydrogen, combine to form the HOMO. “On”implies that normal 6-31G orbitals, centered on 0, N, C, or external H atoms, combine to form the HOMO. “Outside” implies that diffuse functions comprise a dominant fraction of the HOMO and that the maximum in the radical distribution function is clearly external to the cryptand nuclei. The historically derived terms “in-in” and “in-out” refer to the nitrogen ends of the crypt.’ More specifically for this paper, “in-out” implies that one end of the crypt is puckered inward more so than the other and “inin” implies that the nitrogen lone pairs are pointing predominantly toward the center of the cage. Returning to Figure 1, we see that we found three different isomers, Cjh(R), C3h(v), and C, for the H c l 11 molecule (where “R” stands for a Rydberg-like electronic character and “v” stands for a valence-like {or regular) electronic character), and the C3 isomer has the lowest energy. The character of the electron distribution for each of these isomers is significantly different in that the electronic ground state of the Cj isomer has the HOMO electron exterior to the H+cl 11, while in the C3h isomer the HOMO is a hydrogenic 1s orbital inside the crypt and centered on the encapsulated proton. The C3 isomer is the lowest-energy isomer, and it is important to note that the C3h isomer has a significantly expanded cage since this illustrates that the character of the HOMO is sensitive to both electronic and geometric effects. We also note that relative to the separated H + c l l 1 energy the H c l 11 C3 system is bound by only 0.1 eV, while the C3h isomer is unbound by 1.0 eV. The overall effect, on the occupied MO’s of the H+cl 11 (here we will speak exclusively of the C3 ground-state isomer unless otherwise noted), of adding an electron to H+cl 11, while keeping its nuclei fixed, is relatively small. Similarly, the change in geometry induced by this electron is negligible. The adiabatic (allowing the H+cl 11 C3 isomer to relax following neutralization) ionization energy is found to be 1.9 eV. In Figure 3 we display an isosurface of the spin density of H c l 11 at its C3 equilibrium
Ground States of H[lll]-Cryptate and H2[11l]-Cryptate
The Journal of Physical Chemistry, Vol. 98, No. 28, 1994 6969
c
the HOMO density of Hcl 1 1 and could see no difference nt nitrogen, blue balls represent oxygen, and the little 1GL basis. (b) 6-31GL basis plus a set of (2) sptype
Figure 3. Spin density of Hcl 1 1, an isosu between it and the spin density. Color k balls (whether white or red) represen diffuse functions added to each nitro 0.13 0.11
0.09 0.07
Ll
0.05 0.03 0.01 -0.01
0
3
6
9
12
15
R, Distance from intemal H (G) Figure 4. Spin density of Hcl 1 1, spherically averaged about the internal proton. I' and P are defined as in Figure 2. The bases are defined as in Figure 3 (as well as the text). Points to the right of the dashed line include progressively more extrapolated information and are included only as a guide.
geometry. In each part, the illustrated isosurface bounds 50% of the odd electron; Figure 3a corresponds to the 6-31GL basis while Figure 3b corresponds to the 6-31GL+ basis, where the "+" indicates that diffuse functions ({ = 0.064 and 0.01) are also added to the nitrogens. Although the figures show some density on the internal hydrogen and the six carbon atoms that are closest to the "inn nitrogen, they clearly suggest that most of the spin density is "outside" of the crypt, and this conclusion is supported erically averaged radical proton. In this figure we see that ensity is located within 6 bohr (ao). calling the ground state of H c l l l at the additional diffuse ke little difference in the overall description of the . Another very important 11 is that it is concentrated over crypt. We have carried out
calculations of the polarizability on both the C3h and C3 states, and we find that the sum of the diagonal components of the polarizability tensor are about 3 times larger for the C3 than the C3,,ground state and of the same order of magnitude as the sodium anion, suggesting that the HOMO is very polarizable and has essentially no influence on the nuclear configuration of Hcl 11. Finally, similar to the Li(9C3)2 example,' we observe a dramatic reduction in the Fermi contact density a t the chelated center, relative to free a H atom. The Twice Chelated Isomer, Hzclll. We find that all the isomers of Hac1 11 are unbound with respect to the separated H2 + c l 11 components. The lowest-energy complex lies about 1.9 eV above the separated components and consists of a greatly expanded crypt with an intact Hz molecule inside (out-out). The next-lowest-energy isomer is Rydberg-like for both the singlet and triplet states, where the triplet state is 4.6 eV above the separated H2 + c l 11 components and has a vertical electron pair affinity of 6.3 eV. Similar to Hcl 11, we
course, zero ever
well as the lowestensity of the singlet is, of 5 we display the density of r that most of the 2e,in an ellipsoidal orbit
no influence on the geometry of the crypt.
6970 The Journal of Physical Chemistry, Vol. 98. No. 28, 1994
Boehm et al.
...........
Figure 5. HOMO density of H2cl 11 (spin singlet), an isosurface bounding le. Color key: same as Figure 3.
6-31GL)of Hzcl 11 (triplet), an isosurface bounding le. Note: we anticipate that the sum of the densities from the singly is essentially identical to the spin density; consistent with the results found for Hcl 11. Color key: same as Figure 3.
to Previous Results
molecule containin electron distributi
1 is of C3 symmetry, has the a nitrogen with a bond length of ectron in a diffuse orbital which localized around the end of the . A detailed analysis of the ternal proton shows that it is bedding effectively shields
the positive charge of the internal proton, which contributes to the unusual result that the spatial extent of the HOMO is very diffuse (Rydberg-like). A low-lying excited state of Hcl 11 has C3h symmetry and an intact encapsulated H atom centered in the plane defined by the three oxygens. In this isomer the unpaired spin density is entirely internal to the cryptand. The Hzcl 11 cryptand also supports two isomers with remarkably different distributions, both of which are unstable relative
Ground States of H [ 11I]-Cryptate and H2[ 1111-Cryptate
+
to separated H2 cl 11. The lower-energy isomer has an intact H2 molecule internal to the cryptand and has C3h symmetry. Approximately 2.8 eV above it there is an isomer consisting of two internal protons embedded in the N lone pairs and two electrons external to the cryptand cavity. The ground state of this isomer is a triplet in which the two electrons are on opposite sides of the molecule, as expected from the Hcl 11 results. The Rydberg nature of the ground state of H c l 11, coupled with the associated large polarizability, is intriguing and suggests that a crystal constructed from these molecules could have individual electrons trapped in interstitial cavities in much the same way as proposed by Dye for the observed electrides. We have recently studied the electronic structure of the isolated Li(9C3)~and found a remarkably similar situation. The ground state of this molecule is also Rydberg-like, with the diffuse electron essentially external to the encapsulating crown molecule. These similar results on ostensibly disparate systems support our intuition that a common requirement for electride formation is the ability of the host basis molecule to support a low-lying Rydberg-like electronic state.
The Journal of Physical Chemistry, Vole98, No. 28, 1994 6971 coordinate, for each species, and the spin density for H c l 11 in C3 symmetry was similarly derived. Total electron density differences were taken between (H+cl 11 and cl 11) and between ( H c l l l and H+clll ) , each having the crypt at the H + c l l l equilibrium geometry, and between (Hzcl 11 and Hz2+cl11) at the H 2 2 + 11 ~ 1equilibrium geometry. The isosurfaces we have shown are defined as follows: Let xg denote a value of density difference (n(r)). Then the locus of points with n(r) = xg is a three-dimensional isosurface. The value of xg is chosen so that
where f is either + l e or +0.25e, or
xg
is chosen so that
i(r)axo n(r) d 7 = -1 or -0.25 all space
Acknowledgment. This work was supported by a grant from the Center Fundamental Materials Research at Michigan State University. The electronic structure calculations were performed on the university’s Convex, Model C240, while the visualization work was completed on the group’s Ardent, Model 130. We thank the university for its generous allocation of resources.
In other words, each isosurface bounds some preset fraction (M) of an electron. If xg is positive, its isosurface is labeled as electron accepting. If xo is negative, its isosurface is labeled as electron donating. The value of xo is found by adding all elements within the (lOl)3 grid which have a value that is greater (or more negative) than x’, and x’ is parametrically varied until this summation yields the preset fraction. All properties were derived from the GAUSSIAN90 electronic structure package? and important visualization was achieved through a blend of AVS and in-house module^.^
Appendix
References and Notes
In this work we have taken three Hartree-Fock stationary points on which to base electronic structure determinations: H + c l l l and H c l l l (C3 symmetry), optimized with the 6-31G basis augmented by a pair of sp-type diffuse functions (exponents 0.036 and 0.0074 au) centered on the internal hydrogen (L), and HZ2+c111 (c3h symmetry), optimized with the 6-31GL basis. In this basis, the equilibrium geometry of the neutral species is nearly the same as their cationic cousins. Only vertical comparisons (Le., comparisons made between species with common geometries) are made, but small polarizations do remain evident. One might speculate that this residual polarization is related to a relative difference (between the neutral and the cation) in the gradient with respect to nuclear displacements. Electron densities were calculated, within the HF description, on a 14 X 14 X 14 A3 grid with 0.14-A increments in each
(1) Huang, R. H.; Faber, M.K.; Moeggenborg, K.J.; Ward, D. L.; Dye, J. L. Nature 1988, 331, 599. (2) Dye, J. L. Proceedings: Robert A. Welch Foundation Conference on Chemical Research XYXII VALENCY: R.A. Welch Houston. 1988: D 65. (3) Dawes, S.B.; Ward, D. L.; Huang, R. H.; Dye, J. L. J.’Am. Chem. SOC.1986, 108, 3534. (4) Rencsok, R.; Kaplan, T. A.; Harrison, J. F. J. Chem. Phys. 1990,93, 5Rl5 -. ( 5 ) Rencsok, R.; Kaplan, T. A.; Harrison, J. F. J. Chem. Phys. 1993,98,
9758. ( 6 ) Boehm, R. C.; Rencsok, R.; Harrison, J. F.; Kaplan, T. A., in press. (7) Dobler, M. Ionophores and Their Structures; Wiley-Interscience:
New York, 1981. (8) GAUSSIAN90: Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.;Baker, J.;Martin,R. L.;Kahn, L.R.;Stewart, J. J.P.;TopioI,S.;Pople, J. A. Gaussian, Inc., Pittsburgh, PA, 1990. (9) AVS: Stardent Computer, Inc., 1991. In-housemodules were written by D. Young.
