J. Phys. Chem. 1995, 99, 4941-4946
4941
Structure of PLi4 and Its Comparison with SiLi4, CLi4, and Li4: The Importance of Li-Li Interactions Zheng Shi, Jian Wang, and Russell J. Boyd* Department of Chemistry, Dalhousie University, Halifax,Nova Scotia, Canada, B3H 4J3 Received: August 9, 1994; In Final Form: December 5, 1994@
Ab initio calculations which include the effects of electron correlation indicate that Jahn-Teller unstable PLi4 has a CZ,,equilibrium geometry which is only slightly lower (less than 1 kJ/mol at the PMP4/6-311+G(d)//MP2/6-31 l+G(d) level) in energy than the T d structure. Comparison of the optimized structures of PLi4 and SiLi4 shows that the T d to C2,, distortion of SiLi4 leads to a larger reduction of the Li-Li distances than the corresponding changes in PLi4. Moreover, the Li-Li distances are greater in the T d structure of SiLi4 than in the T d structure of PLi4 whereas the converse holds for the C2” structures. These observations are explained in terms of strong Li-Li interactions which have been studied within the framework of the atomsin-molecules theory. The structure of PL4 is determined by a competition between Jahn-Teller distortions which favor a C2,, structure and Li-Li interactions and the valence-shell charge concentration around the phosphorus atom which favor the T d structure. Li-Li interactions play a dominant role in the determination of the structure of some hyperlithiated compounds.
Introduction Lithium compounds have attracted much interest from both theoreticians and experimentalists. As the closest congener of hydrogen, lithium has been considered to be a good candidate for forming bonds analogous to hydrogen bonds.’ Dicoordinate lithium centers have been demonstrated by numerous calculations (see, for example, the pioneering paper of Kollman, Liebman, and Allen2 and a variety of experimental studies. The first experimental proof for the existence of dicoordinate Li was obtained by Ault and PimenteL3 Lithium is not restricted to dicoordination. In fact, lithium forms metal clusters whose electron density distributions have been found to exhibit unusual topological properties. Electron density maxima usually occur at nuclei. However, electron density maxima in Li and Na clusters have also been found at positions other than n ~ c l e i . ~ These electron density maxima, known as nonnuclear attractors, behave as pseudoatoms.s The topology of the electron density reveals that the metal atoms are not linked directly to one another but only indirectly through an intervening pseudoatom. The conductivity and binding in such metallic systems is believed to be due to the network of pseudoatoms.s Furthermore, lithium compounds often form structures which violate conventional chemical bonding rules. A typical example is SiLi4 which has a Cz,,structure, unlike Si& which has a T d structure.6 The C2” structure of SiLi4 cannot be rationalized by either simple covalent or ionic bonding models. There are also a number of lithium compounds which violate the octet rule. Examples include Li30, CL4, and Li4F.’ The first experimental observation in the gas phase of hypervalent PLi4 was reported recently.* The authors assumed a T d structure for PLi4 in their statistical thermodynamics calculations, but they do not report or quote any direct experimental evidence to support their “estimated molecular parameters”. The experimental results, based on Knudseneffusion mass spectrometric measurements, show that PLi4 is stable with respect to PLi3 and Li. In view of the resurgence of interest in hypervalent phosphorus c o m p o ~ n d s ,and ~ the Jahn-Teller instability of a T d constrained PLi4, we report the @Abstractpublished in Advance ACS Ahstracrs, March 15, 1995.
0022-365419512099-4941 $09.0010
results of a theoretical study of the electronic and geometric structures of PLi4 and an analysis of the bonding in this interesting example of a hypervalent hyperlithiated molecule. We also compare the structure of PL4 with P&, CLi4, and SiL4, and with the Li4 cluster. Computational Methods Previous calculations on lithium compounds suggest that the basis set must be chosen carefully. For example, it has been suggested that the bond in CLi2’O is mainly ionic with little directional character and, therefore, the predicted geometry is very dependent upon the adequacy of the basis set of the negatively charged central atom. In this work we used the 6-31G(d) basis set,” the 6-311+G(d) basis setI2 in which a set of diffuse functions was added to the 6-311G(d) basis set of the phosphorus atom, and the 6-311+G(2d) basis set in which a set of diffuse functions and two sets of d orbitals with exponents equal to 0.275 and 0.755 were added to the 6-31 1G basis set of phosphorus. Geometries were fully optimized with the UHF, UMP2 (full), UMP4 (frozen core), and CISD (frozen core) methods by use of the GAUSSIAN 9013and GAUSSIAN 9214programs. Analytic frequency calculations were performed at the UHF and UMP2 levels. PLi4 is a Jahn-Teller unstable molecule with an open-shell electron configuration and therefore the reference configurations must be chosen carefully and precautions must be taken to minimize the effects of spin contamination. Because the electron configuration of the tetrahedral PLi4 radical may give rise to a degenerate electronic state, the multireference configuration interaction (MRCI) method is the preferred approach. Due to the size of the molecule we cannot include enough configurations to avoid the problem of size-consistency in the MRCI method. Consequently, we used the single determinant wave function from the unrestricted Hartree-Fock (UHF) calculations as the reference configuration. We tested the effect of the choice of the reference configuration by choosing various UHF configurations as the initial guess. We observed that the optimized geometries are not sensitive to the choice of the initial reference configurations for PLi4. For spin contamination, in their comparison of unprojected UHF and projected (PHF) wave functions, Rossky and K a r p l ~ s ’ ~
0 1995 American Chemical Society
Shi et al.
4942 J. Phys. Chem., Vol. 99, No. 14, 1995
TABLE 1: Optimized Structures of PLi4"
ti?) UHF
Td C?, Ci, c 4I
UMPZ(ful1)
Td Cz I c 4\
UCISD(frozen core)
Td Cz ,
PMP4(frozen core)
Td
C2,
UHF
Td
CZi
UMPZ(ful1)
Td
CZ,
PMP4(frozen core)h
Td
C2, UHF
Td
CZL
0.8 1 0.76 0.77 1.13 0.80 0.79 0.85 0.80 0.78 0.75 0.75 0.79 0.76 0.79 0.78 0.75 0.75 0.79 0.76
E(aui 6-3 1G(di -370.549 -370.553 -370.554 -370.507 -370.729 -370.731 -370.686 -370.708 -370.710 -370.733 -370.735 6-3 1 1+G(d) -370.584 -370.632 -370.933 -370.933 -370.777 -370.777 6-3 1 1+G(2d) -370.585 -370.588
RP-LII~I 61 96 02 90 90 38 74 35 00 50 37
2.292 2.25 1 2.249 2.323 2.264 2.263 2.25 I 2.278 2.265 2.284 2.288
88 34 56 57 14 25
2.274 2.238 2.250 2.245
71 51
2.273 2.237
LLi,,,PLi,,,
LLi,,,PLi,,,
2.355 2.316
123.3 130.3 73.0
72.3
2.285
167.4 90.0
92.0
2.305
167.6
85.6
2.31 1
176.1
89.5
2.33 1
124.6
73.5
2.263
166.7
90.4
2.330
125.1
73.5
RP-L~(~I
Bond lengths in angstroms, angles in degrees, and energies in hartrees. Energies calculated at the PMP4(SDTQ)/6-31I+G(d)//MP2/6-31 l+G(d) level.
showed that at the lowest order, the UHF results are better than the PHF results. Although spin projection projects out the spin contamination in the wave function, it causes some new problems within the Hartree-Fock framework. For example, additional terms are introduced into the UHF wave function by the spin projection procedure. These extra terms are in general unrelated to the exact perturbative corrections to the UHF state. The PHF wave function, energy, one- and two-electron density matrices, and spin densities have been shownI5 to be in error in the lowest order of perturbation theory, whereas the UHF state leads to the correct one-electron density matrix and spin densities in lowest order. Thus, the PHF result is not always reliable. Nevertheless it has been shown16 that the PMP4 method gives better reaction barriers and more accurate potential energy surfaces for bond dissociations than the UHF, PHF, and UMP4 methods. In this paper the theory of atoms-in-molecules of Bader et aL5 is used to study and rationalize electronic structures. The theory is based on the properties of the total electron density distribution, an observable physical property, rather than on those of a single molecular orbital, which is used as a matter of convenience to construct the approximate wave function. The Laplacian of the electron density distribution provides a direct picture of regions in space in which the electron density is concentrated and depleted. When VQ> 0, the electron density at the point in space is smaller than the average of the electron density at neighboring points and therefore the electron density is depleted. When VQ< 0, the electron density at the point in space is larger than the average of the electron density at neighboring points and the electron density is concentrated. The valence-shell charge concentration (VSCC), the location of which is indicated in this paper by the position of the extremum therein, provides information about the bonding electrons and lone pair electrons in the valence shell and a theoretical basis for the VSEPR model.5 Furthermore, according to the theory of atoms-in-molecules, atoms are uniquely defined in the molecule by zero-flux surfaces. Integration of the electron density within the basin of an atom gives the number of electrons associated with the atom. The virial theorem holds for atoms in molecules, and one can also calculate the energy of an atom in a molecule.
TABLE 2: Analytical Vibrational Frequencies (in an-') of PLL at the UHF/6-31G(d) and UMP2/6-31G(d) Levels UHF Td
Cz ,
C3I
tz
e a1 tz bz bi a1 az al bi al a1 bz e e a1
e a1 at
- 102.68 53.94 448.43 483.71 44.75 52.19 81.86 99.88 22 I .78 403.74 457.40 523.79 564.57 53.15 108.27 167.43 457.03 469.87 573.57
C4,.
UMP2 tz e a1 t?
a1 bi az al bz a1 a1 a1 b?
bz al e bi
b? a1 e
67.09 87.68 445.12 542.56 93.27 119.95 142.11 142.92 148.90 458.94 498.42 510.46 526.95
53.37 9 1.75 250.54 319.35 480.20 49 1.42 547.58
Optimized Structures of PL4 and PI& At the UHF/6-31G(d) level, four stationary points corresponding to structures with T d , C2,., C3!,,and C4,. symmetries, were located. The high spin contamination in the structure ((9) = 1.13) indicates that the UHF result is unreliable. Spin contamination 1:s less serious in the Td, C2,..and C3,. structures, for which the (9) values are 0.8 1, 0.76, and 0.77, respectively (Table 1). The analytic frequency analysis confirmed that the C21,and C31.structures are real minima (no imaginary frequencies), whereas there are three degenerate imaginary frequencies in the T,I structure (Table 2). When electron correlation is included, the shape of the potential energy surface changes. At the uMP2(fu11)/6-31G(d) level, the T(/structure becomes a true minimum as are the C2\.and C41.structures. Assumed structures with C3,.symmetry
Structure of PLi4
J. Phys. Chem., Vol. 99, No. 14, I995 4943
TABLE 3: Optimized Structures of the PHJ
(9) UHF/6-3 1G(d) Td CZ\
E (au)
R P-HW
RP-HW
LH!aPH!a,
LH(ePH(ei
0.80 0.78
-342.832 57 -342.944 82
1.564 1.512
1.397
169.6
101.2
0.77 0.76
-342.976 55 -343.080 20
1.556 1.500
1.397
170.3
101.3
0.75 0.75
-343.014 90 -343.108 62
1.565 1.507
1.401
170.5
101.2
PMP2/6-3 IG(d) (Frozen core)" Td
C?, PMP4/6-3 1G(d) (Frozen core)" Td
CZ, 'I
Units as in Table 1. Geometries were optimized at the UMP2/6-3 lG(d)(frozen core) and UMP4/6-31G(d)(frozen core) levels, respectively.
collapse to the Td structure upon optimization. Although both the UHF and UMP2 methods predict a C2v structure for PLi4, there is a large difference in the structures. If the C2,,structure is viewed as having been formed from a trigonal bipyramid by removal of an atom or ligand from an equatorial position, then the larger angle is denoted by LLi,PLi, and the smaller angle by LLiePLie. The major difference between the UHF and UMP2 CzLstructures is the large increase in LLi,PLi, (123.3' vs 167.4') due to the inclusion of electron correlation. The effect on LLiePLie is less pronounced (72.3' vs 92.0'). The P-Li, bond length increases slightly (2.251 8, vs 2.263 A), while the P-Lie bond length shows a larger decrease (2.355 A vs 2.285 A). We carried out two other types of post-HartreeFock optimization with the 6-31G(d) basis set. A frozen core singles and doubles configuration interaction (UCISD) calculation yielded a C21 structure for PLi4 which is very similar to the UMP2 result, although the UCISD method leads to smaller changes in P-Lie and LLiePLie. A UMP4(frozen core) calculation yields very similar results. With the 6-311+G(d) basis set, the UHF optimized C21 structure has shorter P-Li bond lengths than the 6-31G(d) results, while the bond angles remain very similar. The effects of including electron correlation at the UMP2 level with the 6-31 l+G(d) basis set are qualitatively the same as those observed with the smaller 6-31G(d) basis set. The UHF/63 11fG(2d) results indicate that further expansion of the basis set has virtually no effect on the optimized structures. At all levels studied here, the C21s structure is lower in energy than the Td structure, although the difference is quite small. With the inclusion of electron correlation, the energy difference between the two structures is further reduced. For example, the energy difference is only 0.000 11 au (0.3 kJ/mol) at the PMP4/6-311+G(d) level. This is in contrast with the results for SiLi4, where the inclusion of electron correlation increases the energy difference between the Td and CzVstructures.6 In Table 3 we list the optimized geometries of the P& radical at various theoretical levels. Since no imaginary frequencies are obtained for the Td and the C21.optimized structures at the UHF/6-3 1G(d) and UMP2/6-3 1G(d) levels, both structures correspond to real energy minima. However, unlike PLi4 the C2,. structure of P& has a much lower energy than the Td structure. For example, at the PMP4/6-31G(d) level, the C2v structure of P& is 0.09372 au (246 kJ/mol) lower than the Td structure. Comparison of PL4 with the Optimized Geometries of Lb, CL4, SiLi4, and PI& Our results for PLi4 are compared with previous theoretical calculations on CLi4, SiLi4, and Li4 in Table 4. MRCI calculations on Lid" show that in its lowest singlet state, the most stable structure has a rhombic (&) form, with Li-Li distances of 2.752 and 3.080 8, and a 55 kJ/mol binding energy per atom. The square planar structure (041,) is 43 kJ/mol higher
TABLE 4: Structural Data for Lt, CLio, SiLt, and PLL-. ALi4 RA-LW RA-LW Li4'
3.048 2.948 2.752
Td D4h
D?h CLidh Td 1.909 SiLidb Td 2.367 CZ,. 2.396 PLi4 Td 2.264 CZ,, 2.263
RLi(el-Li(e)
RLi(o)-L.l!ei
LLi!,)ALi(,, LLi!e&i(e)
3.080
3.117 2.459
3.865 3.198
3.246
159.7
82.6
2.285
3.696 3.287
3.336
167.4
92.0
Geometries optimized at the MP2/6-31G(d) level. Bond lengths in angstroms and angles in degrees. Results from ref 6. Results from ref 5. (I
in energy than the D2h structure with a side length of 2.948 A, while the Td structure in which the Li-Li distance is 3.048 8, is 81 kJ/mol higher in energy than the D2h structure. The LiLi distance (3.117 A) in Td CLi4 is not much greater than that in the Lid (Td)cluster (cf. Table 4). A Si atom is much larger than a C atom and therefore the Li-Li distance in Td SiLi4 is very much greater than in.CLi4 and in a Td constrained Lid cluster. Distortion of the Td structure of SiLi4 to the more stable C2v structure causes the Si-Li distance to increase, while the Lie-Li, and Li,-Lie distances decrease. As expected from the relative sizes of Si and P, the P-Li bond in PLi4 is shorter than the Si-Li bond in SiLi4. Therefore, smaller Li-Li distances are expected in the Td structure of PLi4 than in the Td structure of SiLi4. The longer Lie-Lie and Lia-Lia distances in the C2v structure of PLi4 than in the C21,structure of SiLi4 appear, at first glance, to be at odds with the relative sizes of the central atoms. The longer Lie-Lie distance in PLi4 is due to the fact that LLiePLi, is 9.4' larger than LLieSiLie in SiLi4. Two conclusions are evident from Table 4. The Td to Czl. distortion of SiLi4 leads to a larger reduction in the Li-Li distances than the corresponding change in PLi4. Also, whereas the Li-Li distances are greater in the Td structure of SiLi4 than in the Td structure of PLi4, the converse holds for the Czr structures. The above discussion indicates that strong Li-Li interactions may be responsible for the shorter Li-Li internuclear distances. In the following section we study and compare the stability of CLi4, SiLi4, and PLi4 in terms of the atomic energy as calculated according to the atoms-in-molecules theory. We discuss the geometric distortion of these molecules in terms of a JahnTeller distortion and Li-Li interactions. Reed et d 6 have analyzed the CzI,structure of SiLi4 from the natural bonding orbital point of view and rationalized the stability of the Czl, structure by means of a three-center, four-electron bond. Li-Li Interactions To understand the electronic structure of ALi4 molecules, it is helpful to consider first the structure of Li4. Gatti et aL4.I9
4944 J. Phys. Chem., Vol. 99, No. 14, 1995
Shi et al.
TABLE 5: Integrated Charges and Atomic Energies of Lithium Atoms in Lk, SiL4, PLid, and P€I& Qh
F
Vat:'
VrrpC
VI", =
Val,
+ Vrep
li4
D?,, Li(s) Li(1)
0.846 -7.331 92 -19.851 14 5.19087 0.493 -7.426 15 -20.028 89 5.180 03
-14.660 27 -14.848 86
Li
0.573 -7.35674 -20.257 36 5.545 15
-14.71221
Li
0.836 -7.39604 -25.883 92 11.092 20
-14.791 71
Li(a) Li(e)
0.861 -7.385 12 -25.90550 11.13550 0.803 -7.414 54 -26.341 44 11.512 61
-14.77000 -14.828 83
Li
0.752 -7.389 24 -27.033 38 12.255 00
- 14.778 38
Li(a) Li(e)
0.830 -7.372 97 -26.776 40 12.030 26 0.707 -7.396 89 -27.466 67 12.672 68
-14.746 14 -14.793 99
-0.251 -0.596 31 -8.087 88 6.895 57
-1.192 31
H(a) -0.436 -0.720 10 - 10.128 79 8.687 88 H(e) -0.629 -0.860 85 - 12.807 96 11.085 36
- 1.440 91
D4n
SiLid Td C1,
PLi4 Td
Cz \
PH4 Td H CZ,
-1.722 60
(' Calculated at the HF/6-3 1G(d)//MP2/6-3 1G(d) level. All quantities are in units. Net atomic charges. Total electronic energy associated with the Li basins. Attraction energy in the Li basins. e Repulsion energy in the Li basins.
studied the topological properties of Li, (n = 4-6) clusters at the optimized geometries calculated by Beckman et al." Their studies show that at the D2h geometry, Li4 has two pseudoatoms, each located within a triangle of the rhombic structure and bonded directly to three lithium atoms. There is, however, no direct bonding between the lithium atoms. Even in Li2. the lithium atoms are not bonded directly to each other, but rather they are bonded indirectly through the pseudoatom which lies midway between the two lithium nuclei. GVB studies by McAdon and GoddardI8 also led to the conclusion that the electrons in Liz are concentrated at the midpoint between the nuclei, whereas EpiotisI9 has suggested that the bonding in Liz can be considered as two Li cations bridged by a pair of electrons. Using the 6-3 1G(d) basis set we reproduced the topological results of Gatti et aL4.I9for the rhombic structure of Li4, and we carried out equivalent calculations for the D4h structure as well. Our results show that there is only one pseudoatom in the D4h structure. The pseudoatom is located at the center of the molecule. The lithium atoms are all bonded to the pseudoatom, but there is no direct bonding between the lithium atoms. The atomic charge, Q = Z - N , as obtained by subtracting the number of electrons associated with each atomic basin from the atomic number, is listed in Table 5 for each of the lithium atoms. In the D1-h structure of Li4 there is almost twice as much charge on the short diagonal lithium atoms as on the long diagonal lithium atoms. The lithium atoms on the short diagonal are bonded to two pseudoatoms whereas the lithium atoms on the long diagonal are bonded to only one pseudoatom. The charge associated with each pseudoatom is - 1.339. There is only one pseudoatom in the D4h structure. The charge on each lithium is +0.573, and the charge on the pseudoatom is -2.292 which is almost twice as much as the charge on each pseudoatom in the D z structure. ~ We now consider the atomic electronic energy associated with an atomic basin, as calculated within the framework of the atoms-in-molecules t h e ~ r y .The ~ preference of Lid for the D?/,
structure is due to the stronger interactions between the lithium atoms via pseudoatoms in the D21, structure than in the D4h structure." Comparing the average atomic energy of the lithium atoms in Li4 we observe that the D2h structure has a lower average atomic energy than the D4h structure. Analysis of the atomic energy and its components in the D2h and D4h structures of Lid, indicates that it is the lower repulsion energy in the D2h structure that is responsible for the D2h structure being favored over the D4h structure. The gain from the lower repulsion energy is partially offset by the loss in attraction energy. This result is in sharp contrast with an analysis of the Jahn-Teller distortion energies in C b + and BH3+. From the components of the total molecular energy of the methane radical cation2"and the borane radical cation?' it has been shown that the electron-nuclear attraction energy is the dominant contributor to the Jahn-Teller distortion energy and that the change in the interelectronic repulsion energy is in the opposite direction. Comparable analyses of the relative stabilities of two or more states arising from the same electronic configuration have been carried out for a few atomicZ2and m ~ l e c u l a cases. r ~ ~ ~We ~ ~conclude that the distortion of the D4h structure of Li4 into the D2h structure is due to the strong Li-Li interactions via pseudoatoms which can be measured by the atomic energies calculated within the framework of the atoms-in-molecules theory. The strong interactions between Li atoms in SiLi4 is evident from the atomic energies (Table 5). The average Li energy is 0.003 79 au (9.95 kl/mol) lower in the CzVstructure than in the T d structure. The equatorial lithium atoms in the CrVstructure are lower in energy than the lithium atoms in the T d structure mainly due to the large gain in attraction energy. The axial lithium atoms in the CzVstructure are higher in energy than the lithium atoms in the T d structure due to an increase in repulsion energy. The adoption of the CZ, structure by SiLi4 is consistent with the fact that more is gained by the equatorial lithium atoms than is lost by the axial lithium atoms. The above discussion suggests that Li-Li interactions play a dominant role in determining the geometries of some Li containing molecules, such as Li4 and SiLi4. PL4 is JahnTeller unstable and therefore its structure is determined by a competition between Jahn-Teller distortions and distortions due to Li-Li interactions. The lower average lithium atomic energy in the T d structure of PLi4 than in the ClL> structure (-7.389 24 vs -7.384 93 au, respectively) indicates that the Li-Li interactions in PLi4 favor the T d structure, rather than the C2,,structure. The atomic repulsion energy makes the dominant contribution to the stabilization of the T d structure, but it is largely offset by the attraction energy which favors the C2,.structure. As noted above, tetrahedral PLi4 is a Jahn-Teller unstable molecule. Since the electron density in each of the degenerate highest occupied molecular orbitals (HOMO) has the maximum CZ,,symmetry, PLi4 will distort to a CZ,, structure due to the first-order Jahn-Teller effect.Z' The Jahn-Teller distortion is opposed by Li-Li interactions which favor the Td structure. The preferred structure is due to a delicate balance between these two kinds of distortions. Consequently, high-level ab initio calculations predict that the T d and C?,.structures have energies which differ by less than 1 kJ/mol. The effect of Li-Li interactions can be further illustrated by comparing PLi4 and P&, Jahn-Teller unstable molecules with a common central atom. The C?,.structure of P& has a much lower energy (246 kJ/mol) than the T d structure. Also, the average energy of the H atoms is much lower in the C2,. structure than in the T d structure (-0.790 48 vs -0.596 31 au, respectively). The situation is reversed in PLi4: the average lithium atomic energy is lower in the T
