J. Phys. Chem. 1996, 100, 585-593
585
Theoretical Study of the C3P Radical and Its Cation Emma del Rı´o,† Carmen Barrientos,‡ and Antonio Largo*,‡ Departamento de Quı´mica Fı´sica y Analı´tica, Facultad de Quı´mica, UniVersidad de OViedo, 33006 OViedo, Spain, and Departamento de Quı´mica Fı´sica, Facultad de Ciencias, UniVersidad de Valladolid, 47005 Valladolid, Spain ReceiVed: May 22, 1995; In Final Form: August 15, 1995X
An ab initio molecular orbital study has been carried out for the C3P radical and its positive ion, C3P+. Geometries, vibrational frequencies, and infrared intensities have been obtained at the MP2/6-31G* level, whereas MP4 theory has been employed to compute electronic energies. A topological analysis of the electron density for nonlinear species has also been carried out. The neutral species is predicted to have a linear ground state (2Π electronic state), the next lowest-lying isomer (about 15 kcal/mol higher in energy) being a rhomboidal species with 2B1 electronic state. Both isomers have high dipole moments, 2.773 and 3.893 D, respectively, which should favor their experimental detection. In the case of the cation the ground state is also predicted to be a linear structure (3Σ- electronic state). The next low-lying isomer is a triplet rhomboidal structure which lies about 10 kcal/mol higher than the C3P+ ground state at correlated levels. Therefore, it seems that, like their sulfur analogues and contrary to the silicon compounds, the CnP species have linear ground states.
Introduction The study of carbon clusters containing second-row elements has been of interest in recent years for different reasons. For example, binary silicon carbides are used in microelectronic systems,1 but silicon-containing carbon clusters are also of interest in astrophysics. To date, CSi2 and C4Si3 have been detected in the interstellar medium, whereas C2Si has been observed in circumstellar shells.4 In addition, organosulfur clusters of the type CxSx have been the subject of recent experimental work,5-8 but undoubtedly much of the interest raised by these species is due to the interstellar detection of several sulfur-containing carbon clusters, namely, C2S9 and C3S.10 On the other hand, very little is known about the chemistry of binary phosphorus-carbon compounds. However, after the detection of PC11 in space, together with the observation of interstellar PN,12 the interstellar chemistry of phosphorus has received much attention, as exemplified by a number of papers addressing this subject.13-15 Of particular relevance is the study of Millar,15 who, on the basis of laboratory data of Smith et al.,16 concluded that organophosphorus molecules such as C2P, HC2P, or C3P might be detectable in space if they are unreactive with oxygen atoms. Since there is no experimental information on these species, we have undertaken a series of theoretical studies on them. We have already carried out an ab initio study of the C2P radical and its cation,17 as well as of the reaction of P+ with acetylene,18 which has been suggested15 as a possible route for the synthesis of precursors of C2P in space. Not only is the interest on these compounds due to their astrophysical significance but there is also a crucial aspect concerning their molecular structure which is of general relevance. Although C2S and C3S are known to prefer linear conformations,19,20 binary silicon-carbon compounds exhibit a quite different behavior. Both experimental and theoretical studies on C2Si21,22 have shown that the ground state is cyclic, * Author to whom correspondence should be addressed. † Universidad de Oviedo. ‡ Universidad de Valladolid. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-0585$12.00/0
whereas in the case of Si2C23,24 it is strongly bent. Theoretical studies have also shown that in the case of Si2C2 a rhombic structure with a transannular C-C bond is favored over the linear isomer.25,26 C3Si prefers as well a nonlinear arrangement, since Schaefer and co-workers27 have found that ab initio calculations predict a closed-shell cyclic C2V-symmetry structure, which is a four-membered ring with a transannular C-C bond, lying about 4 kcal/mol below the linear triplet isomer. They found another rhomboidal structure with inverted tricoordinate carbon and silicon atoms to be nearly isoenergetic with the linear isomer.27 The structure of phosphorus-carbon clusters remains an open question. In our previous study on C2P17 we found that the ground state is linear (2Π electronic state), but a cyclic structure (2B2 state) lies very close in energy, only about 6 kcal/mol above 2Π. The present study will focus on the structure of the C P 3 system and its cation, C3P+, which is isoelectronic with the C3Si system and therefore also an interesting subject in this context. Computational Methods The geometrical parameters of the different species were obtained at the Hartree-Fock (restricted for singlets, unrestricted for doublets and triplets) and second-order Møller-Plesset (MP2) level with the 6-31G* basis set,28 including all electrons in the calculation. Harmonic vibrational frequencies and IR intensities were computed at the MP2(full)/6-31G* level. On the MP2(full)/6-31G* geometries single-point calculations at the fourth-order Møller-Plesset (MP4) level29,30 with the MC311G** basis set were carried out. This basis set is constructed from the 6-311G** basis set31 for carbon and the McLean and Chandler basis set32 for phosphorus, supplemented with d polarization functions for both atoms. In these calculations we employed the frozen core approximation; that is, inner-shell molecular orbitals were not included for computing electron correlation energies. In the case of open-shell states we will provide projected fourth-order Møller-Plesset values33,34 (PMP4), to lessen the effect of spin contamination on the convergence of the MP series. All calculations were carried out with the GAUSSIAN-92 program package.35 © 1996 American Chemical Society
586 J. Phys. Chem., Vol. 100, No. 2, 1996
del Rı´o et al. infrared intensities are given in Table 1. We have found a linear isomer (structure 1), two four-membered ring structures (2, 3), and a three-membered ring structure (4). The lowest-lying linear state is a 2Π electronic state with the phosphorus atom in the terminal position. Its electronic configuration is
{core}7σ28σ29σ210σ22π411σ23π3
(1)
and the bond distances (close to typical double-bond lengths) suggest that it can be represented by the following valencebond structure:
:CdCdCdP˙ :
Figure 1. MP2/6-31G* and HF/6-31G* (in parentheses) optimized geometries for the different C3P species. Distances are given in angstroms and angles in degrees.
The nature of bonding for nonlinear states was characterized by using Bader’s topological analysis.36 The one-electron density F(r) was analyzed through its gradient vector field ∇F(r), characterizing “bond critical points” (a bond critical point is a minimum of F(r) along the line linking nuclei and a maximum along the interatomic surfaces, i.e. a (3,-1) critical point) and “ring critical points” (a (3,+1) critical point corresponding to a maximum in one direction and a minimum in two directions is denoted as a ring critical point). In addition, the Laplacian of F(r) provides information where the electronic charge is concentrated (∇2F(r) < 0) or depleted (∇2F(r) > 0). Some properties of interest at a critical point, apart from F(r) and ∇2F(r), are the ellipticity () and the total energy density H(r). is defined as ) λ1/λ2 - 1, where λ1 and λ2 are the two negative curvatures of a bond critical point (λ2 being the softest mode). H(r), which is the sum of the potential and kinetic energy density at a critical point, characterizes a bond as covalent (H(r) < 0) or ionic (H(r) > 0). These calculations were performed with the AIMPAC series of programs,37 and the MP2/6-311G* wave functions were employed to compute the electron density. Results and Discussion C3P Radical. We have searched for different isomers on the C3P potential surface, but we will report only the results for the low-lying states. In Figure 1 the MP2/6-31G* optimized geometries of the C3P isomers are shown, whereas the corresponding dipole moments, harmonic vibrational frequencies, and
This structure is consistent with the electronic configuration shown in (1), since the 10σ and 11σ molecular orbitals are essentially 2s and 3s, respectively, atomic orbitals belonging to terminal carbon and phosphorus, whereas the unpaired electron resides mainly in a phosphorus 3p orbital. The lowest-lying quartet linear state was found to lie more than 47 kcal/mol above 2Π at correlated levels (PMP4/6-311G*/ /MP2/6-31G*), and therefore was not considered further. The 2Π state is subject to Renner-Teller splitting, and therefore we give in Table 1 the two different modes (of a′ and a′′ symmetry, respectively) for each π vibrational frequency. ν3 is related to the P-C stretching, whereas ν1 and ν2 correspond to the C-C (asymmetric and symmetric, respectively) stretching frequencies. The IR intensities suggest that the infrared spectrum would be dominated by the ν1 frequency. In addition it is also shown in Table 1 that structure 1 has a relatively high dipole moment of 2.773 D. Since the HF wave function for the linear isomer is somewhat spin-contaminated, we have carried out restricted HF calculations on this species. The RHF geometrical parameters are as follows: r(P-C1) ) 1.536 Å; r(C1-C2) ) 1.347 Å; r(C2-C3) ) 1.275 Å. The main difference with the unrestricted HF geometry is the P-C distance, which is shortened. At the RHF/6-31G* level the ν1 frequency takes a lower value, namely, 2070 cm-1, but is still predicted to be the most intense in the IR spectrum. Two different four-membered ring structures (2 and 3 in Figure 1) have been found. Structure 2 can be viewed as the result of the interaction of a phosphorus atom with a side of the cyclic C3 unit, whereas in structure 3 the phosphorus atom interacts with a bent C3 unit. Structure 2 corresponds to a 2B1 electronic state with the following electronic configuration:
{core}6a127a123b228a122b124b229a1210a123b11
(2)
where the 6a1, 7a1, 3b2, and 4b2 molecular orbitals make the peripheral bonds, the 8a1 orbital is essentially the phosphorus 3s orbital, the 2b1 molecular orbital is delocalized over the entire molecule, giving all the bonds a certain degree of multiple bonding, 9a1 can be associated to the transannular C-C bond, 10a1 represents basically a C2 lone pair, and the unpaired electron is mainly a phosphorus 3px orbital. Structures similar to 2, with inverted tricoordinate sp2-hybridized carbon atoms, have been reported for C4,38-45 Si2C2,25,26 and the C3Si27 system. It is interesting to note that, as shown in Table 1, this rhomboidal structure for C3P is a true minimum on the MP2 surface since all its frequencies are real and that it has a high dipole moment of 3.893 D. The infrared spectrum should be dominated by the ν1 (C-C stretching) and ν6 (bending) vibrational frequencies (1455 and 499 cm-1, respectively, at the MP2/6-31G* level), according to the IR intensities in Table 1. To gain more insight into the nature of bonding in this species, an analysis of the electron density in terms of the Bader theory36
C3P Radical and Its Cation
J. Phys. Chem., Vol. 100, No. 2, 1996 587
TABLE 1: HF/MC-311G* Dipole Moments (D), MP2/6-31G* Vibrational Frequencies (cm-1), and in Parentheses, IR Intensities (km/mol) for the Different C3P Species ν2(a1,σ)
ν3(a1,σ)
ν4(b1,π)a
ν5(b2,π)
ν6(b2)
2354 (2045.9)
1332 (0.5)
754 (3.6)
1455 (75.1) 1190 (0.1) 1112 (9.1) 1641 (63.1)
980 (3.7) 803 (36.9) 807 (12.2) 1302 (124.8)
704 (3.0) 507 (2.7) 390 (45.3) 640 (0.7)
465 (3.1) 939 (274.3) 382 (4.6) 235 (34.5) 301 (21.7) 376 (2.8)
192 (1.9) 244 (0.4) 1089 (4.1) 1600 (233.9) 1639 (70.0) 499 (46.7)
499 (31.8) 204i (-) 316 (19.5) 501i (-)
species
µ
µ1(a1,σ)
1
2.773
2 3 3′ 4
3.893 1.159 1.636 2.851
a
a′′ symmetry for structure 3′.
TABLE 2: Critical Point Data for the Nonlinear C3P Structures structure 2
3 (MP2)
3 (HF) 4
a
type
Ra (Å)
Rbb (Å)
F(r) (au)
∇2F(r) (au)
C1-C2 bond C1-C3 bond C1-P bond C1C2C3 ring C1C3P ring C1-C2 bond C2-P bond (C2-P)′ bondc C1C2P ringc C1-C2 bond C1-P bond C1C2C3P ring C1-C2 bond C1-C3 bond C2-P bond C1C2C3 ring
1.430 1.503 1.783
1.435 1.528 1.785
1.344 1.882 1.882
1.345 1.881 1.988
1.344 2.009
1.346 2.227
1.436 1.342 1.681
1.575 1.346 1.681
0.2658 0.2369 0.1518 0.2345 0.1494 0.3267 0.1172 0.1171 0.1171 0.3404 0.1207 0.1146 0.2547 0.3474 0.1750 0.2525
-0.4561 -0.1139 0.1688 0.0426 0.1503 -0.9516 0.0435 0.0017 0.0081 -1.1755 -0.1102 0.0837 -0.1038 -0.9749 0.4163 0.0847
0.7015 3.2083 1.5959 0.1887 198.7338 581.2363 0.2270 1.5191 3.4952 0.1945 0.1667
H(r) (au) -0.2685 -0.2004 -0.1397 -0.1738 -0.1353 -0.3992 -0.0956 -0.0921 -0.0928 -0.4492 -0.0846 -0.0916 -0.2270 -0.4199 -0.1564 -0.1959
Bond length. b Bond path length. c Spurious critical points.
has been found46 for rhomboidal C3Si and C3Be, both showing transannular C-C bonding. The other four-membered ring, structure 3, also corresponds to a 2B1 electronic state with the following electronic configuration:
{core}6a123b227a122b128a124b229a125b223b11
Figure 2. Gradient map of the electronic charge density for structure 2 obtained at the MP2/6-311G* level. The nuclei are denoted by crosses; bond critical points, by dots; and ring critical points, by triangles.
has been carried out. Figure 2 shows the gradient vector field of the charge density at the MP2/6-311G* level, whereas in Table 2 the most relevant critical point data are collected. It is clearly seen in Figure 2 that there is a bond critical point between carbon atoms C1 and C3 and that the corresponding bond path is displaced from the C1-C3 line toward C2 about 0.1 Å. On the other hand C1-C2 and C1-P bond paths are only slightly curved, as reflected in the nearly coincident values obtained for R and Rb. Therefore, the topological properties of structure 2 are in agreement with the assignment of a molecular orbital to the transannular C-C bond and classify 2 as a bicyclic species. However, it is also clear from Table 2 that the properties of the transannular C1-C3 bond path makes structure 2 near-topologically unstable, since it has a large ellipticity ( ) 3.2083), there is only a small difference in F(r) between the C1 and C3 bond critical point and the C1C2C3 ring critical point, and furthermore, these critical points are spatially separated by only 0.21 Å. It must be emphasized that a similar behavior
(3)
We have also considered the 2A2 state resulting from 3b1 f 1a2 excitation, but this state lies higher than the 2B1 state at all levels of theory (about 3 and 1 kcal/mol at the MP4 and PMP4 levels, respectively). The geometry of the 2B1 state shown in Figure 1 suggests that the phosphorus atom is mainly bonded to the central carbon, since the transannular P-C distance (1.882 Å) is considerably shorter than the peripheral ones (2.009 Å). On the other hand, peripheral C-C bonding is relatively strong, with a bond length of 1.344 Å, close to typical double-bond distances. This fact, together with the CCC angle of 149.9°, reinforces the idea that this molecule may be viewed as a phosphorus atom complexed to a bent C3 unit through the central carbon. This is confirmed by the topological analysis of the MP2 density through the gradient vector field and the Laplacian of F(r), shown in Figure 3. In Figure 3 the absence of bond critical points between phosphorus and the terminal carbons of the C3 unit is evident. However, it is also clear in Figure 3, as well as in the critical point data given in Table 2, that structure 3 is topologically unstable. In first place the ellipticity at the C2-P bond critical point is very high (198.7338), suggesting near bifurcation catastrophe (the C2-P bond is nearly split into two C1-P and C3-P bond paths), but also two additional (spurious) bond critical points (corresponding formally to bond paths between the central carbon and phosphorus) and two ring critical points are found. The last four critical points are only the consequence of an almost constant charge density along the direction nearly perpendicular to the C2-P bond (with values of 0.1171 au). This is also the reason for the unusual appearance of the gradient paths in that region. In any case, bonding of
588 J. Phys. Chem., Vol. 100, No. 2, 1996
del Rı´o et al.
Figure 3. Gradient map of the electronic charge density for structure 3 obtained at the MP2/6-311G* level. The nuclei are denoted by crosses; bond critical points, by dots; and ring critical points, by triangles.
Figure 4. Gradient map of the electronic charge density for structure 4 obtained at the MP2/6-311G* level. The nuclei are denoted by crosses; bond critical points, by dots; and ring critical points, by triangles.
phosphorus to the C3 unit is very weak in structure 3, as illustrated by the low values at the C2-P critical point obtained for both charge density and total energy density. On the other hand, carbon-carbon bonds in structure 3 are relatively strong, compared with those found in structure 2. The topological instability of 3 at the MP2 level is not found at the HF level. We do not report the corresponding gradient vector field map employing the HF wave function to obtain the charge density for the sake of space (although it is available upon request), but the critical point data shown in Table 2 are sufficiently illustrative. Surprisingly there is no C2-P bond critical point at this level, but we find bond critical points between phosphorus and the terminal carbons and a ring critical point along the line connecting phosphorus and the central carbon. Therefore, the T-type structure suggested by the MP2 density is lost, and a covalent four-membered ring is obtained at the HF level. The topological stability/instability of structure 3 at the HF and MP2 levels has its counterpart in this case in the vibrational frequency analysis. Whereas at the HF level structure 3 has all real frequencies and therefore corresponds to a true minimum on the potential surface, it is clearly seen in Table 1 that 3 has an imaginary frequency at the MP2 level and therefore is characterized as a transition state. Following the imaginary b2 frequency, we were able to locate a 2A′′ state (structure 3′) at the MP2 level, whose geometry and vibrational frequencies are also given in Figure 1 and Table 1, respectively. This lowersymmetry species is a true minimum with very different P-C1 and P-C3 bond lengths, suggesting that the phosphorus atom is essentially bonded through C1. This is confirmed by an analysis of the charge density for 3′ (also available upon request), which shows only a P-C1 bond critical point (apart from the C1-C2 and C2-C3 bond critical points) and no ring critical point. Finally, we also searched for three-membered ring structures and found a 2B1 state (structure 4 in Figure 1) in which a cyclic C3 unit interacts through an apex with a phosphorus atom, corresponding to the same electronic configuration (2) found for structure 2. In fact this species has a b2 imaginary frequency (see Table 1) corresponding to the PCC bending mode and therefore can be considered to be the transition state for the degenerate rearrangement of structure 2. In the case of structure 4 the most salient features of its electronic configuration is that now the 2b1 orbital represents a π bond mainly delocalized over the C3 unit, the 4b2 orbital is essentially C2-P π-bonding, and the unpaired electron resides mainly at the phosphorus 3px orbital. The results of the analysis
TABLE 3: Relative Energiesa (kcal/mol) for the C3P States at Different Levels of Theorya HF/6-31G* MP2/6-31G* HF/MC-311G* MP4/MC-311G* PMP4/MC-311G* PMP4+∆ZPVEb
1
2
3
0.0 0.0 0.0 0.0 0.0 0.0
24.3 5.9 24.4 13.3 17.0 15.4
37.9 33.3 38.0 35.6 39.5 36.9
3′
4
32.3 39.5 33.3 35.5 33.1
38.1 19.7 39.4 23.7 26.9 24.4
a The results with the MC-311G* basis set were obtained employing the MP2/6-31G* optimized geometries. The following electronic energies (in hartrees) for 1 were taken as reference values: -454.126 61 (HF/6-31G*), -454.578 74 (MP2/6-31G*), -454.167 40 (HF/MC311G*), -454.677 84 (MP4/MC-311G*), and -454.685 64 (PMP4/ MC-311G*). b Zero-point vibrational energy differences were obtained scaling (according to ref 47) the MP2/6-31G* vibrational frequencies.
of the charge density for structure 4 are shown in Figure 4 and Table 2. The values of the charge density and total energy density at the bond critical points reflect that the C1-C3 and C2-P bonds are the strongest of all cyclic species, confirming the multiple character of the C2-P bond. On the other hand the C1-C2 and C2-C3 bonds (which are strongly curved) are relatively weak and show features of near-topological instability, since they are characterized by a large ellipticity and the charge density at the bond critical point is very close to the value at the ring critical point. The relative energies of the C3P species at different levels of theory are given in Table 3. It is readily seen that at all levels of theory the most stable species is the linear structure 1. At the HF level the next lowest-lying species is the bicyclic structure 2, which is about 24 kcal/mol higher in energy at that level of theory. Inclusion of correlation effects lowers the energies of cyclic species relative to the linear structure. Nevertheless, spin contamination is relatively high for the wave function of structure 1, whereas it is much lower for the other species (the 〈S2〉 expectation values are as follows: 0.985 (structure 1), 0.787 (2), 0.777 (3), 0.851 (3′), and 0.808 (4)). Therefore, the PMP4 values should be more reliable in this case, and these projected values tend to increase the energy gap between cyclic species and the linear structure. The final PMP4+∆ZPVE values predict that structure 2 lies about 15 kcal/mol above the linear isomer, an energy difference which seems high enough to conclude with confidence that the linear structure 1 is in fact the ground state of C3P. It is also interesting to note that the lower symmetry structure 3′ is shown to lie below structure 3 not only at the MP2/6-31G* level but also at higher levels of theory such as MP4 and PMP4/MC-311G*.
C3P Radical and Its Cation
J. Phys. Chem., Vol. 100, No. 2, 1996 589
In the case of the C3Si system27 the ground state is shown to be a cyclic isomer analogous to structure 2, with both linear C3Si and the other four-membered ring isomer (similar to 3) lying about 4 kcal/mol higher in energy. It is interesting to note that for C3P structure 3 lies very high in energy (about 37 kcal/mol at our highest level of theory), even above structure 4, which is the transition state for the rearrangement of 2. It is also evident from Table 3 that at the HF level structure 3 (2B1 electronic state) is stable, and distortion of the C2V symmetry increases the energy. However, at the MP4 and PMP4 levels structure 3′ (2A′′ electronic state) clearly lies below the symmetric structure, suggesting that the prediction of 3 as a transition state is not an artifact of the MP2 level, since higher levels of theory support the same conclusion. It is also worth noting that the isovalent nitrogen compound C3N is known to be an interstellar molecule.48 Theoretical49 and experimental50-52 studies on this species have been carried out, showing that it has a 2Σ+ ground state with the CCCN connectivity. The difference in the electronic ground state with C3P can be ascribed to the formation of a strong C-N triple bond, which compensates the loss of the quite stable system with two double C-C bonds (see the valence-bond picture for the 2Π state of C3P at the beginning of this section), since the 2Σ+ state of C N can be basically depicted as 3
•CtCsCtN: On the other hand, the higher reluctance of phosphorus (compared to nitrogen) to make triple bonds favors to 2Π state over the 2Σ+ one in the case of C3P. We have estimated that the 2Σ+ state lies about 6 kcal/mol (RHF/6-31G*) and 13 kcal/ mol (PMP4/6-311G*) above the 2Π state for the C3P radical. In any case inclusion of correlation effects as well as extension of the basis set favors the latter. C3P+ Cation. We have also searched for different low-lying C3P+ states, which will be discussed in the same order as their neutral counterparts. The MP2/6-31G* optimized geometries are shown in Figure 5, and the dipole moments (taking the center of mass as the origin), vibrational frequencies, and IR intensities are collected in Table 4. The linear triplet state (designate 1t in Figure 5) results from the loss of a 3π electron in electronic configuration 1, and therefore corresponds to a 3Σ- electronic state. The P-C bond distance is noticeably increased in 1t with respect to the bond length in 1, mainly as a consequence of the loss of an electron occupying a π orbital which belongs mainly to phosphorus but which has a certain degree of P-C bonding character. We could not study at the same level of theory the 1∆ and 1Σ states derived from the π2 configuration, since a single-determinant wave function for the open-shell singlet state gives in fact a linear combination of both states, and a two-configuration wave function is required for a proper description. Nevertheless, as in the case of the isoelectronic C3Si system,27 Hund’s rules predict the 3Σ- state to be the lowest-lying linear state. (In this respect, we can mention that the virtually linear 1A′ state in Cs symmetry, which correlates with the open-shell singlet, lies about 11 kcal/mol higher than 1t at the PMP4/MC-311G*/ /MP2/6-31G* level. This result should be taken only as indicative and not as a prediction, since a single-determinant wave function is not appropriate in this case.) The linear triplet isomer has an imaginary bending frequency at the Hartree-Fock level. When correlated methods are employed (either MP2 or CISD), this structure has all real frequencies, but there is an anomalously high bending value (2636 and 2389 cm-1, respectively, at the MP2 and CISD levels) with an unphysically large IR intensity (42 690.1 and 30 933.2
Figure 5. MP2/6-31G* and HF/6-31G* (in parentheses) optimized geometries for the singlet and triplet states of C3P+. Distances are given in angstroms and angles in degrees.
km/mol, respectively, at the MP2 and CISD levels). Optimization without symmetry restrictions at correlated levels leads to nearly the same geometrical parameters and vibrational frequencies. Nevertheless, this anomalous π vibrational frequency seems to be caused by spin contamination, since at the restricted HF/6-31G* level all frequencies are found to be real. Therefore to estimate this bending mode (and the zero-point vibrational energy for this species), we have adopted the value obtained at the RHF/6-31G* level. It can be seen in Table 4 that for the 1t structure the IR spectrum would be dominated by the ν1 frequency (which corresponds essentially to asymmetric C-C stretching). The lowest-lying singlet (1A1) and triplet (3B1) states associated with structure 2 result from the loss of the 3b1 and a 10a1 electron, respectively, from electronic configuration 2. Both structures are true minima at the MP2 level (as well as at the Hartree-Fock level), as can be seen in Table 4. It is readily seen in Figure 5 that the C1-C2 and C1-P bond distances for 2s and 2t are sensibly altered with respect to the values found for the neutral species 2. Whereas the C1-C2 distance in 2s is lengthened about 0.04 Å relative to 2, the same distance is shortened about 0.08 Å in 2t. At the same time the C1-P bond distance is shortened (0.04 Å) in 2s and lengthened (0.03 Å) in 2t. These modifications can be partly attributed to the fact that in 2t there is an unpaired electron (3b1) occupying the phosphorus 3px orbital, and therefore the 2b1 orbital (which confers a certain degree of multiple bonding to the bonds) is extended almost exclusively to the C3 unit. On the other hand, the degree of participation of phosphorus into the delocalized
590 J. Phys. Chem., Vol. 100, No. 2, 1996
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TABLE 4: HF/MC-311G* Dipole Moments (D), MP2/6-31G* Vibrational Frequencies (cm-1), and in Parentheses, IR Intensities (km/mol) for the Different C3P+ Species species
µ
ν1(a1,σ)
ν2(a1,σ)
ν3(a1,σ)
ν4(b1,π)
ν5(b2,π)
ν6(b2)
1t
0.482
2s 2t 3s 3t 4s 4t
3.743 0.340 1.607 1.116 2.827 1.654
2049 (904.0) 2288 (2924.88)a 1305 (267.1) 1690 (26.9) 1082 (3.4) 1230 (0.6) 1344 (2.7) 1614 (89.5)
1245 (13.2) 1378 (56.23)a 953 (9.6) 851 (9.0) 857 (29.4) 924 (8.5) 1219 (39.3) 831 (498.8)
699 (2.4) 514 (57.78)a 668 (0.9) 588 (27.2) 546 (1.9) 724 (11.3) 651 (10.7) 630 (5.5)
2636 (42690.1) 368 (2.28)a 205 (12.9) 440 (0.6) 303 (38.0) 571 (1.1) 242 (0.1) 382 (0.0)
236 (3.7) 137 (0.00)a 1090 (8.1) 1428 (0.7) 1528 (124.0) 2698 (>105) 479 (55.9) 1267 (69.6)
537 (27.0) 586 (21.3) 470 (8.7) 263 (5341.2) 516i (-) 287 (15.7)
a
Estimated at the restricted HF/6-31G* level.
TABLE 5: Critical Point Data for the Nonlinear C3P+ Structures structure
type
Ra (Å)
Rbb (Å)
F(r) (au)
∇2F(r) (au)
H(r) (au)
2s
C1-C2 bond C1-C3 bond C1-P bond C1C2C3 ring C1C3P ring C1-C2 bond C1-P bond C1C2C3P ring C1-C2 bond C2-P bond C1-C2 bond C1-P bond C1C2C3P ring C1-C2 bond C1-C3 bond C2-P bond C1C2C3 ring C1-C2 bond C1-C3 bond C2-P bond C1C2C3 ring
1.473 1.559 1.739
1.477 1.581 1.740 1.351 1.816
1.385 1.787 1.362 1.843
1.385 1.787 1.365 1.860
1.440 1.387 1.671
1.501 1.391 1.671
1.480 1.347 1.655
1.492 1.359 1.655
-0.4623 -0.0512 0.1843 0.0463 0.1172 -0.6949 0.1276 0.1068 -0.8461 0.1525 -0.7521 -0.1312 0.0792 -0.2233 -0.8830 0.3236 0.0897 -0.1902 -0.6431 0.5356 0.1354
0.7425 4.5098 1.2742
1.350 1.812
0.2524 0.2154 0.1697 0.2141 0.1644 0.3133 0.1389 0.1319 0.3047 0.1434 0.3023 0.1452 0.1394 0.2530 0.3272 0.1884 0.2462 0.2356 0.2966 0.1753 0.2265
-0.2396 -0.1678 -0.1659 -0.1504 -0.1593 -0.3581 -0.1235 -0.1110 -0.3542 -0.1315 -0.3617 -0.1333 -0.1259 -0.2357 -0.3697 -0.1819 -0.1863 -0.2054 -0.3354 -0.1504 -0.1607
2t 3s 3t 4s
4t
a
0.3386 0.4950 0.3175 5.5544 0.0683 1.3152 2.1780 0.3402 0.4911 1.0262 0.0640 0.1671
Bond length. b Bond path length.
Figure 6. Gradient maps of the electronic charge density for structure 2s (a) and structure 2t (b) obtained at the MP2/6-311G* level. The nuclei are denoted by crosses; bond critical points, by dots; and ring critical points, by triangles.
π orbital is higher in the case of 1s, which has an empty 3b1 orbital, and therefore the C1-P bond is strengthened whereas the C1-C2 bond is weakened. It is also interesting to note that the transannular C1-C3 bond distance is increased in both singlet and triplet states relative to structure 2 by a considerable amount (0.06 Å). Nevertheless, a careful analysis of the electron density, whose results are shown in Table 5 and in Figure 6, reveals very different topologies for the singlet and triplet species. The singlet state maintains the essential features of structure 2 (see Table 2 and Figure 2), with a transannular bond critical point which has clear signs of topological instability. Charge depletion from the C1-C3 bond to the phosphorus atom reinforces the C1-P bonds. On the other hand, in the case of
structure 2t charge depletion from the transannular bond (which is lost in this structure) reinforces the peripheral bonds. Therefore, 2s shows a bicyclic structure, like the parent neutral species, whereas 2t is best described as a four-membered ring. The two cationic species related to structure 3, which are denoted as 3s and 3t in Figure 5, correspond to 1A1 and 3B1 states, respectively. The 1A1 state is obtained from configuration 3 simply by the loss of the unpaired 3b1 electron, whereas the 3B state results from the loss of a 5b electron simultaneously 1 2 with 3b1 f 1a2 promotion (the resulting electronic configuration being ...9a125b211a21). In the case of the triplet state the unpaired electrons are mainly localized at the C1 and C3 atoms. For both singlet and triplet species the P-C bond lengths are shortened
C3P Radical and Its Cation
J. Phys. Chem., Vol. 100, No. 2, 1996 591
Figure 7. Gradient maps of the electronic charge density for structure 3s (a) and structure 3t (b) obtained at the MP2/6-311G* level. The nuclei are denoted by crosses; bond critical points, by dots; and ring critical points, by triangles.
TABLE 6: Relative Energiesa (kcal/mol) for the C3P+ States at Different Levels of Theory HF/6-31G* MP2/6-31G* HF/MC-311G* MP4/MC-311G* PMP4/MC-311G* PMP4+∆ZPVEb
1t
2s
2t
3s
3t
4s
4t
0.0 0.0 0.0 0.0 0.0 0.0
48.9 0.2 46.4 10.2 17.3 16.7
24.7 -4.6 24.6 4.4 9.3 9.8
50.4 10.0 50.1 12.7 19.8 19.2
57.7 27.2 55.6 29.3 30.4 32.0
75.8 25.5 77.5 28.0 35.1 33.4
61.1 22.3 62.8 24.7 28.9 28.6
a The results with the MC-311G* basis set were obtained employing the MP2/6-31G* optimized geometry. The following electronic energies (in hartrees) for 1t were taken as reference values: -453.832 12 (HF/6-31G*), -454.231 25 (MP2/6-31G*), -453.869 68 (HF/MC311G*), -454.326 77 (MP4/MC-311G*), and -454.338 19 (PMP4/ MC-311G*). b Zero-point vibrational energy differences were obtained scaling (according to ref 47) the MP2/6-31G* vibrational frequencies.
and the C-C bond distances increased. However, although 3s and 3t have similar C1-C2 bond lengths, the P-C1 and P-C2 distances are quite different for each species, suggesting predominant P-C2 bonding in 3s and P-C1 bonding in 3t. This is confirmed by the topological analysis of the electronic density shown in Figure 7 and in Table 5. Structure 3s has a C2-P bond critical point, whereas in the case of 3t there are C1-P and C3-P bond critical points, and along the C2-P line there appears a ring critical point. It can be seen in Table 5 that the C1-P bond critical point of 3t is the only carbon-phosphorus critical point of all C3P+ species which has a negative value for ∇2F(r), which is a typical characteristic of a truly shared interaction.36 Although the neutral species 3 was shown to have an imaginary frequency, structures 3s and 3t are found to be true minima on the MP2/6-31G* potential surface since both have all real frequencies, as can be seen in Table 4. However, the triplet state has an anomalous high b2 frequency (2698 cm-1) with an unphysically large IR intensity (as well as the other b2 vibrational mode). These features are suggestive of a lower symmetry-broken solution. Nevertheless, since structure 3t is a high-lying C3P+ state (see below, Table 6) and our previous study of structure 3 showed that the symmetry-broken solution in that case only lowered its relative energy by some 4 kcal/ mol, we decided not to go further in this problem. Finally the singlet (4s) and triplet (4t) C3P+ structures derived from the three-membered ring structure 4 were also studied. In the case of the triplet two different electronic states were found to lie very close in energy: a 3A2 (...10a124b213b11) and a 3B1 state (...4b2210a113b11). Although the 3A2 state lies slightly lower than the 3B1 state (about 1.2 and 0.1 kcal/mol at the MP4 and PMP4 levels, respectively), the 3A2 state has an imaginary b2
frequency (just like its neutral counterpart, corresponding to the PCC bending mode). Therefore, we have considered in our study the 3B1 state. On the other hand the singlet state (structure 4s) is a transition state for the degenerate rearrangement of structure 2s, since the PCC bending mode has an imaginary frequency (see Table 4). As can be seen in Figure 5, the geometrical parameters of the singlet state are very similar to those of the neutral structure, with the exception of the C1-C3 bond distance, which is lengthened. In the case of the triplet state the P-C2 bond length is slightly shortened, whereas the C1-C2 bond distance is increased relative to structure 4. We do not report the gradient vector field for structures 4s and 4t for the sake of space, since they have the same topological features as those of the neutral structure 4. Nevertheless, the critical point data for these structures are given in Table 5. Comparing with the values for structure 4, shown in Table 2, it can be observed that the C1C2 bond paths are less curved than in 4, especially for the triplet state, and the ellipticity for this bond is considerably smaller for the cationic species. It is interesting to note that, as for the rest of the C3P+ structures, the C-P bond in 4s and 4t is strongly covalent, since the value of H(r) (the energy density at the bond critical point) is negative53 and similar in magnitude to the value for structure 4, even though the phosphorus atom bears a positive charge and the C-P bond should have a certain electrostatic character. If H(r) is negative, the system is stabilized by accumulation of electronic charge in the internuclear region, which corresponds to a covalent interaction. The relative energies of the C3P+ states are given in Table 6. The lowest-lying species at the HF level of theory is the linear triplet state. However, correlation effects favor all other species over 1t, and at the MP2/6-31G* level 2s is nearly isoenergetic and 2t even lies below 1t. However, higher levels of theory favor the linear triplet state, and furthermore, the HF wave function of 1t exhibits the highest spin contamination of all C3P+ triplet states (namely, 〈S2〉 ) 2.422 (1t); 2.083 (2t); 2.258 (3t); 2.097 (4t)). Therefore, projected MP4 values should be more reliable in this case. The final stability order at the PMP4+ ∆ZPVE level points to the triplet linear isomer as the global minimum of C3P+, with the triplet four-membered ring 2t being very close in energy and lying about 10 kcal/mol higher than 1t. Then the two singlet four-membered rings 2s and 3s follow, which lie 16.7 and 19.2 kcal/mol, respectively, above the triplet linear isomer. The three-membered ring species 4s and 4t, as well as the triplet four-membered ring 3t, are high-lying states (about 30 kcal/mol above the ground state). This stability order is in contrast with that found for the
592 J. Phys. Chem., Vol. 100, No. 2, 1996 isoelectronic C3Si system.27 Alberts et al. found that the global minimum of C3Si is a rhomboidal structure similar to 2s, with the linear triplet isomer and the other four-membered ring (the analogue of 3s) lying about 4 kcal/mol higher. A plausible explanation for the difference can be found in the higher degree of participation in multiple bonding for phosphorus than for silicon. Thus linear structures, in which the heteroatom takes part in π-bonding, are favored for phosphorus, whereas silicon prefers to form σ bonds. This could also be the reason for the stabilization of 4t relative to 3t observed in the case of C3P (compared with C3Si, since in this case the former lies about 15 kcal/mol higher than the latter27), since 4t implies an exocyclic heteroatom forming a π bond with carbon. In the case of the C3N+ isovalent system a theoretical study54 also found the linear isomer with a 3Σ- electronic state to be the ground state, followed by a 3Π state (derived from the loss of a σ electron in the 2Σ+ ground state of C3N), which lies very close in energy (about 0.037 eV). The lowest-lying cyclic state (3B1) lies about 1.067 eV above the 3Σ- state. The relative energies of the C3P+ species allow an estimate of the ionization potentials of the two lowest-lying isomers of C3P. The adiabatic ionization potentials are 9.38 eV for linear C3P (2Π) and 9.15 eV for structure 2 of C3P (2B1). The latter is nearly identical to that found for cyclic C2P, whereas the former is about 1 eV higher than that calculated for linear C2P.17 Conclusions An ab initio molecular orbital study of the C3P and C3P+ species has been carried out. The neutral species is predicted to have a linear ground state (structure 1, 2Π electronic state), the next lowest-lying isomer (about 15 kcal/mol higher in energy) being a rhomboidal species (structure 2) with a 2B1 electronic state. A topological analysis of the latter shows that there is a transannular C-C bond, and therefore 2 is in fact a bicyclic species (although topologically unstable). Both species have high dipole moments, 2.773 and 3.893 D, respectively, which should favor their experimental detection. The geometrical parameters lead to the following rotational constants:
1
B ) 2.807GHz
2
A ) 37.292 GHz, B ) 6.321 GHz, C ) 5.405 GHz
Vibrational frequencies and IR intensities have been estimated at the MP2 level. In the case of the ground state the IR spectrum should be dominated by the fundamental of a C-C stretching mode in the region of 2350 cm-1. For structure 2 the most intense line is predicted to appear in the region of 1450 cm-1. In the case of the cation the ground state is also predicted to be a linear structure (3Σ- electronic state). The triplet cyclic structure derived from 2 (structure 2t) lies about 10 kcal/mol higher than the ground state at correlated levels. A topological analysis of 2t reveals that this is in fact a truly four-membered ring, since there is no transannular C-C bonding. The estimated ionization potentials for linear (1) and cyclic (2) C3P isomers are 9.38 and 9.15 eV, respectively. Therefore it seems that, contrary to the CnSi species, the analogues of phosphorus have linear ground states. This is partly due to the fact that silicon prefers to form σ bonds, whereas the tendency of phosphorus to take part in π-bonding favors linear arrangements. In this respect CnP compounds should be considered similar to the CnS series, since it has been shown19,20 that these sulfur compounds prefer as well linear conformations.
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