6819
J. Phys. Chem. 1995,99, 6819-6827
Is Phosphorus Able To Form Double Bonds with Arsenic, Antimony, or Bismuth? An ab Initio Study of the PXH2 Potential Energy Surfaces Loic MahC and Jean-Claude Barthelat" I.R.S.A.M.C.,Laboratoire de Physique Quantique, C.N.R.S. U.R.A. 505, Universitk Paul Sabatier, 118 Route de Narbonne, 31 062 Toulouse Cedex, France Received: October 4, 1994; In Final Form: February 21, 1995"
A systematic study of the singlet and triplet PXH2 potential energy surfaces, X ranging from nitrogen to bismuth, has been undertaken through a b initio methods. Geometries were optimized at the Hartree-Fock level, and single-point energies taking into account the electron correlation effects were calculated. Effective core potentials, including the main relativistic effects, have been used for the heaviest X atoms, i.e. arsenic, antimony, and bismuth. General trends in the structural and energetic properties of the various isomers, when going down group 15, are given. The possibility of forming P-Sb and P-Bi double bonds is c o n f i i e d , as the trans HPSbH and HPBiH isomers are found to be global minima on the singlet potential energy surfaces. The H2PSb and HZPBi isomers in their triplet states appear to be lower in energy than the corresponding trans (closed-shell) isomers, by 0.8 and 7.5 kcdmol, respectively. However, the energy barriers are large enough to prevent any isomerization of the HP-BiH species to HzPBi singlet or triplet species. On the other hand, the thermodynamic stability of the P-X double bond is predicted to decrease when X varies from nitrogen to bismuth, which can explain the difficulties encountered by the experimentalists to synthesize compounds containing P=Sb and P=Bi double bonds.
I. Introduction
\
The chemistry of doubly bonded group 15 elements is being increasingly studied, both at theoretical and experimental levels. An exhaustive review on this subject has been recently published by Weber.' In particular, N-N, P=N, and P=P bonds have been extensively studied theoretically2-*and are now considered as classical by experimentalists. However, the interest in arsenic, antimony, and bismuth is only quite recent. A few experimental results have been published, announcing P=X and X=X bonds (with X = As and Sb) in acyclic9-" compounds, such as
More recently, some cyclicI2 compounds have been synthesized (with X being also possibly phosph~rus'~-'~). In such structures, the P=X bond would contribute to a possible aromatic character of the ring.
I
H
Until now, no P=Bi double bond has been experimentally identified and P-Sb seems to easily d e c o m p o ~ e ~(giving *'~ diphosphene RP-PR) or dimerize.'* Most often, the double bond is reduced to a single P-X bond incorporated into a fourmembered ring. This behavior has been observed for cyclic compounds containing a P=Sb bondI2 and even for acyclic compounds containing a P-As bond.'
* E-mail:
[email protected] @Abstractpublished in Advance ACS Abstracts, April 15, 1995.
P-x
I
/
I
/x-p\
\
P-P
I
/x-x
/
I \
A theoretical investigation on the X=X symmetrical bonds (X = P, As, Sb, and Bi) has been carried out by Nagase et al.I5 The authors c o n f i i e d that such double bonds might be amenable to experiment, even in the case of the heaviest group 15 elements. The purpose of the present work was to enlarge this fiist theoretical approach by studying the P=X bonds. Although our main subject is the practically unknown behavior of the heavier elements As, Sb, and Bi, we included, for the sake of comparison, the widely studied X = N and X = P cases in our calculations. The singlet and triplet PXHz potential energy surfaces (PES) were investigated using an ab initio method, in order to discuss the thermodynamic stability of the P=X double bond, X varying from nitrogen to bismuth. The competition between various isomers on the PES is discussed in terms of electronegativity and size of X. Furthermore, some preliminary calculations were made in order to obtain useful data for comparison, i.e. bond lengths, bond energies, and frequencies for the following bonds: X-H, P-X, and e x . 11. Computational Details
In a first step, the studied structures were optimized at the Hartree-Fock (RHF or ROW) level. Effective core potentials (ECP) of Durand and Barthelat16 were used for every atom of group 15, leaving five electrons in the atomic valence space. For arsenic, antimony, and bismuth, mean relativistic effects were taken into account in the ECPI7 through mass-velocity and Darwin term corrections. Spin-orbit effects were not included in our calculations. The valence electrons were described by a basis set of contracted Gaussian functions of double-C plus polarization (DZP) quality. The exponents for the d polarization functions were taken at 0.95,0.45,0.27, 0.21,
0022-365419512099-6819$09.0010 0 1995 American Chemical Society
MahC and Barthelat
6820 J. Phys. Chem., Vol. 99, No. 18, 1995
TABLE 1: SCF-Calculated Properties of Group 15 Monohydrides: (Bond Lengths in Angstroms, Harmonic Vibrational Frequencies in cm-I and Relative Energies (AE) in kcallmol) (Experimental ValuesU in Parentheses) state
parameter
N
P
As
Sb
Bi
'E+
X-H frequency AE X-H frequency AE X-H
1.028 (1.036) 3605 (3352) 63.6 (60.6) 1.029 (1.034) 3588 ([3188]) 42.7 (35.9) 1.030 (1.036) 1.042b 3555 (3282) 3416b
1.427 2484 43.7 (43.3) 1.428 (1.430) 2478 29.4 22" (21.9) 1.429 (1.422) 1.426b 2466 (2365) 2656b
1.528 2260 42.5 1.528 2257 28.5 1.530 (1.534)
1.689 2016 37.7 1.689 2013 25.3 1.691 (1.723)
1.773 1901 36.3 1.774 1897 24.3 1.776 (1.798)'
2250 (2130)
2004
1889 (1652)'
0.0
0.0
0.0
0.0
0.0
'A 3x-
frequency
AE
a CI calculations, extended basis set (ref 22). SCF DZ+d(P) calculations (ref 2). Averaged over the 0+,1 spin-orbit components of the 32state.
TABLE 2: SCF-Calculated Bond Lengths (in A) and Harmonic Vibrational Frequencies (in cm-') for the P-Xa and P X Bonds (When Available, Experimental Valuesa in Parentheses) parameter P-X bond length frequency P=X bond length frequency frequency scaling factor
N
P
1.717 1.706b 860 1.461 (1.491) 1.47' 1553 (1337) 1554' 0.86
2.245 2.214b 484 1.869 (1.893)
2.364
2.536
2.63 1
370 1.973 (1.999)
324 2.143 (2.205)
292 2.226
896 (781)
696 (604)
586 (500)
533
0.87
0.87
0.85
0.86d
As
Sb
Bi
a The P-X bond lengths are obtained from a complete geometry optimization of H2P-XH2 in the gauche conformation. HF/6-31G* calculations (ref 24). SCF DZ+d(P) calculations (ref 2). Estimated value taken as the average of the scaling factors obtained with N, P, As, and Sb.
and 0.16 for N, P, As, Sb, and Bi, respectively. The exponent for the p polarization function on H was taken at 0.90. The notation DZ+d(P) means the presence of a d polarization function on phosphorus only.2 The geometry optimization was performed, using the HONDO-8 program,'* with a self-consistent-field (SCF) gradient technique. The convergence threshold on the gradient components was fixed at The vibrational frequencies and corresponding normal modes of each state were determined in the same conditions, hence allowing the characterization of each stationary point on the PES as a minimum or a transition structure (TS) and producing zero-point-energy (ZPE) corrections for use in energetic comparisons. The method used was a finite difference of analytical first derivatives. For the trans HPXH isomers, this first step was repeated at the complete active space SCF (CASSCF) level, using a triple-9 plus polarization (TZP) basis set. The active space included the n and n* orbitals. In a second step, electron correlation was taken into account by applying valence shell configuration interaction (CI) to every minimum optimized at the HF level. The basis sets are of TZP quality. The starting point is a pseudopotential HF calculation on the SCF-determined geometry, using the PSHF program,I9 which is derived from the standard HONDO program.20 The CI method is the CIPSI algorithm:21a variational zeroth-order wave function is built up from an iterative selection of the most important determinants, the other ones being treated by secondorder Moller-Plesset perturbation (MP2). At the end, the variational subspace included all determinants whose coefficient in the first-order perturbed wave function was larger than or equal to 0.015. As an estimate of the CI calculations performed, the number of determinants treated variationally ranges from 34 (skewed HPAsH 3A) to 133 (H2PAs IA,), while the number of determinants treated by the perturbative method ranges from 1.3 x lo6 (PSbH2 'A") to 4.8 x lo6 (HPSbH 'A),
111. Preliminary Calculations The following structures have been studied at the SCF level in order to produce references for bond lengths, bond energies, and vibrational frequencies in our PXH2 study. Undoubtedly, each of these particular structures would deserve to be more deeply investigated, especially by including electron correlation and using more extended basis sets. (1) X-H Monohydrides. These molecules were mainly considered as fragments of the trans HPXH isomers and studied with the same basis set of DZP quality. Table 1 summarizes the SCF-predicted bond lengths, vibrational frequencies, and relative energies of the three lowest electronic states (the 3Zground state and the 'A and IZ+excited states). The electronic configuration is lu22u23u2for the IZ+state and 1 a 2 2 u 2 1 n ' 2 ~ ' for the 32- and [ A states. The energy ordering remains the same, i.e. 3Z- < IA < IZ+, whatever the nature of X. We obtain a global good agreement with the experimental and previously published results, i.e. an increasing X-H bond length and decreasing X-H stretching vibrational frequency, when X goes from nitrogen to bismuth. Although we were particularly interested in X-H bond lengths, for which a SCF optimization is generally sufficient, one can notice the importance of electron correlation effects. For example, for the 3Z-,1A energy separation of P-H, the CI value (22 kcal/mo1)22is closer to the experimental one (21.9 kcal/m01)~~ than our SCF value (29.4 kcal/mol). (2) H2P-XH2 and F X Molecules. These molecules were studied in order to obtain P-X single bond and P S X triple bond lengths which could be compared with those of the various isomers of the PXH2 potential energy surfaces. Moreover, we determined vibrational frequencies and a frequency scaling factor for each PEX bond. This scaling has been applied to the SCF-calculated frequencies of the P=X bonds of the trans HPXH isomers, in order to obtain more realistic values. The results conceming P-X and PEX bonds are listed in Table 2. At this level of theory, the predicted triple-bond lengths and
J. Phys. Chem., Vol. 99, No. 18, 1995 6821
PXH2 Potential Energy Surfaces
Closed shell states H\,P-x H
1=7 x, P,
-
0 P-x,
trans 1K,
c,
(P: 'Ap, Cph)
cis ' A , c, (P: 'A,, C2v)
c
TABLE 3: Optimized Geometries of the Trans and Cis HPXH Isomers (Bond Lengths in Angstroms, Bond Angles in Degrees) isomef Darametert' N P As Sb Bi trans 'A' P-X 1.562 2.019 2.128 2.297 2.384
-HH
P-H
H
planar or pyramidal C2v ' A , C,
X-H
1Al,
HPX
Open shell singlet and triplet states
PXH
cis 'A' skewed lS3A,C1 (P : 1,38, C,)
.
-
.P-x
-/ H'
pyramidal
c
1,3~,,,
Figure 1. Studied structures (minima on the PES) with X ranging from nitrogen to bismuth.
vibrational frequencies are quite comparable to the experimental ones. In a classical way, the F X bond length increases and the e X stretching frequency decreases from X = N to X = Bi. For PEX, the SCF-predicted bond shortening with respect to the single P-X bond (H2P-XH2 molecules) ranges from 14.9 to 16.7%. As a comparison, for a CEC triple bond, this shortening is about 22% (experimental bond lengths from ref 25), whereas for the N I N bond, which is known as a very strong bond, the experimental shortening reaches 24% (bond lengths from refs 26 (N-N) and 23 (NEN)). This might indicate a relatively weaker bond between P and X in the diatomic F X molecule. The experimental values of the dissociation energies23of P E N (147 kcdmol), P E P (1 16 kcal/ mol), and -Sb (85 kcal/mol) compared to the high dissociation energy of NEN (225 kcdmol) seem to c o n f i i our predictions.
IV. Minima on the Potential Energy Surfaces. Geometries and Electronic Structures The various isomers investigated, as well as their symmetry group and state, are gathered in Figure 1. Each structure has been identified as a minimum on the corresponding PES. For the X = N 2,4-8 and X = P3,537,8cases, a comparison with previous theoretical works is possible, showing an overall good agreement between all these results. However, Allen et aL3 performed DZP all-electron calculations for P2H2 structures and Trinquier,2 while also using ECP, used a DZ+d(P) basis set for the geometry optimizations of the isomers on the PNH2 PES. Moreover, Trinquier assumed that the open-shell singlet and triplet states have the same geometry. Hoffmann and Kuhlei' have optimized the 'A,, IA", and 3A" states of the H2PN isomer at the CASSCF level, whereas Nguyen et d 6optimized various isomers of the PNH:! PES at the HF/3-21G* level with polarization functions (d symmetry) on phosphorus only. In a more recent paper, Nguyen and Ha7 performed geometry optimizations on various P2H2 and PNH2 isomers at the MP2/ 6-31G** level. Ito and Nagase8 investigated the P2Hz and PNH2
P-X P-H X-H HPX PXH
(1.596) 1.606' 1.431 (1.420) 1.415' 1.014 (1.010) 1.025' 99.7 (99.1) 98.3' 110.1 (110.0) 107.8' 1.555 1.447 1.011 104.9 117.2
(2.056) 2.042' 1.424 (1.415) 1.412' 1.424 (1.415) 1.412' 95.6 (95.6) 94.3' 95.6 (95.6) 94.3' 2.026 1.423 1.423 100.5 100.5
(2.181)
(2.357)
(2.456)
1.424 (1.415)
1.426 (1.416)
1.427 (1.417)
1.525 1.686 (1.524) (1.685)
1.771 (1.770)
95.0 (94.8)
94.0 (94.1)
93.5 (93.6)
94.8 (94.5)
94.7 (93.9)
94.0 (93.1)
2.135 1.421 1.523 99.8 99.6
2.305 1.420 1.686 97.9 99.0
2.392 1.420 1.772 97.8 98.1
a For the trans and cis HPPH, the symmetry of the states are 'Ag and 'AI, respectively. * CASSCF values in parentheses (TZP basis set, this work). MP2/6-31G**-optimized geometries (ref 7).
PES at the HF/6-31G** level. These differences in the computational methods may induce results slightly different from ours. (1) The P=X Double Bonds. Two structures are characteristic of the P=X double bond, namely, the trans and cis HPXH isomers. The geometries of these isomers, determined at both the SCF and CASSCF (for the trans isomer) levels, are summarized in Table 3. Our results for trans HPNH and HPPH are compared to recent MP2/6-31G** geometries determined by Nguyen and Ha,7 showing good agreement. The doublebond lengths are located between the single-bond lengths of H2PXH2 and the triple-bond lengths of PEX. The shortening of the double bond with respect to the single P-X bond ranges from 9.0% (P=N) to 10.1% (P=P) (SCF bond lengths) for all the group 15 atoms. Remember that the experimental shortening for a C-C double bond is about 13%.25 Moreover, Treboux and Barthelat2" predicted a shortening of 10-12% for group 13 X=X double bonds, whereas Nagase et aZ.I5foretold a bond shortening of between 8.9% (Bi=Bi) and 9.7% (As-As) for group 15 symmetrical X=X double bonds. Considering these results, one can already assume the existence of a typical double bond for the trans and cis isomers on the PXH2 PES. For P=P bond lengths, Weber' reported experimental values ranging from 2.001 to 2.049 A, whereas Cowley et U Z . ~ . ' ~ synthesized a substituted phosphaarsene with a phosphorus-arsenic double bond of 2.125 A. Giith et al.I3 obtained a cyclic P=P bond of 2.063 A. Our predicted CASSCF values (P-P, 2.056 A, and P-As, 2.181 A, for the trans isomers) are in good agreement with these experimental values, keeping in mind that the synthesized molecules contain more bulky ligands. SCF and CASSCF vibrational frequencies of the trans isomers are given in Table 4. We determined a scaling factor using the computed and experimental frequencies of the e X bonds, as mentioned in the previous section. We applied this scaling factor to the SCF-calculated vibrational frequencies of the P - X bonds, thus readjusting these frequencies to observable ones. These scaled P-X stretch frequencies are also displayed in Table 4. Note that there is good agreement between these scaled SCF values and the CASSCF frequencies calculated for trans HPPH, HPAsH, HPSbH, and HPBiH. Our CASSCF results for the vibrational frequencies of trans HPPH support a good
6822 J. Phys. Chem., Vol. 99, No. 18, 1995
Mah6 and Barthelat
TABLE 4: SCF, CASSCF, and Corrected Harmonic Vibrational Frequencies of the Trans HPXH Isomers (in cm-l) parameter
syma
P=Xstretch
TABLE 6: SCF-Optimized Geometries of HzPX Isomers (Bond Lengths in Angstroms, Bond Angles in Degrees, and Energy Barriers in kcaymol)
N
P
As
Sb
Bi
SCF A'(A,) scaledb CASSCF
1206 1037
533 464 454
457 388 386
415 357 336
P-Hstretch
SCF A'(A,) CASSCF
2435
X-Hstretch
SCF A'(B,) CASSCF
3725
symbend
SCF A'(A,) CASSCF
1170
asymbend
SCF A'(B,) CASSCF
972
torsion
SCF A"(A,) CASSCF
1076
684 595 599 606' 2476d 2507d 2512' 2508' 2524' 2525' 1045 1044 1056' 730 736 749' 848 775 781'
2485 2466 2458 2521 2502 2415 2264 2032 1912 2274 2023 1926 978 1034
890 882
857 841
687 862
598 597
562 564
786 1108
707 626
672 585
Symmetry in parentheses corresponds to the X = P case. Corrected SCF values, using the scaling factor given in Table 3. DZP two-configuration SCF result (ref 3). Corresponds to the symmetric P-H stretching. e Corresponds to the asymmetric P-H stretching. a
TABLE 5: SCF-Optimized Geometries of the Skewed HPXH Isomers (Bond Lengths in Angstroms and Bond Angles in Degrees) staten
parameter
N
P -
As
Sb
Bi
'A('B)
P-X P-H X-H HPX PXH torsionb P-X P-H X-H HPX PXH torsionb
1.758 1.427 1.020 94.7 109.2 90.9 1.731 1.425 1.018 95.7 11 1.7 91.8
2.255 1.425 1.425 94.8 94.8 90.2 2.235 1.425 1.425 95.5 95.5 89.9
2.377 1.425 1.526 94.6 93.6 90.1 2.358 1.425 1.525 95.3 94.2 90.1
2.555 1.426 1.687 94.6 92.5 89.6 2.539 1.425 1.686 95.2 93.0 89.3
2.649 1.426 1.772 94.5 92.0 89.5 2.635 1.426 1.771 95.0 92.3 89.2
state"
parameter
IAII'A'~ P-X P-H HPX HPH out-of-plane' AETs~ I A" P-x P-H HPX HPH out-of-planec AETs~ 3Aff P-x P-H HPX HPH out-of-planec AETs~
N
P
As
Sb
Bi
1.505 1.405 126.5 107.0 0.0
1.959 1.406 127.5 105.0 0.0
2.083 1.404 127.3 105.4 0.0
1.732 1.420 98.7 96.2 77.0 23.6 1.767 1.420 97.0 95.5 79.6 37.9
2.222 1.419 98.3 95.9 77.5 19.7 2.243 1.420 97.3 95.4 79.1 21.6
2.345 1.420 97.7 95.4 78.5 57.3 2.363 1.420 96.8 95.1 79.8 27.7
2.416 1.412 108.4 99.9 60.6 1.7 2.534 1.420 97.4 95.3 79.0 63.0 2.541 1.420 96.7 95.0 80.1 24.4
2.533 1.414 105.6 98.6 65.7 3.5 2.628 1.421 97.0 95.0 79.6 66.9 2.640 1.421 96.4 94.8
80.5 24.2
The IAl and 'A' states are closed-shell, whereas the 'A" and 3A" states are open-shell. States corresponding to the planar HzPN, H2PP, and H;?PAs isomers and to the pyramidal H;?PSband HzPBi isomers, respectively. The out-of-plane angle is defined as the angle between the H2P plane and the P-X bond. SCF energy barrier corresponding to the planar inversion of H2P.
TABLE 7: SCF-Optimized Geometries of PXH2 Isomers (Bond Lengths in Angstroms, Bond Angles in Degrees, and Energy Barriers in kcaymol) stateo
parameter
N
P
As
Sb
Bi
'AII'A'~ P-X 1.637 1.959 2.207 2.406 2.568 X-H 1.007 1.406 1.508 1.672 1.760 PXH 123.3 127.5 108.5 103.8 97.0 HXH 113.4 105.0 100.0 96.5 93.3 out-of-planec 0.0 0.0 60.5 69.0 79.1 3A(3B) AE=sd 1.0 2.5 14.1 IA" P-x 1.699 2.222 2.353 2.526 2.631 X-H 1.006 1.419 1.520 1.680 1.766 PXH 120.0 98.3 96.0 95.0 93.4 HXH 112.6 95.9 94.3 93.5 92.2 out-of-planec 25.8 77.5 81.2 82.7 85.0 AETs~ 0.1 19.7 25.0 25.4 31.6 States in parentheses correspond to the X = P case. The torsion 3Aff P-x 1.720 2.243 2.369 2.543 2.642 angle is defined as the angle between the HPX and PXH planes. X-H 1.008 1.420 1.520 1.680 1.765 PXH 116.5 97.3 95.3 94.3 93.1 comparison to the all-electron CASSCF results of Allen et ~ l . , ~ HXH 110.4 95.4 94.0 93.3 92.1 out-of-plane' 38.5 79.1 82.2 83.7 85.5 with an average deviation smaller than 1%. AEmd 0.8 27.6 35.5 41.5 54.2 In the cis isomer, the P=X bond length (except for X = N) The 'AI and 'A' states are closed-shell, whereas the IA" and 3A" and the HPX and PXH bond angles are greater than in the trans states are open-shell. States corresponding to the planar PNH2 and isomer, due to the steric repulsion of the hydrogens. In both PPH;?isomers and to the pyramidal PAsH2, PSbH2, and PBiH2 isomers, structures, the angles approach a value of 90" as X goes down respectively. The out-of-plane angle is defined as the angle between group 15. This can be explained by the reluctance of the the XH? plane and the P-X bond. SCF energy barrier corresponding heaviest elements to maintain an sp valence orbital hybridization. to the planar inversion of XH2.
(2) The Skewed HPXH Isomers. These isomers are obtained from the closed-shell trans structure by a closure of approximately 90" of the torsion angle, so that the n orbital is broken. The geometries of these structures are presented in Table 5 . The P-X bond length in the skewed isomers is close to the P-X single-bond length, thus confirming the breaking of the n overlap. Concerning the HPPH 'B state, it can be noticed that we optimized a geometry that is quite comparable to all other skewed HPXH structures, i.e. with a torsion angle of approximately 90", whereas Allen et aL3 optimized a structure with a torsion angle of 109.2", but quite higher in energy. Notice that no significant difference is observed for the corresponding triplet state, when comparing our result with the optimized geometry of Allen and co-workers.
(3) The HzPX and PXH2 Series. The geometries for the HpPX and PXH2 closed-shell states and open-shell singlet and triplet states are presented in Tables 6 and 7, respectively. The HpPN, PNH2, H2PP, and H2PAs closed-shell states are planar isomers. All the other closed-shell and open-shell states are nonplanar isomers. For the nonplanar minima, the energetic barrier corresponding to the planar transition state (determined at the SCF level) is displayed in the same tables. The out-ofplane angle, defined as the angle between the P-X bond and the H2P or H2X plane for the nonplanar states, increases with the size of X and tends toward 90" for PXH2 (1,3A"),although it remains constant (about SO0) for H2PX ('s3A"). The transition state barrier increases in a given series, except for the 3A" HzPX series.
PXH2 Potential Energy Surfaces
J. Phys. Chem., Vol. 99, No. 18, 1995 6823
A general rule for the behavior of the various H2PX and PXH2 closed-shell isomers can be given by taking into account the delocalization of the px lone pair of the central atom into the empty p valence orbital of the terminal one, as shown in the following scheme:
Moreover, a back-donation can occur from the terminal atom (pn orbital) toward the unoccupied d orbital (of the appropriate symmetry) on the central atom.
'0 If these delocalizations are important, the molecules will be constrained to assume a planar geometry which allows a maximum overlap. If delocalizations are weak, the terminal atom will tend to a pyramidal conformation, which is observed when going down group 15.
For the H2PX closed-shell series, the electronegativity of the terminal atom X, with respect to the electronegativity of the central atom P, will govern the geometry and bonding of the molecule (see refs 28 and 29 for an interesting approach to the concept of electronegativity). For H2PN, a strong delocalization from phosphorus toward nitrogen (electronegativity of 3.066 for N and 2.253 for P)28 and a back-donation of the nitrogen lone pair into the 3d orbital of P occur. For H2PP, both delocalizations are still possible (same electronegativity) but smaller. For the other isomers of the series, a weak delocalization happens from P to X, since the electronegativity of P is almost equivalent to the electronegativity of X (2.211 for As, 1.984 for Sb, and 2.102 for Bi).28 The back-donation can occur from X to P, but remains small, too. Evidence is given by the multiplicity of the P-X bond in the H2PN, H2PP, and H2PAs planar isomers. The P-X bond multiplicity, which is intermediate between double and triple, becomes closer to that of the double bond as X varies from nitrogen to arsenic (see Tables 2, 3, and 6). As X goes down group 15, the tendency to pyramidalize prevails over these weak delocalizations, allowing the H2PSb and H2PBi isomers to be nonplanar. However, one can notice the small barrier of the planar transition state (1.7 and 3.5 kcavmol, respectively), which is stabilized by these delocalizations. For the nonplanar isomers, the P-X bond length has a value intermediate between a single-bond and a double-bond length. For the PXH2 closed-shell series, the electronegativity and tendency for pyramidalization of the central atom X will
TABLE 8: Various PX ShorteningLengthening Ratio (%) with Respect to the Single-Bond Length Optimized in the HzP-XHz Molecule bond length variationu molecule state N P As Sb 0.0 0.0 0.0 0.0 H2P-XH2 (gauche) 'A -9.4 trans HP=XH 'A' ('A,)b -9.0 -10.1 -10.0 -9.1 'A' -9.7 -9.7 cis HP=XH -9.4 P=X 'Z+ -14.9 -16.7 -16.5 -15.5 H2PX 'AI ('A'Y -12.3 -12.7 -11.9 -4.7 PXH2 -4.7 -6.6 'Ai ('A')d -5.1 1 A" 0.9 -1.0 -0.8 -0.1 H2PX 'A'? PXH2 -1.0 -0.5 -0.4 3A" H2PX 2.9 -0.1 0.0 0.4 3A" PXHz 0.2 0.2 0.3 skewed HP-XH 2.4 0.4 'A (lB)b 0.5 0.7 skewed HP-XH 3A (3B)b 0.8 -0.4 -0.3 0.1
Bi
0.0
-9.4 -9.1 -15.4 -3.7 -2.4 -0.1 0.0
0.3 0.4 0.7 0.2
A negative value indicates a bond shortening, whereas a positive one indicates a bond lengthening. States in parentheses correspond to the X = P case. States in parentheses correspond to the pyramidalized structure, i.e. for Sb and Bi. d States in parentheses correspond to the pyramidalized structure, Le. for As, Sb, and Bi.
determine the geometry, as the terminal atom is always a phosphorus. For PNH2, the nitrogen cannot delocalize its lone pair toward the phosphorus and there is no back-donation, because the 3d orbital of N is too high in energy to be involved in this phenomenon. The P-N bond length (1.637 A) becomes closer to the P-N single-bond length (1.7 17 A). The molecule remains planar since the -NH2 group has a low tendency to pyramidalize. For PPH2, the situation has been described in the H2PX series. For the other isomers, a weak delocalization can occur from P to X and a weak back-donation from X to P (because of the small difference in electronegativities of P and X). The tendency for the pyramidalization of X prevails, and the bond lengths are intermediate between the single-bond and the double-bond length (Table 7). As for the nonplanar H2PX isomers, the planar transition structure is low in energy. Let us now consider the open-shell states. The delocalizations allowed in the closed-shell states become unfavorable, since the pn orbitals implied in these transfers are now occupied by one electron. The molecule assumes the nonplanar conformation whatever the nature of X, because of the repulsion between the electron pair on the central atom and the single electron on the terminal atom.
The bond lengths in the 'A" and 3A" states are close to the single P-X bond lengths, and this confirms the almost nonexistent delocalization in the H2PX and PXH2 open-shell isomers. The planar transition structure barrier is important, since this form is not stabilized by delocalizations. (4) Trends in P-X Bond Lengths with Respect to the Nature of X. The lengtheninghhortening ratios of the various SCF-calculated PX bond lengths with respect to the single P-X bond length in the H2PXH2 molecule are displayed in Table 8. The bond multiplicities of all the PX bonds in the various isomers can be estimated in that way. In particular, the doubly bonded character of the cis and trans isomers is well characterized. Moreover, the difference in bond multiplicity between planar and pyramidal H2PX and PXH2 isomers appears clearly
6824 J. Phys. Chem., Vol. 99, No. 18, 1995
MahC and Barthelat
TABLE 9: CI Relative Energies for the Lowest Minima on the Singlet and Triplet PES (kcaVmo1)
-
-54
-
-57
-5 1 -48
..... skewed HPXH ..... cis HPXH
-1 8 -1 5 -1 2
-9 -6 -3
N
P
AS
Sb
Bi
-0
p. ......!A ++,
% ,,
"%,
+*,'
1A
J. Phys. Chem., Vol. 99, No. 18, I995 6825
PXH;! Potential Energy Surfaces d l -48 -45 -42 -39 -36 -33 -30 -27 -24 -2 1
relative energy (kcal/mol)
3A" P
50 -
40. \ \
30.
\
I I
20.
-1 8 -1 5
Bi-
P-
H,
I
10.
-1 2 -9 -6 -3 -0 --3 --6 --9
I
Hb
I
'
0.
-lob
N
P
As
Sb
Bi
Figure 4. Evolution of CI relative energies (in kcal/mol) of the openshell triplet states (minima on the PES). Zero energy corresponds to the closed-shell trans HPXH isomer.
HP-BiH isomers in both singlet and triplet states, according to the following scheme: Hb\
,p-Bi
Ha
-
Hb\
g-Bi \ :
Ha
-
Hb\
10
20
\
/
P=Bi
30 40 50
a0
70
80
90
\ loo 1'lO
PBiHa angle (degrees) Figure 5. Energy profiles for the 1,2-H shift between HzPBi and HPBiH isomers. Ha stands for the migrating hydrogen (full line for the singlet state and dotted line for the triplet state). Note that the right part of the singlet curve corresponds to a planar molecule, while the left part is associated with a pyramidalized -PH2 fragment.
TABLE 10: CASSCFRZP Fully Optimized Geometries during the H Migration from H2PBi to HPBiH Hb\
Hb\
P-B(
Ha
parametef
'A'
3A"
Hb\
g-Bi , ,'
rBi
Ha
Six stationary points were identified on the PES through CASSCFlTZP calculation^^^ and then fully optimized at the same level of theory. Energy profiles are presented in Figure 5 , and CASSCF geometries are given in Table 10. For each energy surface, the relative energies of three stationary points, i.e. the two minima and the corresponding TS, are displayed in Table 11, at two levels of theory (CASSCF and CASPT232).It must be noticed that the difference between the two sets of values is very small and will not affect our general conclusion. The singlet and triplet energy surfaces cross during the Ha migration. However, the singlet trans HP=BiH, if formed, could not isomerize to the corresponding triplet H2P-Bi with an intersystem crossing point located sufficiently high in energy. In our case, this point is found to be near the singlet transition structure, which is predicted, in the CASF'T2 approach, to be at 36.8 kcaYmol above the trans HP=BiH. This calculated banier appears to be large enough to guarantee the existence of a HP-BiH species. In a classical way, the cis isomer is less stable than the corresponding trans isomer, due to steric repulsion. In order to explain the evolution of the cis-trans separation observed in Figure 2, we have to consider the dipoles composed by the X-H fragments. The charge distribution, governed by the electronegativities, is X(d+)-H(d-), except for N(d-)-H(d+). The electrostatic repulsion between the P-H and X-H fragments tends to destabilize the cis isomer in the X = P, As, Sb, and Bi cases. An increasing P-X bond length, however, reduces this effect, and we can indeed observe a stabilization of the cis isomer toward the trans isomer, as X goes from phosphorus to bismuth. The cis HPNH isomer is a particular situation,2 as the two dipoles attract each other, thus stabilizing
\
'A
2.586 P-Bi 2.608 2.643 1.757 P-Ha 1.439 1.440 1.449 P-Hb 1.439 1.440 3.162 3.146 1.907 Bi-Ha 102.2 HbPBi 98.6 96.2 26.7 27.1 42.8 PBiH, HaPBiHb 96.7 94.9 57.0 dihedral angle
P-B( Ha
Ha
3A
'A'
3A
2.457 2.620 2.012 3.116 1.448 1.445 1.934 1.812 93.3 93.4 49.1 92.5 84.0 180.0
2.634 3.252 1.446 1.814 95.0 92.1 88.9
Bond lengths are in angstroms and bond angles in degrees.
TABLE 11: Relative Energies (in kcallmol) of Six Stationary Points on the Singlet and Triplet [HzPBi] Energy Surfaces species
CASSCF/TZP
CASFT2F"
trans HPBiH ('A') TS ('A) H2PBi ('A') HPBiH (3A) TS (3A) H2PBi (3A")
7.3 48.3 23.3 25.4 44.7 0.0
7.1 43.9 21.7 26.9 38.4 0.0
Calculated using the CASSCF/TZP-optimized geometries. FT2F means that the perturbation treatment uses the full Fock matrix. (I
the cis isomer with respect to the trans isomer (and shortening P-N). We determined the total bond energy of the P - X double bond at the MP2 level. The (a+n) P=X total bond energy is defined as EMPZ(trans) - (EMPZ(PH) EMPZ(XH)). The P-H and X-H monohydrides are taken in their 32-ground state. If one considers the ('A) skewed HPXH isomer with respect to the corresponding (IA') trans HPXH isomer, the p orbitals have
+
6826 J. Phys. Chem., Vol. 99, No. 18, 1995
Maht and Barthelat
\
-0.02 -0.04'
-0.33 -0.39
-8.12
7c*
7-c n
-9.74
2 -11.35
N
P
As
S b Bi
Figure 6. Frontier orbital energy levels (eV) of the trans isomer. TABLE 12: Bonding Energies of the P=X Double Bonds (kcaUmol) N" P As Sb Bi 48.4 40.7 34.2 89.5 (90.0) 56.1 u+nenergy n energy 40.3 (39.8) 29.8 23.3 19.9 16.7 u energy 49.2 (50.2) 26.3 25.1 20.8 17.5 a Values in parentheses: CIPSI-MPB DZP calculations (ref 2). Geometries were determined with a DZ+d(P) basis set only.
been rotated approximately 90" on P or X, thus breaking the JC component of the P=X bond. The CI energy difference between the trans isomer and the ('A) skewed isomer can be understood as the JC bond energy. The results (total energy, n energy, and (T energy) are displayed in Table 12. It appears clearly that the P=X bonds are less and less stable as X goes down group 15. This could explain the difficulties encountered by Mazieres et ~ 1 . in' ~the synthesis of cyclic P=Sb (dimerization) and P=Bi (no results) bonds. Moreover, Cowley et ul.93'0reported a slow decomposition of their synthesized acyclic phosphastilbene in solution and a failure to obtain a P=Bi bond. More generally, Weber' relates an instability of *As, As-As, and P = S b bonds. Our predictions concerning the stability of the P=X bonds ( ~ 3 5 kcavmol for the less stable P=Bi bond) clearly show that these bonds are not stable enough to be synthesized with H as ligands. As a comparison, the bond energy of a C=C bond is approximately 173 kcal/mol in ethylene.25 This study demonstrates that it should be possible to form P=Bi double bonds. However, the search for effective stabilizing substituents remains. The (T and n energies are almost partitioned, which allows one to predict that these bonds are quite reactive. The n-n* energy level separation is another way for appreciating the reactivity of the P=X bonds. These values are determined on the CASSCF-optimized trans isomers and shown in Figure 6. The n-n* gap diminishes as X proceeds from nitrogen to bismuth. One can therefore predict an increasing reactivity of the P=X bonds as X goes down group 15. We must notice that, for X = N, the n orbital is higher in energy than the JC orbital, as is also the case for C=N and N=N bonds. (2) The Skewed HPXH Isomers. Starting from the trans isomer, the JC component of the P=X bond has been broken by closure of the torsion angle. One can observe, in Figures 3 and 4, that the skewed HPXH isomers, both singlet and triplet, are always less stable than the corresponding trans isomer, but more and more stable as the size of X increases. This trend can be explained by the reducing thermodynamic stability of
the P=X bond, as X goes from nitrogen to bismuth. The double-bonded situation becomes less favorable toward the single one (skewed isomer). (3) The H 9 X and PXHz Series. Except for HzPN, the 3A" state is the most stable for both series (see Table 9). For HzPN, PNH2, HzPP, and HzPAs, the 'A1 (planar) closed-shell isomer is more stable than the IA" (pyramidal) open-shell isomer. As already mentioned in section IV(3), these planar forms are stabilized by delocalizations of lone pair electrons of one of the atoms into the pn orbital of the other. Since the pyramidal closed-shell isomers (H2PSb, PSbH2, H2PBi, and PBiH2) are not stabilized by delocalizations, the corresponding open-shell singlet states become more stable. The situation for PAsHz is somewhat different, since both 'A' and IA" states are pyramidal, but the closed-shell state is the most stable. In fact, the 'A' and 'A" states are nearly degenerate (ZPE-corrected CI energy separation of 0.5 kcal/mol, see Table 9). However, the planar closed-shell transition state is only 1 kcavmol above the 'A' minimum (SCF level, see Table 7), indicating that the electron delocalizations are not negligible, thus stabilizing somewhat the closed-shell PAsH2 form. A constant feature for these two series is the greater stability of the isomer with the heaviest atom of the (P,X) couple as terminal atom, according to Figures 2, 3, and 4. For the H2PX isomers, there are two P-H bonds, whereas there are two X-H bonds for the PXH2 isomers. Remember that the strength of the X-H bond decreases as X goes from nitrogen to bismuth. Experimental values33of the XH bond energy are NH (93 kcal/ mol), PH (78 kcavmol), ASH (71 kcavmol), and SbH (61 kcav mol). We could therefore expect to have the H2PX isomer always more stable than the PXH2 isomer, with an increasing gap between them, when P is bonded to a heavier element. We could also predict a reversed situation for X = N. In fact, Figures 2, 3, and 4 confirm these predictions. This trend is somewhat altered by some other considerations, such as stabilization by electron delocalizations in the closed-shell states (see section IV(3)). This seems to be the case for the planar 'A1 H2PAs isomer, which is not so well located in the closedshell H2PX series with respect to the pyramidal 'A' H2PSb isomer (Figure 2). The series of open-shell states are more regular, as all isomers in that case are pyramidal. Notice, however, that the lA" and 3A" PNHz isomers are also slightly stabilized, because of their low-lying planar transition state (see Table 8), due to the easy inversion of -NH2. In Figures 3 and 4, these isomers appear in the most concave part of the PXHZ curves. In summary, it is reasonable to say that the planar isomers, or the pyramidal isomers having a low-lying planar transition state, are obviously stabilized (see Figures 2-4). VI. Bridged P@-H2)X Structures
For P@-H2)P, Allen et uL3 tried to optimize both a planar rhombus form and a nonplanar boat form, as shown below.
rhombus
boat
All the structures they obtained, at the SCF or CASSCF level, exhibit at least one imaginary vibrational frequency. A qualitative rule governing the existence of bridged structures as minima on the PES has been formulated by Treboux and B a ~ t h e l a tin~ ~ their study of the group 13 X2H2 PES. A bridged structure is
PXHp Potential Energy Surfaces possible only if the parent XH fragment possesses at least one vacant MO in its ground state, allowing the formation of threecenter two-electron bonds. The absence of vacant orbitals in the ground state of group 15 monohydrides (32-)precludes the formation of these bonds, in contrast to the X-H fragments when X belongs to group 13 or 14. A bridged isomer is unlikely to occur on the PXHZ PES. Our calculations have confirmed this prediction. All our attempts to optimize such a bridged isomer have failed.
VII. Conclusion Up to now, all experiments devoted to the synthesis of P=Bi double bonds have failed. Moreover, the F S b bond seems to be highly unstable, whether in acyclic or cyclic compounds. The new insight given by the present study shows that there should be no reason for these double bonds to be out of reach of the experimentalists. In fact, the model molecules, the trans HPSbH and HPBiH are the lowest minima on the singlet PES. However, the thermodynamic energies (computed P=X bond energy) of these bonds are quite weak with hydrogens as ligands. The calculated n-n* gap predicts an increasing reactivity with the size of X. The challenge is now the search for good stabilizing ligands, in order to synthesize stable F S b and F B i bonds. Our prediction conceming P=Sb bonds is the following: a bond length of 2.357 8, and a bond stretch frequency of 386 cm-'. For F B i , these values are 2.456 8, and 336 cm-I, respectively. Through this approach of the heavy main group elements, we hope to bring a contribution to the knowledge about the chemistry of phosphorus and its analogues. This study could be extended by the examination of the other mixed X=Y double bonds, X and Y being any group 15 element. Acknowledgment. We thank Dr. G. Trinquier and Dr. S. Mathieu for useful discussions conceming the chemical aspects of this work. References and Notes (1) Weber, L. Chem. Rev. 1992, 92, 1839 and references therein, (2) Trinquier, G. J. Am. Chem. SOC.1982, 104, 6969. (3) Allen, T. L.; Scheiner, A. C.; Yamaguchi, Y.; Schaefer, H. F., III. J. Am. Chem. SOC.1986, 108, 7579 and references therein for calculations on the P2Hz potential energy surface. (4) Hoffmann, M. R.; Kulher, K. J. Chem. Phys. 1991, 94, 8029. (5) Ha, T.-K.; Nguyen, M. T.; Ruelle, P. Chem. Phys. 1984, 87, 23. (6) Nguyen, M. T.; McGinn, M. A,; Hegarty, A. F. J. Am. Chem. SOC. 1985, 107, 8029. (7) Nguyen, M. T.; Ha, T.-K. Chem. Phys. Lett. 1989, 158, 135. (8) Ito, K.; Nagase, S. Chem. Phys. Lett. 1986, 126, 531. (9) Cowley, A. H.; Lasch, J. G.; Norman, N. C.; Pakulski, M.; Whittlesey, B. R. J. Chem. SOC.,Chem. Commun. 1983,881 and references therein.
J. Phys. Chem., Vol. 99, No. 18, 1995 6827 (10) Cowley, A. H.; Kilduff, J. E.; Lasch, J. G.; Mehrotra, S. K.; Norman, N. C.; Pakulski, M.; Whittlesey, B. R.; Atwood, J. L.; Hunter, W. E. Inorg. Chem. 1984, 23, 2582. (11) Cowley, A. H.; Norman, N. C. Prog. Inorg. Chem. 1986, 34, 1. (12) MaziBres, M.-R.; Rauzy, K.; Bellan, J.; Sanchez, M.; PfisterGuillouzo, G.; Senio, A. Phosphorus, Sulfur Silicon 1993, 76, 45. (13) Guth, W.; Busch, T.; Schoeller, W. W.; Niecke, E.; Krebs, B.; Dartmann, M.; Rademacher, P. New J. Chem. 1989, 13, 309. (14) Rauzy, K.; Mazikres, M.-R.; Page, P.; Sanchez, M.; Bellan, J. Tetrahedron Lett. 1990, 4463. (15) Nagase, S.; Susuki, S.; Kurakake, T. J. Chem. Soc., Chem. Commun. 1990, 1724. (16) Durand, P.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (17) Barthelat, J. C.; Ptlissier, M.; Durand, P. Phys. Rev. A 1981, 21, 1773. (18) Dupuis, M. HONDO-8, from the MOTECC-89 program package; IBM Corp.: Kingston, NY, 1989. (19) Ptlissier, M.; Komiha, N.; Daudey, J.-P. J. Compur. Chem. 1988, 9, 298. (20) Dupuis, M.; King, H. F. J. Chem. Phys. 1978, 68, 3998. (21) (a) Huron, B.; Malrieu, J.-P.; Rancurel, P. J. Chem. Phys. 1973, 58, 5745. (b) Daudey, J.-P.; Malrieu, J.-P. In Current Aspects of Quantum Chemistry; Carbo, T., Ed.; Elsevier: Amsterdam, 1982; p 35. (c) The reliability of our pseudopotential techniques used in conjunction with the CIPSI algorithm is well established. See, for instance, the following ab initio studies: Trinquier, G. J. Am. Chem. SOC.1990, 112,2130. Trinquier, G.; Barthelat J. C. J. Am. Chem. SOC. 1990, 112, 9121. Treboux, G.; Barthelat J. C. J. Am. Chem. SOC.1993, 115, 4870. (22) Cade, P. E. Can. J. Phys. 1968, 46, 1989. (23) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand-Reinhold: New York, 1979. (24) Sudhakar, P. V.; Lammertsma, K. J. Am. Chem. SOC.1991, 113, 1899. (25) Handbook of Chemistry and Physics, 52nd ed.; Weast, R. C., Ed.; The Chemical Rubber Co.: Cleveland, OH, 1971-1972. (26) Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendeman, R. H.; Ramsay, D. A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J. Phys. Chem. Re$ Data 1979, 8, 619. (27) Treboux, G.; Barthelat, J. C. J. Am. Chem. SOC.1993, 115, 4870. (28) Allen, L. C. J. Am. Chem. Soc. 1989, 111, 9003. (29) Allen, L. C. Int. J. Quantum Chem. 1994, 49, 253. (30) For the HP=BiH singlet species, the active space contains all the configurations that can be constructed from distributing the six electrons from the three occupied orbitals (UPH, UB,H, and n p ~ , among ) six orbitals. For each value of the PBiH, angle, partial geometry optimizations of both the lowest singlet and triplet states of HbPBiH, are performed (only the PHb bond length and the HbPBi angle are frozen at 1.418 A and 93.4", respectively). These calculations were carried out with the GAUSSIAN 92 series of programs.3' (31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A,; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92/DFT, Revision G.2; Gaussian, Inc.: Pittsburgh, PA, 1993. (32) Anderson, K.; Blomberg, M. R. A.; Fulscher, M. P.; Kello, V.; Lindh, R.; Malmqvist, P.-A.; Noga, J.; Olsen, J.; Roos, B. 0.;Sadlej, A. J.; Siegbahn, P. E. M.; Urban, M.; Widmark, P.-0. MOLCAS version 2; University of Lund: Sweden, 1991. (33) Purcell, K. F.; Kotz, J. C. Inorganic Chemistry; Holt-Saunders Intemational Editions: Toronto, 1977. JP9426740
