- Email: [email protected]
Theoretical study of low-lying electronic states of BP molecule
Chemical Physics Letters 381 (2003) 720–724 www.elsevier.com/locate/cplett
Theoretical study of low-lying electronic states of BP molecule Beatriz Miguel a, Salama Omar b, Paula Mori-S anchez c, Jose M. Garcıa de la Vega b,* a
Departamento de Ingenierıa Quımica y Ambiental, Universidad Polit ecnica de Cartagena, Paseo Alfonso XIII 44, 30203 Cartagena, Spain b Departamento de Quımica Fısica Aplicada, Facultad de Ciencias, Universidad Aut onoma de Madrid, Cantoblanco, 28049 Madrid, Spain c Department of Chemistry, Duke University, Durham, NC 27708-0354, USA Received 29 July 2003; in final form 26 September 2003 Published online: 4 November 2003
Abstract BP is a molecule that, to date, has not been experimentally characterized. However, theoretical calculations yield a stable molecule, although its ground state is not unequivocally determinated. In this work, potential energy curves for the ground state and the lower excited states of BP molecule have been calculated. They are derived using the MRDCI procedure and employing 6-311+G(2df) basis sets. The spectroscopic constants and excitation energies for the bound states of BP are compared with previous theoretical results. The MRDCI calculations give the 3 P state as the ground , De ¼ 3:15 eV and xe ¼ 954 cm1 . state, with Re ¼ 1:747 A Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Diatomic molecules formed by either two electronegative atoms or one electronegative and one electropositive atom have been well studied experimentally, whereas the diatomic molecules formed by two atoms belonging to electropositive groups have not been studied extensively with either experimental or theoretical techniques [1,2].
*
Corresponding author. Fax: +34-91-3974512. E-mail address: [email protected] (J.M. Garcıa de la Vega).
The most interesting feature of the BP molecule, like BAs, is that it has the smallest indices of ionicity among the III–V family and constitutes an excellent example of an almost perfect covalence heteronuclear diatomic molecule. This low-heteropolarity gives striking features to the BP system. Mori-Sanchez et al. [3–5] have studied the BP compound in its crystalline and molecular structure, using BaderÕs theory of atoms in molecules [6,7]. In the zinc-blende crystal structure, the binding point is located on the internuclear B–P line between first neighbors, moved away 1.30 and 2.41 a.u. from boron and phosphorus atoms, respectively. These bonds display the characteristic topologic properties of interactions of shared
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.09.153
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
shells justified by their high and negative Laplacian, as in prototype covalent bonds. Those authors have also analyzed the transfer of charge and the polarity inversion under pressure in the electron density of the BP crystal. As regards the stability of the BP molecule, however, the deficiency of experimental data and the difficulty for determining its molecular parameters in the fundamental and excited states, implies that the BP molecule is of great interest since it has very close electronic states of different multiplicity. In fact, the few published works on the BP molecule show unclear results. Boldyrev and Simons [8] have studied five electronic states of BP molecule: 1 Rþ ð1r2 1p4 2r2 Þ; 3 P ð1r2 2r2 1p3 3r1 Þ; 3 R ð1r2 2r2 3r2 1p2 Þ; 5 Pð1r2 2r2 1p2 3r1 2p1 Þ and 5 R ð1r2 2r2 1p2 2p2 Þ. They conclude that the 3 P state is the ground state, while the first excited state 1 Rþ lies 0.3 eV above the ground state and the 3 R , 5 P and 5 R electronic states lie at 0.85, 2.4 and 5.5 eV, respectively. Mori-S anchez [5] has analyzed the electron density of the diatomic BP molecule at different computational levels, namely HF, CASSCF and CISD. In these calculations, it is found a competition between the three states of lower energy, 1 þ 3 R , R and 3 P. Moreover, from the results of UHF and CISD calculations it is concluded that 3 P is the fundamental state in agreement with the results of Boldyrev and Simons [8]. However, CASSCF yields 1 Rþ as the ground state. Correlation effects introduced through CASSCF and CISD calculations tend to increase slightly the equilibrium distances and to move the bond point towards the boron atom. Our aim here is to clarify the electronic spectrum of BP. Encouraged by our previous calculations on the ground and excited states of diatomic molecules [9,10], we have decided to perform MRDCI calculations on this unobserved molecule.
2. Calculations for excited states of B and P atoms Using 6-311+G(2d,f) basis sets [11–13] and the method of Buenker and coworkers [14–16], we have carried out MRDCI calculations for the ground 2 P and three lowest excited (4 P, 2 S and 2 D) states of the
721
boron atom and the ground 4 S and four lowest excited (2 D, 2 P, 4 P and 2 P) states of the phosphorus atom . All occupied and virtual atomic orbitals were used in MRDCI steps for the considered states of B and P atoms. That is, 39 and 47 atomic orbitals for B and P atoms, respectively. The number of reference configurations was selected for obtaining a Geisser coefficient (C2 ) higher than 0.97. The selection threshold in the energy was 2 lhartrees. The configuration functions generated (SAFT: Symmetric Adapted Functions Total) vary from 1593 to 3919 for the 2 P and 2 S states of B atom, respectively, and from 6575 to 8003 for 4 S and 2 D states of P atom, respectively. The number of those SAFT selected for final approximated full-CI (SAF: Symmetric Adapted Functions) varies from 1172 to 2549 (2 P and 2 S states) for B atom and from 4823 to 5582 (4 S and 2 D states) for P atom. Extrapolation of the energy to zero threshold gives the MRDCI energy and the use of the multireference version [17] of the Davidson correction [18] allows the full-CI extrapolated energy to be obtained. These MRDCI and full-CI energies are shown in Table 1. With the full CI-energies, we calculate the atomic excitation energies of B and P atoms (in eV) that are collected in Table 1. The atomic excitation energies are in good agreement with the experimental values [19], also given in Table 1. Only for the highest excited state of P atom (2 P) the difference between computed and experimental excitation energies is greater than 0.15 eV. The selected basis set gives a good description of the excitation energies for all the studied states. Therefore, this basis set will give good dissociation energies for the diatomic molecule.
3. MRDCI potential energy curves of BP molecule The calculations described in this study were made with MRDCI code [14–16] and the 6-311+G(2d,f) basis set [11–13]. All the 20 electrons and all the molecular orbitals (MO) were used in the generation of the SAFT: that is 10 occupied and 76 virtual MOs to carry out the excitations on the initial reference configurations. The configurations were selected to achieve a Geisser coefficient higher than 0.90 in all the calculated points along the proposed range of
722
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
Table 1 MRDCI and full CI energies (a.u.), and excitation energies DE (eV) for the ground and excited states of B and P atoms Configuration
Boron atom 2s2 2p1 2s1 2p2 2s2 3s1 2s1 2p2 Phosphorus atom 3s2 3p3 3s2 3p3 3s2 3p3 3s2 3p2 4s1 3s2 3p2 4s1
2
P P 2 S 2 D 4
4
S D 2 P 4 P 2 P 2
MRDCI
Full CI
DE/eV This work
Exp.a
)24.622694 )24.492356 )24.399443 )24.390708
)24.623930 )24.492845 )24.439458 )24.400514
0.00 3.57 5.02 6.08
0.00 3.57 4.96 5.93
)340.946726 )340.889031 )340.854685 )340.685645 )340.671654
)340.951050 )340.894781 )340.861104 )340.690857 )340.676544
0.00 1.53 2.45 7.08 7.47
0.00 1.41 2.32 6.96 7.19
From Ref. [19].
internuclear distances, with a threshold in the energy of 2 lhartrees. In our MRDCI calculations we have considered the two lowest energies in R and P symmetries for singlet and triplet states. Also the 5 R and 5 P states have been included. That is, a total of ten states or 15 roots in the MRDCI calculations. We have computed the estimated full CI energies from , taking into account that for a R ¼ 1.20 to 8.0 A given symmetry the same reference configurations are preserved along the variation of the internuclear distance. The number of initial reference configurations used for the states 1 Rþ , 1 P, 3 R , 3 P, 5 R and 5 P were 81, 80, 84, 80, 20 and 14, respectively, and giving a SAFT of 1939–13 527, 15 167–22 657, 9906–22 314, 11 097–24 559, 8735– 17 066 and 13 516–21 880, respectively. We have computed the spectroscopic constants of these potential energy curves. They have been calculated fitting the potential energy points with the numerical method proposed by Aguado et al. [20]. We find that 3 P state is the ground state with , and only the 1 Rþ state crosses it at Re ¼ 1:747 A R ’ 1:6 A. This ground state dissociates into B(2 P) and P(4 S), so its dissociation energy is considered the zero of energy in Fig. 1 where the potential energy curves are plotted. All the studied excited states dissociate to either B(2 P) + P(2 D) or B(2 P) + P(2 P), except the quintuplet R states that dissociate into B(4 P) + P(2 D). 1 Rþ and 1 P are the first excited states and lie at 0.36 and 0.40 eV
above the ground state, respectively. Both values are slightly higher than that reported in [8] (0.3 eV). Both states present a stable minimum with a similar dissociation energy, where the 1 P minimum is at an internuclear distance which is longer than that for the 1 Rþ minimum. only 0.1 A A third excited state, 21 Rþ is found lying at 1.7 eV from the ground state. 3 R and 5 P are the fourth excited states lying at 2.4 eV. However, 3 R presents a deeper minimum. 23 P, 21 P, 23 R and 5 R states lie at 3.0, 3.7, 3.7 and 4.7 eV, respectively, from the ground state. The disagreement in the spectroscopic data of 3 R state, between the results presented here and 3 5
Σ
2
3 1
1
Σ
Π 3
E (eV)
a
State
Π
0 5 3
-1
1
-2
1 1
-3 1.4
Π
Σ
1.6
Σ
Σ
Π 1.8
3
Π
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
8.0
Fig. 1. MRDCI potential energy curves for BP using 6311+G(2df) basis set.
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
In order to confirm the results shown in this Letter, we have carried out the calculation of the two lowest states of this molecule (3 P and 1 Rþ ) with the B3LYP/6-311G(2d,f) density functional. We have used this functional, which combines BeckeÕs three parameter nonlocal hybrid exchange potential [21] and the nonlocal correlation functional of Lee et al. [22] with the same basis of the above calculations. The potential energy curves are presented in Fig. 2. These potential energy curves for both states are very similar to the previous ones at MRDCI level, and they also cross . The spectroscopic data obtained fitting at 1.6 A the DFT potential energy curves, are 1.741 and
4
E (eV)
those from [8] is due to the fact that they are not the same state. Boldyrev and Simons [8] give the result of the 3 R coming from 1r2 2r2 3r2 1p2 configuration, whereas that here studied corresponds to 1r2 2r1 3r1 1p4 configuration, that has a lower energy. In our case 2 3 R is the state that should be compared with [8] these published previously. The selected basis set, 6-311+G(2d,f) [11–13], also used in [8], has no diffuse functions, and so it is not expected to perform well at longer distances. However, as the MRDCI calculations include a big amount of symmetric adapted functions for all the interatomic distances, this effect is not dramatic, as can be seen in the dissociation limit in Fig. 1. The spectroscopic constants, bond lengths, dissociation energies and vibrational frequencies of the BP molecular states are given in Table 2. The bond lengths fit quite well with the results of [8], while for the vibrational frequencies we found values that agree with those previously published and referred to 1 Rþ , 3 P and 5 P states. Our frequencies corresponding to 3 R and 5 R states are about 400 and 300 cm1 larger, respectively, than those published. The reported frequency for 3 R agrees better with our result for the 23 R . Our calculations show that the two lowest excited states are 1 Rþ and 1 P. Both states show a similar De (see Table 2) but their minima . are separated by 0.1 A
723
1
2
Σ
0
3
-2
-4
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Π
2.6
2.8
3.0
Fig. 2. DFT-B3LYP potential energy curves for BP using 6-311+G(2df) basis set.
Table 2 ), dissociation energies (eV) and vibrational frequencies (cm1 ) at the minima in the CI Spectroscopic constants: bond lengths (A potential curves of ground and excited states of BP molecule State
3
P Rþ 1 P 2 1 Rþ 3 R 5 P 2 3P 2 1P 2 3 R 5 R 1
a b
This work
Ref. [8]
Re
De
xe
1.747 1.671 1.753 1.908 1.694 1.989 2.019 1.989 1.828 1.812
3.15 4.23 4.31 2.87 2.31 0.70 1.52 0.87 0.98 3.85
954 973 945 721 925 520 522 543 730 851
From [8] QCISD(T)/6-311+G(2df) level. From [8] MP2/6-311+G(2df) level.
Re a 1.758 1.684
De a
xe b
3.06
1148 1072
1.972 1.97
618 618
1.943 2.101
585 514
724
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
for the bond distance of 3 P and 1 Rþ 1.657 A states, respectively, and 957 and 1081 cm1 , for the vibrational frequencies, respectively. These results are in good agreement with those obtained with the MRDCI potential energy curves.
4. Concluding remarks We conclude that this molecule shows a 3 P ground state with a minimum at a bond distance , and exhibits two very close excited of 1.747 A 1 þ states of R and 1 P symmetries. Moreover, this molecule is stable for its ground state De ¼ 3:15 eV and for a few of the excited state, in spite of the lack of experimental data. In this Letter, we have found slight differences between the potential energy curves obtained with the MRDCI and DFT methods for 3 P and 1 Rþ states. The spectroscopic data obtained at DFT and MRDCI levels for both states are in good agreement.
Acknowledgements This work was performed under the auspices of the DGI Project BQU2001-0152 and by the Fundaci on Seneca del Centro de Coordinaci on de la Investigaci on de la Regi on de Murcia under Project PB/28/FS/02. S.M. gratefully acknowledges a grant from the Agencia Espa~ nola de Cooperaci on Internacional. P.M-S. thanks her Fullbright postdoctoral grant at Duke University.
References [1] K.P. Huber, G. Herzberg, in: Molecular Spectra and Molecular Structure, vol. 4, Van Nostrand Reinhold, New York, 1979. [2] E. Hirota, Chem. Rev. 92 (1992) 141. [3] A.M. Pendas, M.A. Blanco, A. Costales, P. Mori-Sanchez, V. Lua~ na, Phys. Rev. Lett. 83 (1999) 1930. [4] P. Mori-Sanchez, A. Martın Pendas, V. Lua~ na, Phys. Rev. B 63 (2001) 125103. [5] P. Mori-Sanchez, Ph.D. Thesis, Universidad de Oviedo, Spain, 2002. [6] R.F.W. Bader, Atom in Molecules: A Quantum Theory, Oxford University Press, Oxford, 1990. [7] R.F.W. Bader, Phys. Rev. B 13 (1994) 348. [8] A.I. Boldyrev, J. Simons, J. Phys. Chem. 97 (1993) 6149. [9] A. Aguado, J.M. Garcıa de la Vega, B. Miguel, J. Chem. Soc., Faraday Trans. 93 (1997) 29. [10] J.M. Garcıa de la Vega, B. Miguel, Theor. Chem. Acc. 104 (2000) 189. [11] R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem. Phys. 72 (1980) 650. [12] A.D. McLean, G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [13] T. Clark, J. Chandrasekhar, G.W. Spitznagel, P.v.R. Schleyer, J. Comput. Chem. 4 (1983) 294. [14] R.J. Buenker, S.D. Peyerimhoff, Theoret. Chim. Acta 35 (1974) 33. [15] R.J. Buenker, S.D. Peyerimhoff, W. Bustcher, Mol. Phys. 35 (1978) 771. [16] R.J. Buenker, R.A. Phillips, J. Mol. Struct. (Theochem) 123 (1985) 291. [17] P.J. Bruna, S.D. Peyerimhoff, R.J. Buenker, Chem. Phys. Lett. 72 (1974) 278. [18] S.R. Langhoff, E.R. Davidson, Int. J. Quantum Chem. 8 (1974) 61. [19] C.E. Moore, Atomic Energy Levels, Natl. Bur. Stand, U.S.GPO, Washington, DC, 1952. [20] A. Aguado, J.J. Camacho, M. Paniagua, J. Mol. Struct. (Theochem) 254 (1992) 135. [21] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [22] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.
Theoretical study of low-lying electronic states of BP molecule Beatriz Miguel a, Salama Omar b, Paula Mori-S anchez c, Jose M. Garcıa de la Vega b,* a
Departamento de Ingenierıa Quımica y Ambiental, Universidad Polit ecnica de Cartagena, Paseo Alfonso XIII 44, 30203 Cartagena, Spain b Departamento de Quımica Fısica Aplicada, Facultad de Ciencias, Universidad Aut onoma de Madrid, Cantoblanco, 28049 Madrid, Spain c Department of Chemistry, Duke University, Durham, NC 27708-0354, USA Received 29 July 2003; in final form 26 September 2003 Published online: 4 November 2003
Abstract BP is a molecule that, to date, has not been experimentally characterized. However, theoretical calculations yield a stable molecule, although its ground state is not unequivocally determinated. In this work, potential energy curves for the ground state and the lower excited states of BP molecule have been calculated. They are derived using the MRDCI procedure and employing 6-311+G(2df) basis sets. The spectroscopic constants and excitation energies for the bound states of BP are compared with previous theoretical results. The MRDCI calculations give the 3 P state as the ground , De ¼ 3:15 eV and xe ¼ 954 cm1 . state, with Re ¼ 1:747 A Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Diatomic molecules formed by either two electronegative atoms or one electronegative and one electropositive atom have been well studied experimentally, whereas the diatomic molecules formed by two atoms belonging to electropositive groups have not been studied extensively with either experimental or theoretical techniques [1,2].
*
Corresponding author. Fax: +34-91-3974512. E-mail address: [email protected] (J.M. Garcıa de la Vega).
The most interesting feature of the BP molecule, like BAs, is that it has the smallest indices of ionicity among the III–V family and constitutes an excellent example of an almost perfect covalence heteronuclear diatomic molecule. This low-heteropolarity gives striking features to the BP system. Mori-Sanchez et al. [3–5] have studied the BP compound in its crystalline and molecular structure, using BaderÕs theory of atoms in molecules [6,7]. In the zinc-blende crystal structure, the binding point is located on the internuclear B–P line between first neighbors, moved away 1.30 and 2.41 a.u. from boron and phosphorus atoms, respectively. These bonds display the characteristic topologic properties of interactions of shared
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.09.153
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
shells justified by their high and negative Laplacian, as in prototype covalent bonds. Those authors have also analyzed the transfer of charge and the polarity inversion under pressure in the electron density of the BP crystal. As regards the stability of the BP molecule, however, the deficiency of experimental data and the difficulty for determining its molecular parameters in the fundamental and excited states, implies that the BP molecule is of great interest since it has very close electronic states of different multiplicity. In fact, the few published works on the BP molecule show unclear results. Boldyrev and Simons [8] have studied five electronic states of BP molecule: 1 Rþ ð1r2 1p4 2r2 Þ; 3 P ð1r2 2r2 1p3 3r1 Þ; 3 R ð1r2 2r2 3r2 1p2 Þ; 5 Pð1r2 2r2 1p2 3r1 2p1 Þ and 5 R ð1r2 2r2 1p2 2p2 Þ. They conclude that the 3 P state is the ground state, while the first excited state 1 Rþ lies 0.3 eV above the ground state and the 3 R , 5 P and 5 R electronic states lie at 0.85, 2.4 and 5.5 eV, respectively. Mori-S anchez [5] has analyzed the electron density of the diatomic BP molecule at different computational levels, namely HF, CASSCF and CISD. In these calculations, it is found a competition between the three states of lower energy, 1 þ 3 R , R and 3 P. Moreover, from the results of UHF and CISD calculations it is concluded that 3 P is the fundamental state in agreement with the results of Boldyrev and Simons [8]. However, CASSCF yields 1 Rþ as the ground state. Correlation effects introduced through CASSCF and CISD calculations tend to increase slightly the equilibrium distances and to move the bond point towards the boron atom. Our aim here is to clarify the electronic spectrum of BP. Encouraged by our previous calculations on the ground and excited states of diatomic molecules [9,10], we have decided to perform MRDCI calculations on this unobserved molecule.
2. Calculations for excited states of B and P atoms Using 6-311+G(2d,f) basis sets [11–13] and the method of Buenker and coworkers [14–16], we have carried out MRDCI calculations for the ground 2 P and three lowest excited (4 P, 2 S and 2 D) states of the
721
boron atom and the ground 4 S and four lowest excited (2 D, 2 P, 4 P and 2 P) states of the phosphorus atom . All occupied and virtual atomic orbitals were used in MRDCI steps for the considered states of B and P atoms. That is, 39 and 47 atomic orbitals for B and P atoms, respectively. The number of reference configurations was selected for obtaining a Geisser coefficient (C2 ) higher than 0.97. The selection threshold in the energy was 2 lhartrees. The configuration functions generated (SAFT: Symmetric Adapted Functions Total) vary from 1593 to 3919 for the 2 P and 2 S states of B atom, respectively, and from 6575 to 8003 for 4 S and 2 D states of P atom, respectively. The number of those SAFT selected for final approximated full-CI (SAF: Symmetric Adapted Functions) varies from 1172 to 2549 (2 P and 2 S states) for B atom and from 4823 to 5582 (4 S and 2 D states) for P atom. Extrapolation of the energy to zero threshold gives the MRDCI energy and the use of the multireference version [17] of the Davidson correction [18] allows the full-CI extrapolated energy to be obtained. These MRDCI and full-CI energies are shown in Table 1. With the full CI-energies, we calculate the atomic excitation energies of B and P atoms (in eV) that are collected in Table 1. The atomic excitation energies are in good agreement with the experimental values [19], also given in Table 1. Only for the highest excited state of P atom (2 P) the difference between computed and experimental excitation energies is greater than 0.15 eV. The selected basis set gives a good description of the excitation energies for all the studied states. Therefore, this basis set will give good dissociation energies for the diatomic molecule.
3. MRDCI potential energy curves of BP molecule The calculations described in this study were made with MRDCI code [14–16] and the 6-311+G(2d,f) basis set [11–13]. All the 20 electrons and all the molecular orbitals (MO) were used in the generation of the SAFT: that is 10 occupied and 76 virtual MOs to carry out the excitations on the initial reference configurations. The configurations were selected to achieve a Geisser coefficient higher than 0.90 in all the calculated points along the proposed range of
722
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
Table 1 MRDCI and full CI energies (a.u.), and excitation energies DE (eV) for the ground and excited states of B and P atoms Configuration
Boron atom 2s2 2p1 2s1 2p2 2s2 3s1 2s1 2p2 Phosphorus atom 3s2 3p3 3s2 3p3 3s2 3p3 3s2 3p2 4s1 3s2 3p2 4s1
2
P P 2 S 2 D 4
4
S D 2 P 4 P 2 P 2
MRDCI
Full CI
DE/eV This work
Exp.a
)24.622694 )24.492356 )24.399443 )24.390708
)24.623930 )24.492845 )24.439458 )24.400514
0.00 3.57 5.02 6.08
0.00 3.57 4.96 5.93
)340.946726 )340.889031 )340.854685 )340.685645 )340.671654
)340.951050 )340.894781 )340.861104 )340.690857 )340.676544
0.00 1.53 2.45 7.08 7.47
0.00 1.41 2.32 6.96 7.19
From Ref. [19].
internuclear distances, with a threshold in the energy of 2 lhartrees. In our MRDCI calculations we have considered the two lowest energies in R and P symmetries for singlet and triplet states. Also the 5 R and 5 P states have been included. That is, a total of ten states or 15 roots in the MRDCI calculations. We have computed the estimated full CI energies from , taking into account that for a R ¼ 1.20 to 8.0 A given symmetry the same reference configurations are preserved along the variation of the internuclear distance. The number of initial reference configurations used for the states 1 Rþ , 1 P, 3 R , 3 P, 5 R and 5 P were 81, 80, 84, 80, 20 and 14, respectively, and giving a SAFT of 1939–13 527, 15 167–22 657, 9906–22 314, 11 097–24 559, 8735– 17 066 and 13 516–21 880, respectively. We have computed the spectroscopic constants of these potential energy curves. They have been calculated fitting the potential energy points with the numerical method proposed by Aguado et al. [20]. We find that 3 P state is the ground state with , and only the 1 Rþ state crosses it at Re ¼ 1:747 A R ’ 1:6 A. This ground state dissociates into B(2 P) and P(4 S), so its dissociation energy is considered the zero of energy in Fig. 1 where the potential energy curves are plotted. All the studied excited states dissociate to either B(2 P) + P(2 D) or B(2 P) + P(2 P), except the quintuplet R states that dissociate into B(4 P) + P(2 D). 1 Rþ and 1 P are the first excited states and lie at 0.36 and 0.40 eV
above the ground state, respectively. Both values are slightly higher than that reported in [8] (0.3 eV). Both states present a stable minimum with a similar dissociation energy, where the 1 P minimum is at an internuclear distance which is longer than that for the 1 Rþ minimum. only 0.1 A A third excited state, 21 Rþ is found lying at 1.7 eV from the ground state. 3 R and 5 P are the fourth excited states lying at 2.4 eV. However, 3 R presents a deeper minimum. 23 P, 21 P, 23 R and 5 R states lie at 3.0, 3.7, 3.7 and 4.7 eV, respectively, from the ground state. The disagreement in the spectroscopic data of 3 R state, between the results presented here and 3 5
Σ
2
3 1
1
Σ
Π 3
E (eV)
a
State
Π
0 5 3
-1
1
-2
1 1
-3 1.4
Π
Σ
1.6
Σ
Σ
Π 1.8
3
Π
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
8.0
Fig. 1. MRDCI potential energy curves for BP using 6311+G(2df) basis set.
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
In order to confirm the results shown in this Letter, we have carried out the calculation of the two lowest states of this molecule (3 P and 1 Rþ ) with the B3LYP/6-311G(2d,f) density functional. We have used this functional, which combines BeckeÕs three parameter nonlocal hybrid exchange potential [21] and the nonlocal correlation functional of Lee et al. [22] with the same basis of the above calculations. The potential energy curves are presented in Fig. 2. These potential energy curves for both states are very similar to the previous ones at MRDCI level, and they also cross . The spectroscopic data obtained fitting at 1.6 A the DFT potential energy curves, are 1.741 and
4
E (eV)
those from [8] is due to the fact that they are not the same state. Boldyrev and Simons [8] give the result of the 3 R coming from 1r2 2r2 3r2 1p2 configuration, whereas that here studied corresponds to 1r2 2r1 3r1 1p4 configuration, that has a lower energy. In our case 2 3 R is the state that should be compared with [8] these published previously. The selected basis set, 6-311+G(2d,f) [11–13], also used in [8], has no diffuse functions, and so it is not expected to perform well at longer distances. However, as the MRDCI calculations include a big amount of symmetric adapted functions for all the interatomic distances, this effect is not dramatic, as can be seen in the dissociation limit in Fig. 1. The spectroscopic constants, bond lengths, dissociation energies and vibrational frequencies of the BP molecular states are given in Table 2. The bond lengths fit quite well with the results of [8], while for the vibrational frequencies we found values that agree with those previously published and referred to 1 Rþ , 3 P and 5 P states. Our frequencies corresponding to 3 R and 5 R states are about 400 and 300 cm1 larger, respectively, than those published. The reported frequency for 3 R agrees better with our result for the 23 R . Our calculations show that the two lowest excited states are 1 Rþ and 1 P. Both states show a similar De (see Table 2) but their minima . are separated by 0.1 A
723
1
2
Σ
0
3
-2
-4
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Π
2.6
2.8
3.0
Fig. 2. DFT-B3LYP potential energy curves for BP using 6-311+G(2df) basis set.
Table 2 ), dissociation energies (eV) and vibrational frequencies (cm1 ) at the minima in the CI Spectroscopic constants: bond lengths (A potential curves of ground and excited states of BP molecule State
3
P Rþ 1 P 2 1 Rþ 3 R 5 P 2 3P 2 1P 2 3 R 5 R 1
a b
This work
Ref. [8]
Re
De
xe
1.747 1.671 1.753 1.908 1.694 1.989 2.019 1.989 1.828 1.812
3.15 4.23 4.31 2.87 2.31 0.70 1.52 0.87 0.98 3.85
954 973 945 721 925 520 522 543 730 851
From [8] QCISD(T)/6-311+G(2df) level. From [8] MP2/6-311+G(2df) level.
Re a 1.758 1.684
De a
xe b
3.06
1148 1072
1.972 1.97
618 618
1.943 2.101
585 514
724
B. Miguel et al. / Chemical Physics Letters 381 (2003) 720–724
for the bond distance of 3 P and 1 Rþ 1.657 A states, respectively, and 957 and 1081 cm1 , for the vibrational frequencies, respectively. These results are in good agreement with those obtained with the MRDCI potential energy curves.
4. Concluding remarks We conclude that this molecule shows a 3 P ground state with a minimum at a bond distance , and exhibits two very close excited of 1.747 A 1 þ states of R and 1 P symmetries. Moreover, this molecule is stable for its ground state De ¼ 3:15 eV and for a few of the excited state, in spite of the lack of experimental data. In this Letter, we have found slight differences between the potential energy curves obtained with the MRDCI and DFT methods for 3 P and 1 Rþ states. The spectroscopic data obtained at DFT and MRDCI levels for both states are in good agreement.
Acknowledgements This work was performed under the auspices of the DGI Project BQU2001-0152 and by the Fundaci on Seneca del Centro de Coordinaci on de la Investigaci on de la Regi on de Murcia under Project PB/28/FS/02. S.M. gratefully acknowledges a grant from the Agencia Espa~ nola de Cooperaci on Internacional. P.M-S. thanks her Fullbright postdoctoral grant at Duke University.
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