- Email: [email protected]
Theoretical study on PbS, PbO and their anions
Chemical Physics Letters 370 (2003) 39–43 www.elsevier.com/locate/cplett
Theoretical study on PbS, PbO and their anions Z.J. Wu
*
Key Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, No. 159, Renmin Street, Changchun 130022, PR China Department of Chemistry, Dalhousie University, Halifax, NS, Canada B3H 4J3 Received 10 December 2002; in final form 10 December 2002
Abstract Equilibrium geometries, harmonic vibrational frequencies, and dissociation energies were determined for PbS, PbS , PbO and PbO molecules by density functional methods (B3LYP, B3PW91, BLYP and BHLYP), molecular orbital method (MP2) and quadratic CI calculation by including single and double substitutions (QCISD). The calculated results indicate that all methods used in this study have good performance in predicting the geometries, and in most cases harmonic vibrational frequencies. For dissociation energy, BHLYP gives the best agreement with experiments and previous theoretical studies on PbO, compared with other methods used in this study. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Neutral lead monoxide has been the subject of considerable experimental investigations [1,2] and several theoretical studies [3–7]. A good summary for experimental molecular constants, i.e., equilibrium bond distance, harmonic vibrational frequency, dissociation energy, etc., of neutral PbO can be found in [1]. Theoretical studies on PbO focused mainly on the ground state by various methods, such as all electron Dirac–Hartree–Fock calculations [3], all electron Dirac–Fock–Roothaan calculations [4], nonrelativistic Hartree– Fock–Roothaan calculations [5], nonrelativistic single-configuration pseudo-potential calculations [6], nonrelativistic multi-configuration pseudo*
Fax: +86-431-568-5653. E-mail address: [email protected].
potential calculations [6], and relativistic quantum calculations including configuration interaction and spin–orbit interaction [7]. In addition, lowlying states of PbO are also calculated [7]. A decade ago, PbO was studied experimentally by photoelectron spectroscopy [8], and molecular constants were determined [8]. On the other hand, the optical spectroscopy of PbS has been examined by a number of experimental investigations and molecular constants for its ground state and several excited states have been summarized [1]. Quite recently, PbS has also been studied by photoelectron spectroscopy [9]. Molecular constants have been determined as well [9]. To my knowledge, theoretical work is not available for PbS, PbS and PbO molecules till now. The great availability of accurate experimental data coupled with the advances of theoretical methods, in particular the density functional theory (DFT),
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00067-8
40
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43
prompted us to systematically examine the geometries, harmonic vibrational frequencies and electronic properties of PbS, PbS , PbO and PbO molecules. Therefore, in this Letter, we studied PbO, PbS and their anions by using diverse theoretical methods, i.e., density functional methods, molecular orbital method based on second-order Møller–Plesset perturbation theory (MP2) and quadratic CI calculation by including single and double substitutions. Our calculated results are discussed and compared with experiments and previous theoretical studies on PbO.
HF/DFT hybrid exchange functional (B3) [13], pure DFT exchange functional of 1988 (B) [14], a modification of the half-and-half HF/DFT hybrid method (BH) [15], or Perdew–Wang 1991 (PW91) [12]. The basis set used in this study is LANL2DZ for lead in which Hay–Wadt [17] 4-valence electron (6s2 6p2 of Pb) relativistic effective core potential (RECP) is considered, 6-311+G* for oxygen and sulfur, i.e., general basis set is used as implemented in GA U S S I A N 98 [10]. The calculated dissociation energies and adiabatic electron affinities were corrected by the zero-point vibrational energies. All energies are in eV.
2. Theoretical methods 3. Results and discussion All geometry optimizations were performed using the GA U S S I A N 98 suite of programs [10]. Equilibrium geometries, harmonic vibrational frequencies, dissociation energies and electron affinities (EAs) were determined for lead monoxide, lead sulfide and their anions by using four different exchange-correlation functionals (denoted as B3LYP, B3PW91, BLYP and BHLYP) [11–15], molecular orbital method based on second-order Møller–Plesset perturbation theory (MP2), and quadratic CI calculation by including single and double substitutions (QCISD) [16]. For the density functionals, the correlation functional is from either Lee, Yang and Parr (LYP) [11], or Perdew– Wang 1991 (PW91) [12], while the exchange functional is either from BeckeÕs three-parameter
The calculated equilibrium bond distances, harmonic vibrational frequencies, dissociation energies and EAs are listed in Table 1 for PbS and PbS molecules, Table 2 for PbO and PbO molecules. 3.1. PbS and PbS molecules It can be seen from Table 1 that for PbS, the calculated bond distances from the diverse theoretical methods are in general agreement with experimental value [1], in particular for B3LYP, in which the agreement with experiment is excellent. The largest deviation for the bond distance (also the shortest) is from BHLYP calculation, which is only
Table 1 ), harmonic vibrational frequencies xe (cm 1 ), dissociation energies De (eV) of PbS and Comparison of equilibrium bond distances re (A PbS and electron affinities EA (eV) of PbS under various theoretical methods with experiments B3LYP
B3PW91
BLYP
BHLYP
MP2
QCISD
Exp.
PbS re xe De EA
2.280 422.3 4.549 0.760
2.275 428.8 4.501 0.826
2.305 401.3 4.878 0.546
2.255 445.0 4.011 0.724
2.293 412.8 4.180 0.098
2.296 398.2 3.929 0.192
2.2868a 429.4 3.43 1.049
PbS re xe De
2.403 342.8 3.114
2.395 350.1 3.205
2.430 324.8 3.317
2.378 361.0 2.793
2.393 389.0 2.836
2.411 339.2 2.719
2.390b 367 2.40
a b
Ref. [1]. Ref. [9].
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43
41
Table 2 ), harmonic vibrational frequencies xe (cm 1 ), dissociation energies De (eV) of PbO Comparison of equilibrium bond distances re (A and PbO and electron affinities EA (eV) of PbO under various theoretical methods with experiments and previous theoretical studies on PbO B3LYP
B3PW91
BLYP
BHLYP
MP2
QCISD
Exp.
Other theoretical methods
PbO re
1.857
1.856
1.883
1.827
1.901
1.902
1.9218a
xe
712.7
715.2
672.5
759.6
649.0
547.6
721.0
1.907c 1.871d 1.893e 873f 867d 785e
De
5.121
4.896
5.806
4.033
5.590
4.748
3.83
1.882f 1.897g
1.868h
1.861i 1.915j
2.02k
800f 881g
862
862i 748j
715
1.3f
)1.00
3.7j
3.0
1.4g EA
0.281
0.346
0.085
0.202
)0.475
)0.358
0.722
PbO re xe De
1.943 599.7 3.790
1.941 602.4 3.790
1.972 563.3 4.211
1.910 641.9 3.170
1.985 592.5 4.115
1.980 493.5 3.534
1.995b 588 3.09
a
Ref. [1]. Ref. [8]. c Nonrelativistic Hartree–Fock calculation. Various relativistic effective core potential (RECP) calculations show similar results, for the details, see [3], similar situation applies to first-order perturbation calculationsd and Dirac–Hartree–Fock calculationse . d First-order perturbation calculations [3]. e Dirac–Hartree–Fock calculations [3]. f Dirac–Fock–Roothaan calculations, after considering correlation energy correction, De lies in 3.5–3.8 eV [4]. g Hartree–Fock–Roothaan calculations, after considering correlation energy correction, De lies in 3.6–3.9 eV [4]. h Nonrelativistic Hartree–Fock–Roothaan calculations [5]. i Nonrelativistic single-configuration pseudo-potential calculations [6]. j Nonrelativistic multi-configuration pseudo-potential calculations [6]. k CI calculations using relativistic pseudo-potentials [7]. b
shorter than experimental value 2.2868 A . 0.0318 A The longest bond distance is from QCISD calcu longer than experimental lation, which is 0.0092 A value. For the methods used in this study, the calculated harmonic vibrational frequencies are in excellent agreement with experimental value, the largest deviation is 31.2 cm 1 from QCISD calculation. For the calculated dissociation energy, the best agreement with experiment is from QCISD and BHLYP calculations, which are 0.499 and 0.581 eV higher than experimental value 3.43 eV [1], respectively. The worst is from BLYP calculation, in which the calculated value is 1.448 eV higher than experimental value. The calculated EAs are lower than that of experimental value, in which B3LYP, B3PW91 and BHLYP give relatively better results. While MP2 and QCISD have the worst performance in predicting EA.
For PbS , the calculated bond distances and harmonic vibrational frequencies are in agreement with experiment [9] (Table 1). BHLYP, MP2 and QCISD have better performance in predicting the dissociation energies than B3LYP, B3PW91 and BLYP compared with experiment (Table 1). The deviation of the calculated molecular constants from experiment is smaller than those in PbS. For instance, for dissociation energy, the largest deviation from experiment is from BLYP calculation, which is 0.917 eV higher than experimental value 2.40 eV [9] (compared with 1.448 eV higher than experimental value 3.43 eV for PbS [1] at the same theoretical method). Among all the methods, BHLYP and QCISD give the best molecular constants for PbS compared with experiment [9]. In brief, the above calculations suggest that for both PbS and PbS molecules, BHLYP gives the best
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Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43
overall performance compared with other theoretical methods used in this study and experiments [1,9].
In addition, our calculations also reveal that for all the studied molecules, BHLYP calculation gives the shortest bond distances among the methods used in this study.
3.2. PbO and PbO molecules For PbO, the calculated bond distances are at BHLYP level to 1.902 A at from 1.827 A QCISD level (Table 2), in agreement with experi [1] and various previous mental value 1.9218 A theoretical studies [3–7]. For harmonic vibrational frequencies, B3LYP, B3PW91 and BHLYP give the best agreement with experiment [1] compared with BLYP, MP2 and QCISD, in which QCISD gives the worst harmonic vibrational frequency compared with experiment (173.4 cm 1 lower than experimental value 721.0 cm 1 [1]). The calculated dissociation energy from BHLYP calculation is in excellent agreement with experiment, which is only 0.203 eV higher than experimental value [1]. Our calculated dissociation energy is comparable with previous theoretical study using nonrelativistic multi-configuration pseudo-potential calculations (3.7 eV) [6], and much better than other previous theoretical studies [4,5,7]. In addition, for B3LYP, B3PW91, BLYP, MP2 and QCISD, the calculated dissociation energy is overestimated considerably, which is even 1.976 eV (the worst case) higher than experimental value in BLYP. Similar to PbS, EA is underestimated considerably for PbO compared with experiment (Table 2). In particular, EAs from MP2 and QCISD are even negative, which means that the energy of the anions is higher than its neutral counterparts. On the other hand, for PbO , it can be seen (Table 2) that the calculated bond distances and harmonic vibrational frequencies are in agreement with experiment [8]. For dissociation energy, BHLYP gives nearly the same result as experiment, which is only 0.08 eV higher than experimental value 3.09 eV [8]. The largest deviation from experiment is from BLYP calculation, which is 1.121 eV higher than experimental value. Therefore, similar to PbS and PbS molecules, for PbO and PbO molecules, BHLYP gives the best overall agreement with experiments [1,8] and previous theoretical studies on PbO [3–7], compared with other methods used in this study.
4. Conclusions Density functional methods, i.e., B3LYP, B3PW91, BLYP, BHLYP, molecular orbital method (MP2) and QCISD have been used in the study of molecular constants of PbS, PbO and their anions. The calculated results indicate that compared with experiments, all considered methods in this study have good performance in predicting the equilibrium bond distances, and in most cases harmonic vibrational frequencies. While for dissociation energy and EA, especially for dissociation energy, density functional method with half-and-half HF/DFT hybrid method (BHLYP) gives the best agreement with experiments and previous theoretical study on PbO, compared with other methods used in this study. For all the studied molecules, BHLYP gives the shortest bond distances among the methods used in this study. BLYP is the worst in predicting the dissociation energies. EA is underestimated considerably by the current methods, in particular for PbO. MP2 and QCISD even predict negative EA for PbO. Dissociation energy is overestimated by different amount depending on the methods.
Acknowledgements The author gratefully acknowledges the Natural Sciences and Engineering Research Council of Canada, the Killam Trusts of Canada and Changchun Institute of Applied Chemistry of China for financial support.
References [1] K.P. Huber, G. Herzberg, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979. [2] J. Drowart, R. Colin, G. Exsteen, Trans. Faraday Soc. 61 (1965) 1376. [3] K.G. Dyall, J. Chem. Phys. 98 (1993) 2191.
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43 [4] O. Matsuoka, L. Pisani, E. Clementi, Chem. Phys. Lett. 202 (1993) 13. [5] G.M. Schwenzer, D.H. Liskow, H.F. Schaefer III, P.S. Bagus, B. Liu, A.D. McLean, M. Yoshimine, J. Chem. Phys. 58 (1973) 3181. [6] H. Basch, W.J. Stevens, M. Krauss, J. Chem. Phys. 74 (1981) 2416. [7] K. Balasubramanian, K.S. Pitzer, J. Phys. Chem. 87 (1983) 4857. [8] M.L. Park, M.K. Gilles, R.F. Gunion, W.C. Lineberger, Chem. Phys. Lett. 210 (1993) 55. [9] C.A. Fancher, H.L. de Clercq, K.H. Bowen, Chem. Phys. Lett. 366 (2002) 197.
43
[10] M.J. Frisch et al., GA U S S I A N 98, Gaussian Inc., Pittsburgh, PA, 1998. [11] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [12] J.P. Perdew, Y. Wang, in: P. Ziesche, H. Eschrig (Eds.), Electronic Structures of SolidsÕ91, Akademie-Verlag, Berlin, 1991. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [15] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [16] J.A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 87 (1987) 5968. [17] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 284.
Theoretical study on PbS, PbO and their anions Z.J. Wu
*
Key Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, No. 159, Renmin Street, Changchun 130022, PR China Department of Chemistry, Dalhousie University, Halifax, NS, Canada B3H 4J3 Received 10 December 2002; in final form 10 December 2002
Abstract Equilibrium geometries, harmonic vibrational frequencies, and dissociation energies were determined for PbS, PbS , PbO and PbO molecules by density functional methods (B3LYP, B3PW91, BLYP and BHLYP), molecular orbital method (MP2) and quadratic CI calculation by including single and double substitutions (QCISD). The calculated results indicate that all methods used in this study have good performance in predicting the geometries, and in most cases harmonic vibrational frequencies. For dissociation energy, BHLYP gives the best agreement with experiments and previous theoretical studies on PbO, compared with other methods used in this study. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Neutral lead monoxide has been the subject of considerable experimental investigations [1,2] and several theoretical studies [3–7]. A good summary for experimental molecular constants, i.e., equilibrium bond distance, harmonic vibrational frequency, dissociation energy, etc., of neutral PbO can be found in [1]. Theoretical studies on PbO focused mainly on the ground state by various methods, such as all electron Dirac–Hartree–Fock calculations [3], all electron Dirac–Fock–Roothaan calculations [4], nonrelativistic Hartree– Fock–Roothaan calculations [5], nonrelativistic single-configuration pseudo-potential calculations [6], nonrelativistic multi-configuration pseudo*
Fax: +86-431-568-5653. E-mail address: [email protected].
potential calculations [6], and relativistic quantum calculations including configuration interaction and spin–orbit interaction [7]. In addition, lowlying states of PbO are also calculated [7]. A decade ago, PbO was studied experimentally by photoelectron spectroscopy [8], and molecular constants were determined [8]. On the other hand, the optical spectroscopy of PbS has been examined by a number of experimental investigations and molecular constants for its ground state and several excited states have been summarized [1]. Quite recently, PbS has also been studied by photoelectron spectroscopy [9]. Molecular constants have been determined as well [9]. To my knowledge, theoretical work is not available for PbS, PbS and PbO molecules till now. The great availability of accurate experimental data coupled with the advances of theoretical methods, in particular the density functional theory (DFT),
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00067-8
40
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43
prompted us to systematically examine the geometries, harmonic vibrational frequencies and electronic properties of PbS, PbS , PbO and PbO molecules. Therefore, in this Letter, we studied PbO, PbS and their anions by using diverse theoretical methods, i.e., density functional methods, molecular orbital method based on second-order Møller–Plesset perturbation theory (MP2) and quadratic CI calculation by including single and double substitutions. Our calculated results are discussed and compared with experiments and previous theoretical studies on PbO.
HF/DFT hybrid exchange functional (B3) [13], pure DFT exchange functional of 1988 (B) [14], a modification of the half-and-half HF/DFT hybrid method (BH) [15], or Perdew–Wang 1991 (PW91) [12]. The basis set used in this study is LANL2DZ for lead in which Hay–Wadt [17] 4-valence electron (6s2 6p2 of Pb) relativistic effective core potential (RECP) is considered, 6-311+G* for oxygen and sulfur, i.e., general basis set is used as implemented in GA U S S I A N 98 [10]. The calculated dissociation energies and adiabatic electron affinities were corrected by the zero-point vibrational energies. All energies are in eV.
2. Theoretical methods 3. Results and discussion All geometry optimizations were performed using the GA U S S I A N 98 suite of programs [10]. Equilibrium geometries, harmonic vibrational frequencies, dissociation energies and electron affinities (EAs) were determined for lead monoxide, lead sulfide and their anions by using four different exchange-correlation functionals (denoted as B3LYP, B3PW91, BLYP and BHLYP) [11–15], molecular orbital method based on second-order Møller–Plesset perturbation theory (MP2), and quadratic CI calculation by including single and double substitutions (QCISD) [16]. For the density functionals, the correlation functional is from either Lee, Yang and Parr (LYP) [11], or Perdew– Wang 1991 (PW91) [12], while the exchange functional is either from BeckeÕs three-parameter
The calculated equilibrium bond distances, harmonic vibrational frequencies, dissociation energies and EAs are listed in Table 1 for PbS and PbS molecules, Table 2 for PbO and PbO molecules. 3.1. PbS and PbS molecules It can be seen from Table 1 that for PbS, the calculated bond distances from the diverse theoretical methods are in general agreement with experimental value [1], in particular for B3LYP, in which the agreement with experiment is excellent. The largest deviation for the bond distance (also the shortest) is from BHLYP calculation, which is only
Table 1 ), harmonic vibrational frequencies xe (cm 1 ), dissociation energies De (eV) of PbS and Comparison of equilibrium bond distances re (A PbS and electron affinities EA (eV) of PbS under various theoretical methods with experiments B3LYP
B3PW91
BLYP
BHLYP
MP2
QCISD
Exp.
PbS re xe De EA
2.280 422.3 4.549 0.760
2.275 428.8 4.501 0.826
2.305 401.3 4.878 0.546
2.255 445.0 4.011 0.724
2.293 412.8 4.180 0.098
2.296 398.2 3.929 0.192
2.2868a 429.4 3.43 1.049
PbS re xe De
2.403 342.8 3.114
2.395 350.1 3.205
2.430 324.8 3.317
2.378 361.0 2.793
2.393 389.0 2.836
2.411 339.2 2.719
2.390b 367 2.40
a b
Ref. [1]. Ref. [9].
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43
41
Table 2 ), harmonic vibrational frequencies xe (cm 1 ), dissociation energies De (eV) of PbO Comparison of equilibrium bond distances re (A and PbO and electron affinities EA (eV) of PbO under various theoretical methods with experiments and previous theoretical studies on PbO B3LYP
B3PW91
BLYP
BHLYP
MP2
QCISD
Exp.
Other theoretical methods
PbO re
1.857
1.856
1.883
1.827
1.901
1.902
1.9218a
xe
712.7
715.2
672.5
759.6
649.0
547.6
721.0
1.907c 1.871d 1.893e 873f 867d 785e
De
5.121
4.896
5.806
4.033
5.590
4.748
3.83
1.882f 1.897g
1.868h
1.861i 1.915j
2.02k
800f 881g
862
862i 748j
715
1.3f
)1.00
3.7j
3.0
1.4g EA
0.281
0.346
0.085
0.202
)0.475
)0.358
0.722
PbO re xe De
1.943 599.7 3.790
1.941 602.4 3.790
1.972 563.3 4.211
1.910 641.9 3.170
1.985 592.5 4.115
1.980 493.5 3.534
1.995b 588 3.09
a
Ref. [1]. Ref. [8]. c Nonrelativistic Hartree–Fock calculation. Various relativistic effective core potential (RECP) calculations show similar results, for the details, see [3], similar situation applies to first-order perturbation calculationsd and Dirac–Hartree–Fock calculationse . d First-order perturbation calculations [3]. e Dirac–Hartree–Fock calculations [3]. f Dirac–Fock–Roothaan calculations, after considering correlation energy correction, De lies in 3.5–3.8 eV [4]. g Hartree–Fock–Roothaan calculations, after considering correlation energy correction, De lies in 3.6–3.9 eV [4]. h Nonrelativistic Hartree–Fock–Roothaan calculations [5]. i Nonrelativistic single-configuration pseudo-potential calculations [6]. j Nonrelativistic multi-configuration pseudo-potential calculations [6]. k CI calculations using relativistic pseudo-potentials [7]. b
shorter than experimental value 2.2868 A . 0.0318 A The longest bond distance is from QCISD calcu longer than experimental lation, which is 0.0092 A value. For the methods used in this study, the calculated harmonic vibrational frequencies are in excellent agreement with experimental value, the largest deviation is 31.2 cm 1 from QCISD calculation. For the calculated dissociation energy, the best agreement with experiment is from QCISD and BHLYP calculations, which are 0.499 and 0.581 eV higher than experimental value 3.43 eV [1], respectively. The worst is from BLYP calculation, in which the calculated value is 1.448 eV higher than experimental value. The calculated EAs are lower than that of experimental value, in which B3LYP, B3PW91 and BHLYP give relatively better results. While MP2 and QCISD have the worst performance in predicting EA.
For PbS , the calculated bond distances and harmonic vibrational frequencies are in agreement with experiment [9] (Table 1). BHLYP, MP2 and QCISD have better performance in predicting the dissociation energies than B3LYP, B3PW91 and BLYP compared with experiment (Table 1). The deviation of the calculated molecular constants from experiment is smaller than those in PbS. For instance, for dissociation energy, the largest deviation from experiment is from BLYP calculation, which is 0.917 eV higher than experimental value 2.40 eV [9] (compared with 1.448 eV higher than experimental value 3.43 eV for PbS [1] at the same theoretical method). Among all the methods, BHLYP and QCISD give the best molecular constants for PbS compared with experiment [9]. In brief, the above calculations suggest that for both PbS and PbS molecules, BHLYP gives the best
42
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43
overall performance compared with other theoretical methods used in this study and experiments [1,9].
In addition, our calculations also reveal that for all the studied molecules, BHLYP calculation gives the shortest bond distances among the methods used in this study.
3.2. PbO and PbO molecules For PbO, the calculated bond distances are at BHLYP level to 1.902 A at from 1.827 A QCISD level (Table 2), in agreement with experi [1] and various previous mental value 1.9218 A theoretical studies [3–7]. For harmonic vibrational frequencies, B3LYP, B3PW91 and BHLYP give the best agreement with experiment [1] compared with BLYP, MP2 and QCISD, in which QCISD gives the worst harmonic vibrational frequency compared with experiment (173.4 cm 1 lower than experimental value 721.0 cm 1 [1]). The calculated dissociation energy from BHLYP calculation is in excellent agreement with experiment, which is only 0.203 eV higher than experimental value [1]. Our calculated dissociation energy is comparable with previous theoretical study using nonrelativistic multi-configuration pseudo-potential calculations (3.7 eV) [6], and much better than other previous theoretical studies [4,5,7]. In addition, for B3LYP, B3PW91, BLYP, MP2 and QCISD, the calculated dissociation energy is overestimated considerably, which is even 1.976 eV (the worst case) higher than experimental value in BLYP. Similar to PbS, EA is underestimated considerably for PbO compared with experiment (Table 2). In particular, EAs from MP2 and QCISD are even negative, which means that the energy of the anions is higher than its neutral counterparts. On the other hand, for PbO , it can be seen (Table 2) that the calculated bond distances and harmonic vibrational frequencies are in agreement with experiment [8]. For dissociation energy, BHLYP gives nearly the same result as experiment, which is only 0.08 eV higher than experimental value 3.09 eV [8]. The largest deviation from experiment is from BLYP calculation, which is 1.121 eV higher than experimental value. Therefore, similar to PbS and PbS molecules, for PbO and PbO molecules, BHLYP gives the best overall agreement with experiments [1,8] and previous theoretical studies on PbO [3–7], compared with other methods used in this study.
4. Conclusions Density functional methods, i.e., B3LYP, B3PW91, BLYP, BHLYP, molecular orbital method (MP2) and QCISD have been used in the study of molecular constants of PbS, PbO and their anions. The calculated results indicate that compared with experiments, all considered methods in this study have good performance in predicting the equilibrium bond distances, and in most cases harmonic vibrational frequencies. While for dissociation energy and EA, especially for dissociation energy, density functional method with half-and-half HF/DFT hybrid method (BHLYP) gives the best agreement with experiments and previous theoretical study on PbO, compared with other methods used in this study. For all the studied molecules, BHLYP gives the shortest bond distances among the methods used in this study. BLYP is the worst in predicting the dissociation energies. EA is underestimated considerably by the current methods, in particular for PbO. MP2 and QCISD even predict negative EA for PbO. Dissociation energy is overestimated by different amount depending on the methods.
Acknowledgements The author gratefully acknowledges the Natural Sciences and Engineering Research Council of Canada, the Killam Trusts of Canada and Changchun Institute of Applied Chemistry of China for financial support.
References [1] K.P. Huber, G. Herzberg, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979. [2] J. Drowart, R. Colin, G. Exsteen, Trans. Faraday Soc. 61 (1965) 1376. [3] K.G. Dyall, J. Chem. Phys. 98 (1993) 2191.
Z.J. Wu / Chemical Physics Letters 370 (2003) 39–43 [4] O. Matsuoka, L. Pisani, E. Clementi, Chem. Phys. Lett. 202 (1993) 13. [5] G.M. Schwenzer, D.H. Liskow, H.F. Schaefer III, P.S. Bagus, B. Liu, A.D. McLean, M. Yoshimine, J. Chem. Phys. 58 (1973) 3181. [6] H. Basch, W.J. Stevens, M. Krauss, J. Chem. Phys. 74 (1981) 2416. [7] K. Balasubramanian, K.S. Pitzer, J. Phys. Chem. 87 (1983) 4857. [8] M.L. Park, M.K. Gilles, R.F. Gunion, W.C. Lineberger, Chem. Phys. Lett. 210 (1993) 55. [9] C.A. Fancher, H.L. de Clercq, K.H. Bowen, Chem. Phys. Lett. 366 (2002) 197.
43
[10] M.J. Frisch et al., GA U S S I A N 98, Gaussian Inc., Pittsburgh, PA, 1998. [11] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [12] J.P. Perdew, Y. Wang, in: P. Ziesche, H. Eschrig (Eds.), Electronic Structures of SolidsÕ91, Akademie-Verlag, Berlin, 1991. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [15] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [16] J.A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 87 (1987) 5968. [17] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 284.