Theoretical study on structures and stability of GeSiN and GeCP radicals
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Theoretical study on structures and stability of GeSiN and GeCP radicals Yi Pan a , Guang-hui Chen a, * , Di Wu b , Zhi Lv a , Zhi-ru Li b , Dan Li a , Xiao-chun Huang a a Department of Chemistry, Shantou University, Guangdong 515063, People’s Republic of China b State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China article info Article history: Received 7 September 2009 In final form 18 January 2010 Available online 20 January 2010 abstract The structures, isomerization and spectroscopies of GeSiN and GeCP radicals are explored at density func- tional theory and ab initio levels. For GeSiN, the global minimum is linear GeNSi 1, in agreement of the mass spectra detection, which can be qualitatively described as a resonance hybrid of |Ge@N|–Si| and |Ge–N|@Si|, where the latter contributes more. As to GeCP, the lowest-lying isomer is linear GeCP 1 res- onating between |Ge–C„P| and |Ge@C@P| with the former contributes more, followed by a cyclic iso- mer cGeCP 2 at 8.8 kcal/mol. All above three species with large kinetic stability (about 10 kcal/mol barrier) should be experimentally important. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Germanium-containing chemistry has attracted continuing interest from various fields. Several small germanium-containing species, including free radicals, positive ions and anions have been studied due to their important roles in organometallic chemistry and semiconductor material science [1–5]. Ge-containing clusters doped with VA elements N and P, such as Ge 2 N [6], GeN 2 [7], Ge 2 N 2 [8] and Ge 2 P 2 [9], have also attracted broadly attention. In addition, two ternary analogs of Ge 2 N, i.e., GeCN [10] and GeSiN [6], have received theoretical or experimental study. It was pre- dicted that linear species GeCN and GeNC on GeCN PES are kinet- ically and thermodynamically stable and with the former as global minimum [10]; mass spectra study of GeSiN just suggested Ge–N– Si arrangement is the most possible form [6], yet no theoretical study of GeSiN has been reported up to now. Moreover, the theo- retical study on silicon analog, i.e., SiCN, has shown that linear spe- cies SiCN and SiNC of SiCN radical are of large kinetic and thermodynamic stability just like GeCN radical [11]. The dicarbide analogs of them, i.e., C 2 N, C 2 P and C 2 As also received experimental and theoretical study due to their spectroscopic importance as Renner–Teller molecules or possible interstellar molecules [12,13]. Binary germanium silicides and germanium carbides are com- monly used as indirect wide band-gap semiconductor material [14,15]. During the N-doped GeSi-vaporization and P-doped GeC- vaporization process the smaller triatomic species such as GeSiN and GeCP could be generated. The knowledge about the structures, kinetics, energies and bonding nature of various GeSiN and GeCP isomers is critical to understanding of the initial step of N-doped GeSi-vaporization and P-doped GeC-vaporization process. So, it is of interest to explore the properties of radicals GeSiN and GeCP as congeners of GeCN [10] and SiCN [11]. The theoretical study on the triatomic GeCN has shown that the global minimum is a lin- ear isomer |Ge–C@N| followed by a linear isomer |Ge–N@C| at just 5.0 kcal/mol with large kinetic stability [10]. Naturally we may raise following questions: Do GeSiN and GeCP radicals have kinetically and thermodynamically stable linear isomers just like congeners GeCN and SiCN? Do they have kinetically stable cyclic species which are different from SiCN and GeCN radicals? Also, the GeSiN and GeCP radicals may have isomers that contain GeN or GeC multiple bonds and may thus be good targets for exploring the stability of GeN or GeC multiple bonding. Indeed, the chemistry of GeN and GeC multiple bonding has attracted much interest [15]. To the best of our knowledge, the important radicals like GeSiN and GeCP have not been studied theoretically before. In this Letter, we will investigate the structures, isomerization, bonding nature and spectroscopies of the both radicals theoretically. Generally, such triatomic radicals with 13 valence electrons are subject to Renner–Teller effect [16–25], so the estimated effect of relevant linear isomers GeSiN and GeCP are also made. 2. Computational methods All calculations are performed with the GAUSSIAN03 program and MOLCAS 6.2 (for CASSCF calculation only) packages [26,27]. The opti- mized geometries and harmonic vibrational frequencies of the local minima and transition states are obtained at the Becke three param- eter Lee–Yang–Parr B3LYP/6-311G(d) [28] theory level. Single-point calculations are performed at the CCSD(T)/6-311G(2df) [29] level using the B3LYP/6-311G(d) optimized geometries. To confirm whether the obtained transition states connect the right isomers, 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.01.019 * Corresponding author. E-mail address: [email protected] (G.-h. Chen). Chemical Physics Letters 487 (2010) 171–176 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Transcript of Theoretical study on structures and stability of GeSiN and GeCP radicals
Chemical Physics Letters 487 (2010) 171–176
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier .com/ locate /cplet t
Theoretical study on structures and stability of GeSiN and GeCP radicals
Yi Pan a, Guang-hui Chen a,*, Di Wu b, Zhi Lv a, Zhi-ru Li b, Dan Li a, Xiao-chun Huang a
a Department of Chemistry, Shantou University, Guangdong 515063, People’s Republic of Chinab State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China
a r t i c l e i n f o
Article history:Received 7 September 2009In final form 18 January 2010Available online 20 January 2010
0009-2614/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.cplett.2010.01.019
* Corresponding author.E-mail address: [email protected] (G.-h. Chen).
a b s t r a c t
The structures, isomerization and spectroscopies of GeSiN and GeCP radicals are explored at density func-tional theory and ab initio levels. For GeSiN, the global minimum is linear GeNSi 1, in agreement of themass spectra detection, which can be qualitatively described as a resonance hybrid of |Ge@N|–Si|� and�|Ge–N|@Si|, where the latter contributes more. As to GeCP, the lowest-lying isomer is linear GeCP 1 res-onating between �|Ge–C„P| and |Ge@C@P|� with the former contributes more, followed by a cyclic iso-mer cGeCP 2 at 8.8 kcal/mol. All above three species with large kinetic stability (about 10 kcal/molbarrier) should be experimentally important.
� 2010 Elsevier B.V. All rights reserved.
1. Introduction
Germanium-containing chemistry has attracted continuinginterest from various fields. Several small germanium-containingspecies, including free radicals, positive ions and anions have beenstudied due to their important roles in organometallic chemistryand semiconductor material science [1–5]. Ge-containing clustersdoped with VA elements N and P, such as Ge2N [6], GeN2 [7],Ge2N2 [8] and Ge2P2 [9], have also attracted broadly attention. Inaddition, two ternary analogs of Ge2N, i.e., GeCN [10] and GeSiN[6], have received theoretical or experimental study. It was pre-dicted that linear species GeCN and GeNC on GeCN PES are kinet-ically and thermodynamically stable and with the former as globalminimum [10]; mass spectra study of GeSiN just suggested Ge–N–Si arrangement is the most possible form [6], yet no theoreticalstudy of GeSiN has been reported up to now. Moreover, the theo-retical study on silicon analog, i.e., SiCN, has shown that linear spe-cies SiCN and SiNC of SiCN radical are of large kinetic andthermodynamic stability just like GeCN radical [11]. The dicarbideanalogs of them, i.e., C2N, C2P and C2As also received experimentaland theoretical study due to their spectroscopic importance asRenner–Teller molecules or possible interstellar molecules [12,13].
Binary germanium silicides and germanium carbides are com-monly used as indirect wide band-gap semiconductor material[14,15]. During the N-doped GeSi-vaporization and P-doped GeC-vaporization process the smaller triatomic species such as GeSiNand GeCP could be generated. The knowledge about the structures,kinetics, energies and bonding nature of various GeSiN and GeCPisomers is critical to understanding of the initial step of N-doped
ll rights reserved.
GeSi-vaporization and P-doped GeC-vaporization process. So, it isof interest to explore the properties of radicals GeSiN and GeCPas congeners of GeCN [10] and SiCN [11]. The theoretical studyon the triatomic GeCN has shown that the global minimum is a lin-ear isomer �|Ge–C@N| followed by a linear isomer �|Ge–N@C| atjust 5.0 kcal/mol with large kinetic stability [10]. Naturally wemay raise following questions: Do GeSiN and GeCP radicals havekinetically and thermodynamically stable linear isomers just likecongeners GeCN and SiCN? Do they have kinetically stable cyclicspecies which are different from SiCN and GeCN radicals? Also,the GeSiN and GeCP radicals may have isomers that contain GeNor GeC multiple bonds and may thus be good targets for exploringthe stability of GeN or GeC multiple bonding. Indeed, the chemistryof GeN and GeC multiple bonding has attracted much interest [15].To the best of our knowledge, the important radicals like GeSiN andGeCP have not been studied theoretically before. In this Letter, wewill investigate the structures, isomerization, bonding nature andspectroscopies of the both radicals theoretically. Generally, suchtriatomic radicals with 13 valence electrons are subject toRenner–Teller effect [16–25], so the estimated effect of relevantlinear isomers GeSiN and GeCP are also made.
2. Computational methods
All calculations are performed with the GAUSSIAN03 program andMOLCAS 6.2 (for CASSCF calculation only) packages [26,27]. The opti-mized geometries and harmonic vibrational frequencies of the localminima and transition states are obtained at the Becke three param-eter Lee–Yang–Parr B3LYP/6-311G(d) [28] theory level. Single-pointcalculations are performed at the CCSD(T)/6-311G(2df) [29] levelusing the B3LYP/6-311G(d) optimized geometries. To confirmwhether the obtained transition states connect the right isomers,
172 Y. Pan et al. / Chemical Physics Letters 487 (2010) 171–176
the intrinsic reaction coordinate (IRC) calculations are performed atthe same B3LYP/6-311G(d) level. The structures, frequencies andenergetics of the relevant species are refined at the QCISD/6-311G(d) and CCSD(T)/6-311+G(2df) (energy only) levels. The zero-point vibrational energies (ZPVEs) at the B3LYP/6-311G(d) andQCISD/6-311G(d) levels are also included for energy correction,respectively.
Choice of B3LYP is motivated by its good performance for thegeometry optimizations and prediction of vibrational frequenciesfor both isomers and transition states based on much previousworks [30–34]. Moreover, B3LYP is able to suppress effectivelythe problem of spin contaminants.
3. Results and discussion
To be concise, the results are organized as follows. In Section3.1, we present a rough discussion on the stability of the isomers.Then for the most relevant species, we give a detailed discussion onthe structural and bonding properties in Section 3.2. Where possi-ble, comparisons with the related species are made. In Section 3.3,the Renner–Teller effect on the relevant linear isomers isestimated. In Section 3.4, we analyze the possible relevance ofthe isomers in laboratory. Unless otherwise specified, the relativeenergies are at the CCSD(T)/6-311+G(2df)//QCISD/6-311G(d)+ZPVElevel (simplified as CCSD(T)//QCISD) and the CCSD(T)/6-311G(2df)//B3LYP/6-311G(d)+ZPVE level (simplified as CCSD(T)//B3LYP).
Fig. 2. Schematic potential-energy surface of GeSiN at CCSD(T)/6-311G(2df)//B3LYP/6-311G(d)+ZPVE level. The relative energies in parentheses are at CCSD(T)/6-311G+(2df)//QCISD/6-311G(d)+ZPVE level.
3.1. PESs of GeSiN and GeCP
The optimized geometries of the isomers (m) and transitionstates (TSm/n), as well as potential-energy surface (PES) of GeSiNare respectively shown in Figs. 1 and 2, while those of GeCP areshown in Figs. 3 and 4, respectively. The corresponding harmonicvibrational frequencies as well as infrared intensities, dipole mo-ments and rotational constants for the GeSiN and GeCP speciesare listed in Table 1, while the total and relative energies of all spe-cies are collected in Table 2. The relative energies of various disso-ciation fragments are listed in Table 3. The comparisons of bonding
Fig. 1. Optimized geometries of GeSiN isomers, transition states and fragments of the dithe QCISD/6-311G(d) level. Bond lengths are in angstroms, angles in degrees.
nature of linear species of GeSiN and GeCP with those of congenersSiCN and GeCN are listed in Table 4.
On the GeSiN PES, three linear isomers, i.e., GeNSi 1 (0.0, 0.0),GeSiN 3 (66.3) and SiGeN 4 (84.5) with all 2P electronic statesand one cyclic isomer cGeSiN 2 (5.5) with 2A0 electronic state areobtained. The normal and italic values in parentheses are relativeenergies obtained at the CCSD(T)//B3LYP and CCSD(T)//QCISD lev-els, respectively. Since GeSiN and GeCP are Renner–Teller type rad-icals with 13 valence electrons, in their bent configuration, thereshould be two states of 2A0 and 2A00. As to GeSiN radical, afternumerous search, unfortunately we failed to find the bent struc-ture with 2A00 electronic state with only cGeNSi. The failure maybe ascribed to the fact that the HOMO–LUMO gap at the B3LYP le-vel is usually very small. As a result, the A00 LUMO-orbital of the 2A00
ssociation at B3LYP/6-311G(d) level and the geometrical parameters in italics are at
Fig. 3. Optimized geometries of GeCP isomers, transition states and fragments of the dissociation at B3LYP/6-311G(d) level and the geometrical parameters in italics are atthe QCISD/6-311G(d) level. Bond lengths are in angstroms, angles in degrees.
Fig. 4. Schematic potential-energy surface of GeCP at CCSD(T)/6-311G(2df)//B3LYP/6-311G(d)+ZPVE level. The relative energies in parentheses are at CCSD(T)/6-311G+(2df)//QCISD/6-311G(d)+ZPVE level.
Y. Pan et al. / Chemical Physics Letters 487 (2010) 171–176 173
state is easily switched to the A0 HOMO-orbital of the lower-energy2A0 state. As shown in Fig. 2, on the PES of GeSiN, as Renner–Tellerradical, there are two isomerization paths between linear GeNSi 1and SiGeN 4: doublet A0: 1 ? 2 ? 4 and doublet A00: 1 ? 4. Sincethe relative energies of all the possible dissociation products arerather high-lying relative to isomer 1 (more than 107 kcal/mol atthe CCSD(T)//B3LYP level as shown in Table 3), we do not attemptto search any dissociation transition state. So the isomerizationprocess governs the kinetic stability of GeSiN isomers. As shownin Fig. 2, the isomerization barriers are 1 (10.5, 9.6, 1 ? 2 conver-sion) > 2 (5.0, 2 ? 1) > 4 (3.6, 4 ? 1) > 3 (0.7, 3 ? 2) (kcal/mol).The italic value in parentheses is for CCSD(T)6-311+G(2df)//QCISD/6-311G(d) single-point calculation. We find that only iso-mer 1 is both thermodynamically and kinetically stable, while iso-mers 2, 3 and 4 with either high energy or poor kinetic stabilitywould be less likely existed.
On the PES of GeCP, two linear isomers including GeCP 1 (0.0,0.0) and CGeP 4 (87.6) with both 2P electronic states, one cyclicisomer cGeCP 2 (9.5, 8.8) with 2A0 electronic state and a bent GePC3 (50.9) with 2A00 electronic state are obtained. As shown in Fig. 4,on the PES, there are two isomerization paths between linear iso-mers GeCP 1 and CGeP 4, which are similar to that of GeSiN:1 ? 2 ? 4 in doublet A0 and 1 ? 4 in doublet A00. Since the relativeenergies of all the possible dissociation products are rather high-lying relative to isomer 1 (more than 94 kcal/mol at theCCSD(T)//B3LYP level as shown in Table 3), we do not attempt tosearch any dissociation transition state. The isomerization barriersare 1 (22.2, 22.7, 1 ? 2) > 2 (13.2, 13.4, 2 ? 1) > 4 (9.2, 4 ? 1) > 3(�0.3, 3 ? 1) (kcal/mol) as shown in Fig. 4. Note that the negativevalue of 3 ? 1 barrier results from the higher-level single-pointcalculation at lower-level optimized geometry. We can find thatonly isomers 1 and 2 with large thermodynamic and kinetic stabil-ity are expected to have very long lifetime once formed.
By the optimization at the CASSCF(13,12)/6-311G(d) level oftheory, the 2R+ states of linear GeNSi and GeCP are obtained. TheGeN and NSi bonds length of GeNSi (2R+) are 2.0852 and1.6169 Å, respectively, and it is energetically 90.9 kcal/mol aboveground state GeNSi (2P). The GeC and CP bonds length ofGeCP(2R+) are 1.8278 and 1.6305 Å, respectively, and it is energet-ically 84.0 kcal/mol above ground state GeCP (2P). Due to the highenergy of the two excited states, we think that they are of minorimportance and will not discuss them further.
It is of interest to compare above two PESs with congenersGeCN [10] and SiCN [11]. For the linear isomers, like GeCN andSiCN, linear GeCP is the global minimum with large kinetic stabil-ity. Contrary to linear GeNC and SiNC, linear GePC is not a mini-mum with two imaginary frequencies corresponding to two‘bend’ vibrational modes at B3LYP level. The two distinct imaginaryvibrational frequencies are along its bending coordinate [for exam-ple, x2(P+) = 80i cm�1 and x2(P�) = 29i cm�1 at the B3LYP/6-311G(d) level of theory]. The eigenvector of the two imaginarybending frequencies with the larger magnitude [x2(P+)] leads tothe 2A0 state with a cyclic molecular geometry, whereas the[x2(P�)] mode leads to the 2A00 state when the molecule is bent.As a result, the 2A0 state is lower lying in the vicinity of Cs symme-tried isomers. Linear GeNSi is determined as kinetically stable glo-bal minimum whereas the GeCN and SiCN typed GeSiN isenergetically very high-lying (66.3 kcal/mol); like highly locatedlinear CGeN (148.0 kcal/mol) on the GeCN PES [10], both linear
Table 1Harmonic vibrational frequencies (cm�1), infrared intensities (km/mol) (in parentheses), dipole moments (D) and rotational constants (GHz) of GeSiN and GeCP structures at theB3LYP/6-311G(d) level.
Species Frequencies (infrared intensity) Dipole moments Rotational constants
GeNSi 1 142 (7, p) 216 (19, p) 451 (0, r) 1048 (39, r) 0.0484 2.08948GeNSi 1a 132 (7, p, x�) 206 (16, p, x+) 434 (4, r) 1081 (5, r) 0.5652 2.06832cGeSiN 2 243 (3, a0) 657 (28, a0) 904 (17, a0) 1.3046 31.98312 3.51366 3.16586GeSiN 3 59 (13, p) 91 (9, p) 271 (39, r) 1032 (238, r) 5.3522 1.99870SiGeN 4 66 (8, p) 86 (5, p) 325 (46, r) 792 (122, r) 4.2133 2.85312TS1/2 558i (62, a0) 238 (21, a0) 1025 (88, a0) 4.5687 29.63323 2.49715 2.30308TS1/4 71i (6, a0) 320 (23, a0) 796 (35, a0) 3.8133 19.84233 3.70646 3.12309TS2/3 590i (73, a0) 237 (21, a0) 1017 (91, a0) 4.5720 29.63972 2.49528 2.30152TS2/4 177i (11, a0) 279 (19, a0) 734 (154, a0) 3.8333 19.27928 3.38581 2.88003GeCP 1 145 (4, p) 221 (12, p) 395 (15, r) 1269 (0, r) 0.6400 1.88322GeCP 1a 156 (4, p, x�) 217 (10, p, x+) 378 (22, r) 1305 (5, r) 0.2950 1.85341cGeCP 2 299 (7, a0) 612 (31, a0) 1010 (4, a0) 1.6019 28.34706 3.75797 3.31809cGeCP 2a 305 (5, a0) 604 (26, a0) 1008 (11, a0) 1.4649 27.86874 3.79305 3.33865GePC 3 111 (10, a0) 288 (22, a0) 1048 (64, a0) 3.7282 27.47377 2.91627 2.63642CGeP 4 30 (6, p) 81 (4, p) 503 (0, r) 653 (108, r) 0.8447 3.13723TS1/2 467i (193, a0) 513 (206, a0) 1155 (59, a0) 1.1335 47.75961 2.53385 2.40619TS1/3 184i (6, a0) 261 (38, a0) 1110 (58, a0) 3.4342 22.32313 3.12013 2.73750TS1/4 151i (2, a0) 376 (2, a0) 612 (6, a0) 1.8854 13.77206 4.77656 3.54652TS2/4 287i (11, a0) 348 (8, a0) 710 (48, a0) 1.5253 17.13157 3.91359 3.18581
a At the QCISD/6-311G(d) level.
Table 2Relative energies (kcal/mol) of the GeSiN and GeCP structures and transition states at the B3LYP/6-311G(d) level and single-point CCSD(T)/6-311G(2df) levels. For the relevantisomers, the CCSD(T)/6-311+G(2df)//QCISD/6-311G(d) values are included also. The symbols in parenthesis of the column denote the electronic states.
Species B3LYPd DZPVEB3LYP
CCSD(T)d
//B3LYPcTotal 1 QCISDc DZPVE
QCISDCCSD(T)e
//QCISDcTotal 2
GeNSi 1 (4G)a 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0cGeSiN 2 (2A0) 10.4 �0.1 5.6 5.5GeSiN 3 (2G) 67.9 �0.6 66.9 66.3SiGeN 4 (2G) 87.6 �0.8 85.3 84.5TS1/2 (2A0) 15.3 �0.3 10.8 10.5 12.7 �0.2 9.8 9.6TS1/4 (2A00) 90.0 �1.1 89.2 88.1TS2/3 (2A0) 74.5 �0.8 67.8 67.0TS2/4 (2A0) 97.2 �1.2 95.8 94.6GeCP 1 (2G)b 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0cGeCP 2 (2A0) 13.7 �0.2 9.7 9.5 15.3 �0.2 9.0 8.8GePC 3 (2A00) 54.2 �0.8 51.7 50.9CGeP 4 (2G) 93.0 �1.1 88.7 87.6TS1/2 (2A0) 26.2 �0.5 23.2 22.7 24.6 �0.4 22.6 22.2TS1/3 (2A00) 55.0 �0.9 51.5 50.6TS1/4 (2A00) 95.2 �1.5 98.3 96.8TS2/4 (2A0) 101.0 �1.4 102.5 101.1
a The total energies of reference isomer GeNSi 1 at the B3LYP/6-311G(d) level is �2421.2629239 a.u., at QCISD/6-311G(d) level is �2419.027289, at CCSD(T)//B3LYP level is�2419.1069925 a.u., at CCSD(T)//QCISD level is �2419.1097075. The ZPVE at B3LYP and QCISD are 2.65537, 2.64966 a.u., respectively.
b The total energies of reference isomer GeCP 1 at the B3LYP/6-311G(d) level is �2456.4166011 a.u., at QCISD/6-311G(d) level is �2454.1900436, at CCSD(T)//B3LYP level is�2454.2672554 a.u., at CCSD(T)//QCISD level is �2454.2693542. The ZPVE at B3LYP and QCISD are 2.90209, 2.94130 a.u., respectively.
c The basis set is 6-311G(d) for B3LYP and QCISD.d The basis set is 6-311G(2df) for CCSD(T).e The basis set is 6-311+G(2df) for CCSD(T).
174 Y. Pan et al. / Chemical Physics Letters 487 (2010) 171–176
SiGeN and CGeP are energetically very high-lying (more than80 kcal/mol relative to global minimum). It seems that linear iso-mers with high-row elements, such as Ge and Si, in the middlehave poor thermodynamic stability due to the elements Ge andSi prefer to form r-bonding than lower-row elements (C, N). Itshould be noted that no ring-formed SiCN isomer has been re-ported so far. However, unlike kinetically unstable ring-formedisomers cGeCN and cGeSiN, the cyclic cGeCP is kinetically stablewith an isomerization barrier at 13.4 kcal/mol. So when the N atomof GeCN is substituted by P atom, the cyclic form is not only ther-modynamically stable but also kinetically stable. Such situation isvery similar to the discrepancy between SiC2N [36] and SiC2P [37]where the C2v symmetried ring-formed species with C–C cross-bonding on SiC2P PES is kinetically stable while that of SiC2N is
not. Like the explanation in the Letter of SiC2P that we ascribedto that smaller electronegativity difference between Si and Y(Y = P) in C2v symmetried SiCCY (Y = N, P) favors the delocalizationwithin the cyclic molecule thus is responsible for its kinetic stabil-ity [37]. Here we can also ascribe to that the smaller electronega-tivity difference of Ge and P in GeCY (Y = N, P) favors its kineticstability.
3.2. Properties of GeNSi 1, GeCP 1 and cGeCP 2
Under experimental condition in low temperature, such kineticstability (barrier about 10 kcal/mol) and thermodynamic stability(under 10 kcal/mol) are large enough to allow the existence ofthe three species, i.e., GeNSi 1, GeCP 1 and cGeCP 2. On the PES
Table 3Relative energies (kcal/mol) of dissociation fragments of the GeSiN and GeCPstructures at B3LYP/6-311G(d) and single-point CCSD(T)/6-311G(2df) levels. Thesymbols in parentheses of column denote the electronic states.
Species B3LYPc DZPVEB3LYP
CCSD(T)d
//B3LYPTotal
Ge(3P) + SiN(2G)a 111.3 �1.0 108.3 107.3Si(3P) + GeN(2G) 131.3 �1.3 129.0 127.7N(2D)e + GeSi(3R) 201.2 �2.1 199.1N(4S) + GeSi(3R) 146.2 �2.1 139.8 137.7Ge(3P) + CP(2G)b 99.8 �1.1 95.2 94.1C(3P) + GeP(2G) 148.8 �2.1 143.0 140.9P(2D)e + GeC(3G) 166.6 �1.7 164.9P(4S) + GeC(3G) 134.3 �1.7 128.8 127.1
a The total energies of reference isomer GeNSi 1 at the B3LYP and single-pointCCSD(T) levels as well as the ZPVE at the B3LYP level are listed at the ‘footnote a’ ofthe Table 2.
b The total energies of reference isomer GeCP 1 at the B3LYP and single-pointCCSD(T) levels as well as the ZPVE at the B3LYP level are listed at the ‘footnote b’ ofthe Table 2.
c The basis set is 6-311G(d) for B3LYP.d The basis set is 6-311G(2df) for CCSD(T).e Due to the multi-configuration nature of N(2D)and P(2D), total energies of
E(N(2D)) and E(P(2D)) are calculated with formula: E(N(2D)) = N(4S) +DEexp((N(2D) � N(4S)) and E(P(2D)) = P(4S) + DEexp((P(2D) � P(4S)), respectively.DEexp((N(2D) � N(4S)) and DEexp((P(2D) � P(4S)) are 54.9 and 32.3 kcal/mol,respectively. Ref. [35].
Table 4Bond lengths (in Å) and Wiberg bond orders (BO) of the 2G electronic state of the XNY(X = Ge, C; Y = Si, C) and XCY (X = Ge, Si; Y = P, N) species at B3LYP/6-311G(d) level.
(X, Y) 2G
R(XN) BO(XN) R(NY) BO(NY)
XNY(Ge, Si) 1.7714 0.9489 1.6181 1.2484(Ge, C) 1.8773 0.5827 1.1857 2.3184(C, Si) 1.1915 2.2218 1.7584 0.6320XCY
R(XC) BO(XC) R(CY) BO(CY)
(Ge, P) 1.8712 1.0264 1.5838 2.4122(Ge, N) 1.9593 0.8126 1.1648 2.8338(Si, N) 1.8697 0.8515 1.1731 2.7971
Y. Pan et al. / Chemical Physics Letters 487 (2010) 171–176 175
of GeSiN, the ground state GeNSi 1 has a slightly longer NSi bond(1.6181 Å) than that of typical N@Si double bond (1.6005 Å inNH@SiH2) [38]. The GeN bond in 1 (1.7714 Å) is well betweenGe@N double bond (1.7121 Å in GeH2@NH) and the typical Ge–Nsingle bond (1.8536 Å in GeH3NH2). Natural bond orbital (NBO)analysis shows that the Wiberg bond orders of GeN and NSi are0.9489 and 1.2484, respectively. Then isomer 1 may be best de-scribed as a resonant structure between |Ge@N|–Si|� and �|Ge–N|@Si|. The symbols ‘�’ and ‘|’ denote the single electron andlone-pair electrons, respectively. The NBO natural spin density dis-tribution (0.6958, �0.1108 and 0.4149 e, for Ge, N and Si,respectively) suggests that the latter structure which is similar to�|Ge–N@C|, bears somewhat more weight than the former. Fromthe comparison of geometric parameters for linear GeNSi, GeNCand CNSi listed in Table 4, we find that Wiberg bond order ofGe–N (0.9489) in GeNSi is much smaller than bond order of C–N(2.2218) in CNSi; bond order of N–Si (1.2484) in GeNSi is muchsmaller than that of N–C (2.3184) in GeNC. Besides, bond orderof Ge–N (0.9489) is weaker than that of Si–N (1.2484) within GeN-Si. So, we can draw a conclusion that element Ge even prefers toform single bond then the lower-row element Si.
For the lowest-lying isomer GeCP 1 (2G) in GeCP species, theGe–C bond (1.8712 Å) is between the typical Ge@C double bond(1.7779 Å in GeH2CH2) and the Ge–C single bond (1.9680 Å in
GeH3CH3). The CP bond (1.5838 Å) is between the normal C„P tri-ple (1.5394 Å in HCP) and C@P double bond (1.6698 Å in CH2@PH).Then isomer 1 may be best described as a resonant structurebetween �|Ge–C„P| and |Ge@C@P|�. NBO analysis shows that Wi-berg bond orders of GeC and CP are 1.0264 and 2.4122, respec-tively. After taken NBO natural spin density distribution (0.6922,�0.1117 and 0.4195 e, for Ge, C and P, respectively) into consider-ation, the former structure bears somewhat more weight than thelatter. From the geometric parameters of linear GeCP, GeCN andSiCN listed in Table 4, we can find that the Ge–C bond order(0.8126) in GeCN is lower than the Si–C bond order (0.8515) inSiCN, which confirm further that third-row element Ge does not fa-vor the formation of multiple bond like lower-row elements Si andC.
As to the second low-lying cyclic isomer cGeCP 2, the GeP bond(2.4139 Å) is close to Ge–P single bond (2.3485 Å in GeH3PH2). TheCP bond (1.6637 Å) is very close to the typical C@P double bond(1.6698 Å). The Ge–C bond (1.9274 Å) is between the Ge@C doublebond (1.7779 Å) and the typical Ge–C single bond (1.9680 Å). Wi-berg bond orders (0.8322, 1.9420 and 1.0036 for GeP, CP and Ge–C bond, respectively) and NBO natural spin density distribution(0.2714, 0.1637 and 0.5650 e for Ge, P and C, respectively) indicatethat isomer 2 could be viewed as below resonant structures, andthe last structure takes more weight.
Ge P
C
Ge P
C
Ge P
C
So, no important triple GeN or GeC bonding can be found fromthe three relevant isomers.
3.3. Renner–Teller interactions
Similar to the congeners C2N, C2P, SiCN and GeCN radicals with13 valence electrons, the present linear GeNSi and GeCP isomersare subject to Renner–Teller effect [16–25]. The Renner parametere is a dimensionless constant used to describe the Renner–Tellersplitting of the bending potential and may be expressed as
e ¼ ðxþÞ2 � ðx�Þ2
ðxþÞ2 þ ðx�Þ2;
where the two bending modes x+ and x� can be obtained compu-tationally. The actual bending mode observed experimentally is anaveraged bending frequency and may be written as
~x ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12ðxþÞ2 þ ðx�Þ2h ir
At the QCISD/6-311G(d) level, the Renner parameters e andaveraged harmonic bending frequencies ~x are e = 0.418 and~x2 = 173 cm�1 for the GeNSi, and e = 0.319, ~x2 = 189 cm�1 for theGeCP. The GeNSi isomer presents a larger Renner parameter thandoes the GeCP, whereas GeCP species has a higher averaged bend-ing frequency than GeNSi.
3.4. Laboratory implications
In the mass spectra experiment in 1974 by Muenow, GeNSi wasprepared by the reaction formulae Si2N(g) + Ge(g) = GeN-Si(g) + Si(g) [6]. But he could not identify the accurate form ofthe obtained isomer and just suggested the production was likelylinear GeNSi. Considering the kinetic and thermodynamic stabilityof GeNSi 1 in present theoretical calculation, we can confirm this
176 Y. Pan et al. / Chemical Physics Letters 487 (2010) 171–176
speculation. For GeCP radical, both GeCP 1 and cGeCP 2 have con-siderable kinetic stabilities towards isomerization or dissociationand should also be observable in laboratory. During the processof N-doped GeSi-vaporization and P-doped GeC-vaporization, for-mation of both thermodynamically and kinetically stable linearGeNSi 1, GeCP 1 and ring-formed cGeCP 2 are very feasible. Onthe other hand, the [Ge, Si, N] and [Ge, C, P] species may playimportant roles in chemistry vapor deposition processes, in filmformation and in the synthesis of ceramic materials. Knowledgeof the structures, stabilities and bonding properties of the [Ge, Si,N] and [Ge, C, P] species are very useful for understanding thechemical vaporization processes of GeSiN and GeCP films, and forgaining insight of the atomic or radical interaction with substratesand ion reaction. The present theoretical study is expected to stim-ulate future laboratory detection of above three isomers further.
To confirm the reliability of calculation, a high-level QCISD/6-311(d) calculation was also performed on the three thermodynam-ically and kinetically stable isomers further. The isomer GeNSi 1has the main vibrational stretching band at 1081 cm�1 and dipolemoment of 0.5652 D. The isomer GeCP 1 has the main vibrationalstretching band at 1305 cm�1 while the cyclic isomer cGeCP 2has the dominant vibrational band at 1008 cm�1 with dipole mo-ments 0.2950 and 1.4649 D, respectively. All of the vibrational fre-quencies and rotational constants of various isomers listed in Table2 are hoped to be useful for future experimental detection.
4. Conclusion
A series of computational methods including DFT and ab initiowere applied for the radicals GeSiN and GeCP. Three low-lying spe-cies, including not only linear GeNSi 1 and GeCP 1 but also ring-formed cGeCP 2 were found to have both considerable thermody-namic and kinetic stability to be of experimental interest. Presenttheoretical work proves that it should be the linear GeNSi 1 pro-duced in previous mass spectra experiment [6]. Note that no suchkinetically stable cyclic isomer as cGeCP 2 has been found withcongeners SiCN and GeCN radicals. At the high-level CCSD(T)/6-311+G(2df)//QCISD/6-311G(d)+ZPVE calculation, GeNSi 1 is a linearisomer which resonates between |Ge@N|–Si|� and �|Ge–N|@Si|with the latter contributes more weight. As to GeCP radical, GeCP1 is also a linear form resonated between �|Ge–C„P| and|Ge@C@P|�, where the former bears somewhat more weight. Thesecond low-lying isomer is a cyclic isomer cGeCP 2 at 8.8 kcal/mol with a large isomerization barrier as 13.4 kcal/mol. On thecontrary, similar ring-formed cGeSiN and cGeCN are not kineticallystable ones. No GeN or GeC triple bonding can be found withinGeSiN and GeCP radicals. The Renner parameters and averagedharmonic bending frequencies were predicted to be 0.418 and173 cm�1 for GeNSi as well as 0.319 and 189 cm�1 for GeCP.Harmonic vibrational frequencies, dipole moments, rotationalconstants and relative energies were provided as a basis for futurelaboratory identification of the relevant GeSiN and GeCP radicals.
Acknowledgments
This work was supported by 211 project foundation of ShantouUniversity and Guangdong Province. The authors are greatlythankful to the reviewers’ invaluable comments. In addition, weowe gratitude to Mr. Philip Wang and Miss Carol Hong’s help inEnglish polish.
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