- Email: [email protected]
Unusual geometries and spectroscopic properties of electronic states of In2N2
Chemical Physics Letters 439 (2007) 288–295 www.elsevier.com/locate/cplett
Unusual geometries and spectroscopic properties of electronic states of In2N2 Zhiji Cao a, Krishnan Balasubramanian b
a,b,c,*
a Department of Mathematics and Computer Science, California State University, East Bay, Hayward, CA, United States University of California, Chemistry and Material Science Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, United States c Glenn T Seaborg Center, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, United States
Received 31 January 2007; in final form 22 March 2007 Available online 31 March 2007
Abstract Twenty electronic states of In2N2 are computed using a complete active space multi-configuration self-consistent field followed by multi-reference singles + doubles configuration interaction (MRSDCI) computations. In contrast to other III–V tetramers, In2N2 exhibits nearly degenerate T-shaped triplet states and linear In–In–N–N 3R state. The 1Ag state with a rhombus structure was found to be 0.94 eV higher. Our computations show that anion photodetachment spectra of In2N2 could be substantially different from the spectra of Ga2P2 and related tetramers observed by Neumark and coworkers. The computed vibrational and Raman spectra are provided. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Mixed semi-conductor clusters, especially those of the groups III and V have been the focus of several spectroscopic and theoretical studies [1–27], as these species are used in the fabrication of ultra-fast devices, blue–green lasers and semi-conductor injection lasers. Interestingly these clusters exhibit dramatic variations in properties as a function of cluster size. A detailed study of the properties of such clusters, especially their excited electronic states, could provide significant insight into their spectra and structures. Smalley and coworkers [1] pioneered the spectroscopic study of III–V semi-conductor clusters by demonstrating that laser vaporization of a gallium arsenide foil and subsequent supersonic expansion results in a plethora of GaxAsy clusters of various sizes with dramatic variations in abundance for smaller sizes and culminating into a binomial distribution for larger sizes. Subsequently, a number of * Corresponding author. Address: University of California, Chemistry and Material Science Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, United States. Fax: +1 925 422 6810. E-mail address: [email protected] (K. Balasubramanian).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.03.108
experimental techniques have been employed to probe the low-lying electronic states of group III–V clusters. Neumark and coworkers [2–12] have studied a number of group III–V semi-conductor clusters, especially InxPy, GaxPy, GaxAsy, and AlxPy using anion photodetachment spectroscopy. These experimental studies have yielded the electron affinities, information on the low-lying excited states, and vibrational frequencies of the neutral and anionic clusters. Weltner and coworkers [13–15] have used a matrix-isolation technique to obtain GaX, Ga2X, GaX2, and InX molecules, where X=P, As, and Sb, as well as Ga2As3. They have used electron-spin resonance (ESR) and far-infrared spectroscopic methods to probe the ground states of matrix-isolated clusters. On the basis of the observed hyperfine patterns, the spin multiplicities and the geometries of the ground states of these species could be deduced. Theoretical studies of electronic, structural, and vibrational properties of group III–V clusters have been carried out mostly on the ground states [17–21], although there have been computational studies on the excited states as well [22–27]. Pandey and coworkers [17–20] have carried out systematic theoretical studies of neutral and anionic group III nitride MnNn (M = Al, Ga, and In; n = 1–6)
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
clusters in the ground states within the framework of DFT. Their works were focused on the structural properties, stability, electronic structure, and the changes of these properties upon electron attachment. Our research group [22–26] has carried out systematic theoretical studies of neutral GaxAsy, AlxPy, and InxPy etc., as well as their ions up to 5 atoms using ab initio CASSCF/MRSDCI techniques, focusing on the properties of both the ground and lowlying excited electronic states. Thus a primary focus of our work is predicting spectroscopic properties of the excited states of these clusters. Indium nitride is quite unusual in that as shown here, its bonding characteristics differ substantially from the analogs. For example four-atom mixed clusters like Ga2As2 [27] exhibit a rhombus ground state, whereas, as shown here, In2N2 is very unusual in exhibiting two nearly degenerate T-shaped ground states and a rhombus structure which is 0.94 eV higher in energy. There are very few studies on InxNy clusters up to now. Zhou and Andrews [16] have provided the first infrared spectroscopic evidence for InN, In2N, InN2, In3N, and InN3 species, which are identified from nitrogen and gallium isotopic shifts, mixed isotopic splittings, and density functional theory calculations. Pandey and coworkers [17–20] have studied structures, stabilities, and vibrational properties of neutral and ionized clusters of InxNy up to 12 atoms within the frame of DFT. As demonstrated by our past work, the ground and low-lying electronic states of group III–V clusters could be of multireference in character, and electron correlation effects are significant, especially for energy separations. In this work we consider a systematic study on several low-lying electronic states of the neutral In2N2 using high-level ab initio CASSCF and MRSDCI techniques that included up to 7 million configurations. Both ground and several low-lying excited electronic states are optimized and their energy separations are computed. 2. Computational details We have computed the electronic states of In2N2 with different kinds of geometric arrangements and optimizing each of those geometries. All the computations were carried out in the C2v symmetry with the z-axis chosen as the C2 axis. A complete active space MCSCF (CASSCF) method followed by multi-reference singles + doubles configuration interaction (MRSDCI) is employed. All calculations were carried out using relativistic effective core potentials (RECPs) [28,29] for the core electrons of In and N atoms with the outer 5s25p1 shells for the In atom and the outer 2s22p3 for the N atom retained in the valence space, respectively. The In basis set from Ref. [29] was augmented with the one set of 6-component 5d (ad = 0.2129) and a set of s and p diffuse functions (as = 0.02, ap = 0.0145). The N basis was enhanced with a set of 3d polarization function (ad = 0.8) and a set of s and p diffuse functions (as = 0.1734, ap = 0.1904). The final basis sets for the In atoms were of (4s4p1d) quality, whereas the basis sets
289
for the N atoms are of (4s4p1d) quality. Moreover, for the purpose of comparison, the ground state of In2N2 was also calculated at the MP2 and CCSD(T) levels with relativistic effective core potentials (RECPs) [29] that retained the outer 4d105s25p1 shells for indium. The In basis set from Ref. [29] was augmented with two sets of s and p diffuse functions (as1 = 0.02, as2 = 0.0054, ap1 = 0.0145, ap2 = 0.0045) and a set of 4f function (af = 0.45). The final basis sets for the In atoms were of (5s5p4d1f) quality. In the CASSCF computations the valence 2s and 2p orbitals of N, as well as 5s and 5p orbitals of the In atoms were included in the active space. Among the valence orbitals we chose to include the lowest thirteen orbitals in the CASSCF active space to keep the computations tractable. This resulted in an active space spanning five a1, three b2, three b1, and two a2 orbitals, in C2v, which we label 5332-CAS for the rhombic In2N2. We adopted an equivalent 6331-CAS for a T-shaped In2N2 (labeled InInNN(T)) containing a N–N bond in a horizontal orientation, and a 6331-CAS for another T-shaped In2N2 (labeled InInNN(T2)) containing a In–In bond in the horizontal orientation, a 7330-CAS for the linear InInNN, a 7330CAS for the linear InNInN, and a 5512-CAS for the linear InNNIn, respectively. We ensured that each of these active spaces produced the lowest energy for the lowest state. Sixteen electrons of In2N2 were distributed in all possible ways among these orbitals at the CASSCF level. The MRSDCI calculations included all configurations in the CASSCF with absolute values of coefficients P0.03 as reference configurations. Multireference Davidson corrections to the MRSDCI energies for uncoupled quadruple clusters were calculated and the energy separations thus computed were labeled as MRSDCI + Q results. The MRSDCI included up to 7 million configurations, and geometry optimizations were carried out at the MRSDCI level. The vibrational frequencies were computed at the MP2 level. The CASSCF/ MRSDCI calculations were carried out using a modified version of the ALCHEMY II1 codes to include RECPs [30]. The MP2 and CCSD(T) calculations were made using GAUSSIAN 03 codes [31]. 3. Results and discussion We were able to seek six kinds of structures and twenty electronic states of In2N2 at the CASSCF and MRSDCI levels. Structural parameters along with the energy separations are given in Tables 1 and 2 at the CASSCF and MRSDCI levels, respectively. The geometrical structures are depicted in Fig. 1. As can be seen from both Tables 1 and 2, In2N2 is quite interesting in that unlike heaver group V tetraatomic clusters such as Ga2As2, there are two nearly degenerate states as candidates for the ground electronic
1 The major authors of ALCHEMY II are B. Liu, B. Lengsfiled and M. Yoshimine.
290
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 1 Geometries and energy separations of the electronic states of In2N2 at the CASSCF level System
Symmetry
State
In–In ˚) (A
N–N ˚) (A
In–N ˚) (A
N–In–N (°)
DE (eV)
InInNN(T)
C2v
3
3.091 3.342 2.832 3.209 3.189 2.852 2.906 2.474 4.447 4.361 5.173 3.838 3.831 4.215 3.118
1.100 1.114 1.100 1.101 1.085 1.100 1.103 1.100 1.253 1.313 1.181 1.611 1.599 1.692 2.749 1.189 1.198 1.201 1.215
5.299 4.884 4.088 4.500 4.151 3.932 3.885 4.628 2.310 2.277 2.653 2.081 2.076 2.271 2.079 2.188 2.174 2.391 1.940 1.972, 1.822, 2.024
11.9 13.1 40.5 (In1-N1-In2) 41.8 (In1-N1-In2) 45.2 (In1-N1-In2)
0.00 0.11 0.05 0.12 5.79 0.23 0.96 1.05 1.34 3.30 4.25 5.09 5.28 5.45 6.36 1.98 2.38 3.73 5.45 4.83
B1 A1 3 B1 1 A1 3 A1 3 R 1 + R 3 P 1 Ag 3 B3u 1 B3u 3 B1g 1 Au 3 B3g 3 B1u 1 þ Rg 3 Pu 3 þ Rg 3 Ru 3 R 1
InInNN(T2)
C2v
InInNN
C1v
In2N2
D2h
InNNIn
D1h
InNInN
C1v
Table 2 Geometries and energy separations of the electronic states of In2N2 at the MRSDCI level ˚) ˚) System Symmetry State In–In (A N–N (A InInNN(T)
C2v
3
B1 A1 3 B1 1 A1 3 A1 3 R 1 + R 3 P 1 Ag 3 B3u 1 B3u 3 B1g 1 Au 3 B1u 3 B3g 3 Pu 1 þ Rg 3 þ Rg 3 Ru 3 R 1
InInNN(T2)
C2v
InInNN
C1v
In2N2
D2h
InNNIn
D1h
InNInN In2 ð3 Pu Þ þ N2 ð1 Rþ gÞ In2 ð3 Pu Þ þ N2 ð1 Rþ g Þ (CCSD(T)) In2 ð3 Pu Þ þ N2 ð1 Rþ g Þ (MP2) In2 ð3 Pu Þ þ N2 ð1 Rþ g Þ (CCSD(T)) 2Inð2 PÞ þ N2 ð1 Rþ gÞ 2In(2P) + 2N(4S)
C1v
a b
3.045 3.315 2.785 2.967 3.079 2.802 2.851 2.489 4.362 4.303 5.110 3.825 3.820 3.069 4.202
1.111 1.112 1.110 1.109 1.104 1.122 1.111 1.111 1.266 1.335 1.203 1.574 1.565 2.740 1.685 1.227 1.225 1.244 1.258
31.5 33.5 25.7 45.5 45.3 43.7 82.8
˚) In–N (A
N–In–N (°)
DEa (eV)
5.344 4.912 4.070 4.449 4.113 3.951 3.940 4.610 2.271 2.253 2.625 2.068 2.064 2.057 2.264 2.051 2.128 2.373 1.919 1.968, 1.809, 2.052
11.9 13.0 40.0 (In1-N1-In2) 39.0 (In1-N1-In2) 43.9 (In1-N1-In2)
0.00 (0.00) 0.38 (0.38) 0.09 (0.08) 0.51 (0.53) 4.46 (4.26) 0.33 (0.19) 0.76 (0.68) 0.87 (0.86) 0.94 (0.77) 2.24 (1.89) 3.03 (2.76) 3.86 (3.45) 4.01 (3.59) 4.77 (4.17) 4.73 (4.49) 1.55 (1.24) 1.83 (1.56) 3.37 (3.16) 4.47 (4.03) 4.60 (4.45) 0.03 (0.04) 0.02 0.03b 0.02b 0.94 (1.03) 11.80 (11.04)
32.3 34.5 26.5 44.7 44.5 83.5 43.7
The values in parentheses are the Davidson corrected energies. RECPs retained the outer 4d105s25p1 shells for indium.
state both of 3B1 symmetry, one with T-shaped structure (InInNN(T)), and the other with a T2 shape (see Fig. 1). The T-shaped structure contains an N–N bond in a hori˚ , while zontal orientation with a bond length of 1.111 A ˚ the closest In–N bond distances are 5.344 A. The N–N
˚ is very close to the N2 bond length bond length of 1.111 A 1 þ ˚ of 1.098 A in its Rg ground state. Thus this should be described as a loose complex of In2 with N2. A 1A1 excited state of the same T-geometry is only 0.38 eV above with the ˚ . The other T-shaped strucIn–N bond distance of 4.912 A
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
In2
N2 N1
In1
N1
In1
N2
InInNN(T), C2v
In2
InInNN(T2), C2v
N1 In2
In1
N1
N2
In1
InInNN, C ∞v
In2
N1
N2
InNNIn, D∞h
N2
In2
In 2N2, D2h
In1
In2
N1
In1
N2
InNInN, C∞v
Fig. 1. The geometrical arrangement of the structures of In2N2 clusters.
ture, InInNN(T2), contains a In–In bond in a horizontal orientation and there exists a 1A1 excited state. They are 0.09 eV and 0.13 eV above the corresponding 3B1 and 1A1 states of InInNN(T). A 3R state of linear InInNN geometry was found to be 0.33 eV above the InInNN(T) 3B1 ˚ and the ground state. The In–In bond length is 2.802 A ˚ close to the N2 dimer bond length. N–N length is 1.122 A This suggests that the T-shaped and linear structures are all loose complexes of In2 and N2 where the operation of charge donation and back donation binds the two moieties together. The rhombus structure, which happens to be a low-lying geometry of Ga2As2, exhibits a closed shell 1Ag state with an acute N–In–N bond angle of 32.3 and In–N bond ˚ . But this structure is 0.94 eV above the lengths of 2.271 A 3 InInNN(T) B1 ground state. The rhombic structure of In2N2 is analogous to the corresponding structures of In2 P2 [23] and In2As2 [24] that have been considered before. ˚ is elongated relative to The N–N bond length of 1.266 A ˚ the N2 bond length of 1.098 A in its 1 Rþ g ground state due to the formation of In–N bonds. At the B3LYP level, Kandalm et al. [17] have also found the rhombic state of In2N2 in the D2h symmetry to be a singlet state, which is consistent with our results. However their computed geometrical parameters differ significantly from ours, for ˚ compared to example, their In–N distances are 2.44 A ˚ our MRSDCI result of 2.271 A. There are other significant differences in the computed energy separations between the current work and those in Ref. [17] that we discuss below. As can be seen from both Tables 1 and 2, we have found several excited state for In2N2. Most excited states exhibit rhombus structures. The first excited electronic state is the 3B3u state, which is 1.30 eV above the rhombic 1Ag state. And its geometry is very close to the rhombus 1Ag state. The In–N and N–N bond lengths change by ˚ and 0.069 A ˚ . The lowest state of linear InNNIn 0.018 A was found to be a 3Pu state with the N–N bond length ˚ and the In–N bond length of 2.051 A ˚ . This state of 1.227 A 3 is however 1.55 eV above the InInNN(T) B1 ground state.
291
In addition, a 3R state was found to be the lowest state of linear InNInN. The results shown in Table 2 have been obtained at the MRSDCI level and are thus more accurate than the CASSCF results shown on Table 1. This is because dynamic electron correlation effects are not included at the CASSCF level. By comparing the results in Tables 1 and 2, it is seen that for most low-lying electronic states, higher-order electron correlation effects do not substantially alter the geometries. The In–N bond lengths change ˚ except for the 3Pu state of linear InNat most by 0.06 A NIn. And the N–N bond lengths change at most by ˚. 0.043 A The energy separations are very sensitive to electron correlation effects as seen from Tables 1 and 2. For example, it is seen that the 1Ag state of rhombic In2N2 is 1.34 eV higher than the T-shaped 3B1 state at the CASSCF level, while the value is decreased to 0.94 eV at the MRSDCI level and 0.77 eV at the MRSDCI + Q level. Since the T-shaped and linear InInNN are loose complexes of In2 and N2, electron correlation effects seem to introduce considerable changes. The previous work by Kandalam et al. [17] considers both In2N2 and Ga2N2 at the DFT levels. There are significant differences between our MRSDCI results and Kandalam et al. DFT results. Whereas Kandalm et al. [17] find the ground state of In2N2 to be In–In–N–N triplet state with an unspecified spatial symmetry, we find the 3R In– In–N–N state to be 0.33 eV above the T-shaped triplet ground state of ours. The energy difference between the triplet state with In–In–N–N geometry and the linear InNNIn that Kandam et al. obtain is only 0.35 eV, which differs from our MRSDCI + Q result of 1.22 eV. In addition, in our work T-shaped InInNN(T) and InInNN(T2) structures are found more stable than the linear In–In– N–N structure. The bond lengths calculated in Ref. [17] tend to be uniformly long, for example, in Ref. [17] the ˚ for the In–In–N–N In–N distance is reported as 4.66 A ˚ structure whereas we find the same distance to be 3.951 A at the MRSDCI level. The In–N distances for the 1Ag ˚ in rhombic structure reported in Ref. [17] are 2.44 A ˚ . These subcontrast to our MRSDCI results of 2.271 A stantial differences in bond lengths could also result in greater differences in the computed energy separations. It should be noted that Kandalam et al. [17] have used a smaller basis set and do not appear to include relativistic effects for In, and it has been well established that relativistic effects tend to contract the 5s orbital of In resulting in shorter In–N bonds and hence different energy separations. The dissociation and atomization energies of In2N2 were computed as supermolecular computations at the MRSDCI and MRSDCI + Q levels. As demonstrated in Table 2, the dissociation energy of In2N2 to yield In2 (3Pu) and N2 ð1 Rþ gÞ is computed as 0.03 eV for the 3B1 state of InInNN(T) at the MRSDCI level and 0.04 eV at the MRSDCI + Q level. Moreover, the dissociation energy is computed as 0.03 eV at the MP2 level and 0.02 eV at the CCSD(T) level with RECPs retained the outer 4d105s25p1 shells for indium,
353.67 351.48 382.82 382.82 430.08 426.05
C
56824.3 0 45471.5
B
2157(0.0509, 13.8574)
A
2137(0.1149, 16.6733) 249(139.5168, 349.2182) 1344(0.0000, 7355.9529)
x7
23(0.0625, 0.1595) 125(0.0377, 57.5698) 29(0.1307, 57.5705) 29(0.0718, 217.3589) 447(255.6191, 0.0000) 548(0.0000, 324.2245)
x6 x5
22(0.1015, 0.3915) 29(0.1307, 57.5705) 156(30.8169, 0.0000)
x4
D1h D1h C2v C1v D2h N2 In2 InInNN(T) InInNN In2N2
1
Rþ g 3 Pu 3 B1 3 R 1 Ag
2139(0.0000, 125(0.0000, 2(0.0126, i4(0.0917, 106(2.8896,
9.3382) 61.1256) 13.8276) 7(0.0003, 8.5810) 34.5203) i4(0.0917, 34.5203) 0.0000) 125(0.0000, 519.1183)
x3 x2 x1
Vibrational frequency (IR intensity, Raman activity) State Symmetry System
which are consistent with the MRSDCI and the CCSD(T) results with RECPs retained the outer 5s25p1 shells for indium. It does not change much by involving the 4d orbitals of Indium in the valence space indicating that the RECPs retained the outer 5s25p1 shells for indium are quite reasonable for the low-lying states of In2N2. The small dissociation energy suggests that In2N2 is a weak complex of In2 and N2. The dissociation energy of In2N2 to yield two In atoms and N2 ð1 Rþ g Þ ground state is computed as 1.03 eV. The difference between the two dissociation energies gives the De (dissociation energy) of In2, which is obtained as 0.99 eV at the MRSDCI + Q level. It is close to the 0.87 eV deduced by Froben et al. [32]. The atomization energy to fully separate In2N2 into two In (2P) and two nitrogen atoms (4S) is calculated to be 11.04 eV for the InInNN(T) and 10.27 eV for rhombic In2N2, respectively. This is consistent with our anticipation that the N–N bonding is considerably stronger than that of the In–In bond in In2N2, and plays a more important role in the properties for the electronic states of In2N2. Moreover the difference between the energies of products 2In + N2 and 2In + 2N in Table 2 is De of N2 (=10.01 eV), which agrees reasonably with the experimental D0 value of N2 (9.75 eV). The zero-point corrected result is much closer. Although there are no spectroscopic studies on the In2N2 clusters, Neumark and co-workers [3,5] have obtained the anion photoelectron spectroscopy of indium phosphide clusters of up to 27 atoms. Among the various clusters, the In2P2 cluster exhibits a well-resolved spectrum with five peaks. Relative to the lowest energy peak, the energy separations are 0.70, 1.02, 1.73, and 2.42 eV, respectively. In a previous study on the In2P2 cluster, Feng et al. [23] found the 1Ag state with a rhombus structure as the ground state. The first excited state is the 3B2g state which was computed at 1.26 eV above the ground state. It is evident that the first peak of the photoelectron 1 spectrum of In2 P 2 is due to the Ag ground state of In2P2. The second and third peaks correspond to the other kind of structures instead of rhombus structure. There are two electronic states near the 1.7 eV region, namely, 1Au and 1 B2g states which were computed at 1.650 and 1.659 eV above the ground state, respectively. In addition, the fifth peak of photoelectron spectrum of In2 P 2 corresponds to the 3B3u excited state of In2P2 which was computed at 2.425 eV. The spectra of In2N2 are likely to differ substantially from the spectra of In2P2 primarily due to the T-shaped and T2-shaped ground states and the rhombic structure is 0.94 eV higher than the InInNN(T) 3B1 ground state. It is very clear that the competition of four different geometries for the lowest lying excited states of In2N2 would complicate the spectra. Moreover in contrast to In2P2 the energy separations of even the rhombic excited states of In2N2 are larger and thus all of the excited rhombic states of rhombic geometry may not be accessible in the PES spectra of the anions for In2N2.
Rotational constant
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 3 Harmonic vibrational frequencies (cm1) and rotational constants (MHz) of In2N2 with IR intensity and Raman activity in the parentheses at the MP2 level
292
System
Symmetry
State
Total
Gross population
In
N
In
4.994 4.993 4.994, 4.997, 5.012, 4.988, 4.989, 4.988, 5.410 5.492 5.284 5.566 5.574 5.546 5.459 5.443 5.367 5.339 5.528 6.069,
1.753, 1.797, 1.740 1.800 1.656 1.711, 1.678, 1.723, 1.785 1.764 1.808 1.500 1.472 1.349 1.766 1.797 1.807 1.815 1.402 1.783,
s InInNN(T)
C2v
InInNN(T2)
C2v
InInNN
C1v
In2N2
D2h
InNNIn
D1h
InNInN
C1v
3
B1 1 A1 3 B1 1 A1 3 A1 3 R 1 + R 3 P 1 Ag 3 B3u 1 B3u 3 B1g 1 Au 3 B1u 3 B3g 3 Pu 1 þ Rg 3 þ Rg 3 Ru 3 R
3.015, 3.016, 3.007 3.005 3.007 3.013, 3.011, 3.027, 2.590 2.508 2.716 2.434 2.426 2.454 2.541 2.557 2.633 2.661 2.472 2.537,
2.997 2.998
3.007 3.007 2.986
2.136
4.992 4.992 4.974 4.991 4.993 4.998
5.257
Overlap In–N
Dipole moment (D)
0.009 0.007 0.007 0.007 0.007 0.015 0.012 0.005 0.282 0.292 0.019 0.542 0.563 0.724 0.273 0.094 0.113 0.040 0.195 0.373 (In1-N1)
0.008 0.022 0.073 0.027 0.201 0.153 0.143 0.049
N p 1.756 1.796
1.734 1.712 1.763
0.890
1.121, 1.087, 1.120 1.058 1.143 1.146, 1.172, 1.155, 0.671 0.594 0.752 0.812 0.836 0.961 0.634 0.687 0.737 0.721 1.046 0.699,
d 1.099 1.068
1.120 1.141 1.073
1.102
0.142, 0.132, 0.146 0.148 0.208 0.155, 0.160, 0.150, 0.133 0.150 0.156 0.122 0.118 0.143 0.140 0.073 0.089 0.125 0.025 0.055,
0.142 0.134
0.154 0.155 0.149
0.144
s
p
1.778 1.775 1.751, 1.759, 1.727, 1.763, 1.757, 1.785, 1.819 1.825 1.821 1.823 1.820 1.860 1.880 1.498 1.532 1.624 1.473 1.707,
3.130 3.131 3.158, 3.153, 3.202, 3.144, 3.148, 3.118, 3.525 3.605 3.383 3.703 3.713 3.667 3.552 3.977 3.770 3.651 3.985 4.341,
1.791 1.788 1.796 1.791 1.786 1.778
1.890
3.114 3.116 3.093 3.114 3.120 3.133
3.341
0.404
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 4 The Mulliken population analyses for the low-lying electronic states of In2N2
293
294
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 3 shows vibrational frequencies and rotational constants of lowest states of T-shaped, linear, and rhombus In2N2 together with In2 and N2 for comparison. At the MP2 level the 3R state of linear In2N2 is a genuine minimum structure, while it has two degenerate soft imaginary frequencies (i4 cm1). As seen from Table 3, the In–In stretching vibrational frequencies are 125 cm1 for InInNN(T), and 125 cm1 for rhombus In2N2, respectively, which are very close to the 125 cm1 of free In2. The N–N stretching frequencies obtained at 2137 cm1 for InInNN(T) and 2157 cm1 for linear InInNN are close to 2139 cm1 of free N2, which confirms the weak interaction between In2 and N2 in the T-shaped and linear In2N2. Moreover, the N–N stretching frequency of rhombus structure is obtained at 1344 cm1 which is consistent with the longer N–N bond. The contributions of the leading configurations of most of the electronic states are below 82% indicating the significance of electron correlation effects from multiple references. The leading configurations of the 3B1 states of the InInNN(T) and InInNN(T2) are 1a21 2a21 3a21 4a21 5a21 6a11 1b22 1b21 2b11 and 1a21 2a21 3a21 4a21 5a11 1b22 2b22 1b21 2b11 , respectively, which contribute up to 81%. The 1A1 excited states of these geometries are obtained by the promotion of an electron from the 2b1 orbital to the single-occupied a1 orbital. The 3 R state of linear InInNN is predominantly composed of the 1r22r23r24r25r21p42p2 configuration. The 1R+ excited state has the same leading configuration but this configuration contributes only 41% indicating substantial multi-reference character. The 1a2g 2a2g 1b21u 1b22u 1b23u portion of the electronic configuration is common for the low-lying electronic states of rhombic In2N2. The differences arise from the occupancies for the 3ag, 2b2u, 2b3u, 1b1g, and 1b3g orbitals. Consequently, analysis of the compositions of these orbitals could provide insight into the nature of the low-lying electronic states. The 3ag orbital is composed of [N1(2py)– N2(2py)]–[In1(5s) + In2(5s)], which is a bonding r orbital. The 2b2u orbital is an antibonding [N1(2s)–N2(2s)] orbital. The 2b3u orbital is composed of [N1(2px) + N2(2px)] + [In1(5px) + In2(5px)], which contains a p bonding interaction between two N atoms and r antibonding interactions between In and N. The 1b1g orbital is mainly [N1(2px)– N2(2px)] + [In1(5py)–In2(5py)], which contains a p antibonding interaction between two N atoms and p bonding interactions between In and N. The 1b3g orbital is made of [N1(2pz)–N2(2pz)], and it is an antibonding orbital. The leading configuration of the rhombic 1Ag state is 2 1ag 2a2g 3a2g 1b21u 1b22u 1b23u 2b23u 1b21g which makes an 81% contribution. All the excited states arise from transfer of electrons from the bonding to the antibonding orbitals, resulting in energies above the 1Ag state. For example, the 3B3u and 1B3u excited states are obtained by the promotion of an electron from the 1b1g HOMO to the 2b2u LUMO. The 3B1g excited state is formed by the promotion of an electron from the 2b3u orbital to the 2b2u orbital.
Table 4 shows the Mulliken population distributions. As seen from Table 4, all of the electronic states in In2N2 exhibit charge transfers from In to N resulting in In+N ionic bonds. In the case of two T-shaped structures the charge transfers between N2 and In2 are approximately equal so that the overall gross populations of In and N are closest to their atomic values. A critical examination of the individual atomic populations reveals that the N transfers 0.22 e from its 2s orbital to In(5p) whereas In(5s) transfers about 0.25e to N(2p). This dative exchange of charges facilitates the formation of a loose complex between the species resulting in T-shaped structures. A similar feature is seen in the triplet state of the linear In–In–N–N isomer. The In(d) population suggests charge polarization in these structures. All electronic states exhibit reduced s populations compared to atomic populations, consistent with the anticipated hybridization with the p orbitals. The N(2p) populations in all of the electronic states of In2N2 are uniformly larger than 3, which suggests that most of the charge transfers from the In atoms is received by the N(2p) orbitals. In addition, the d populations of the In atoms are noticeably larger than 0, and thus the participation of the 5d polarization is quite significant. In comparing the populations of the ground state with the low-lying excited electronic states, it is seen that the excited states exhibit larger In(5p) populations and smaller In(5s) populations, suggesting 5s to 5p promotions on In in the excited states. These features result in the enhancement of the In–N bonding, as seen from the larger In–N overlap populations and decrease in the N–N bonding in the excited electronic states. 4. Conclusions Twenty electronic states of the In2N2 cluster are computed using the CASSCF/MRSDCI technique. Results show that in contrast to other III–V tetramers, In2N2 exhibits two nearly degenerate T-shaped 3B1 states that are found to be the ground state candidates followed by a low-lying linear In–In–N–N 3R state. The 1Ag state with a rhombus structure was found to be 0.94 eV higher. A number of other excited states with rhombus and other geometries are found. We have computed the various dissociation and atomization energies. Our computations show that the anion photodetachment spectra of In2N2 would be substantially different from the corresponding spectra of Ga2P2 and related tetramers observed by Neumark and coworkers. Acknowledgement This research was supported by the US National Science Foundation under Grant No. CHE-0540251. The work at Lawrence Livermore National Laboratory was performed under the auspices of US Department of Energy by the University of California under Contract No. W-7405Eng-48.
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
References [1] S.C. Obrien, Y. Liu, Q. Zhang, J.R. Heath, F.K. Tittel, R.F. Curl, R.E. Smalley, J. Chem. Phys. 84 (1986) 4074. [2] C.C. Arnold, D.M. Neumark, Can. J. Phys. 72 (1994) 1322. [3] C.S. Xu, E. Debeer, D.W. Arnold, C.C. Arnold, D.M. Neumark, J. Chem. Phys. 101 (1994) 5406. [4] T.R. Taylor, K.R. Asmis, C.S. Xu, D.M. Neumark, Chem. Phys. Lett. 297 (1998) 133. [5] K.R. Asmis, T.R. Taylor, D.M. Neumark, Chem. Phys. Lett. 308 (1999) 347. [6] T.R. Taylor, K.R. Asmis, H. Gomez, D.M. Neumark, Eur. Phys. J.D 9 (1999) 317. [7] H. Gomez, T.R. Taylor, D.M. Neumark, J. Phys. Chem. A 105 (2001) 6886. [8] T.R. Taylor, H. Gomez, K.R. Asmis, D.M. Neumark, J. Chem. Phys. 115 (2001) 4620. [9] H. Gomez, T.R. Taylor, Y. Zhao, D.M. Neumark, J. Chem. Phys. 117 (2002) 8644. [10] G. Meloni, M.J. Ferguson, S.M. Sheehan, H. Gomez, Z. Liu, D.M. Neumark, Chem. Phys. Lett. 392 (2004) 90. [11] G. Meloni, S.M. Sheehan, B.F. Parsons, D.M. Neumark, J. Phys. Chem. A 110 (2006) 3527. [12] S.M. Sheehan, G. Meloni, B.F. Parsons, N. Wehres, D.M. Neumark, J. Chem. Phys. 124 (2006). [13] S. Li, R.J. Vanzee, W. Weltner, J. Phys. Chem. 97 (1993) 11393.
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
295
R.J. Vanzee, S. Li, W. Weltner, J. Chem. Phys. 98 (1993) 4335. S. Li, R.J. Vanzee, W. Weltner, J. Phys. Chem. 98 (1994) 2275. M.F. Zhou, L. Andrews, J. Phys. Chem. A 104 (2000) 1648. A.K. Kandalam, R. Pandey, M.A. Blanco, A. Costales, J.M. Recio, J. Phys. Chem. B 104 (2000) 4361. A. Costales, A.K. Kandalam, A.M. Pendas, M.A. Blanco, J.M. Recio, R. Pandey, J. Phys. Chem. B 104 (2000) 4368. A. Costales, M.A. Blanco, A.M. Pendas, A.K. Kandalam, R. Pandey, J. Am. Chem. Soc. 124 (2002) 4116. A. Costales, R. Pandey, J. Phys. Chem. A 107 (2003) 191. C.J. Zhang, J. Chem. Phys. 124 (2006) 184316. K. Balasubramanian, J. Chem. Phys. 87 (1987) 3518. P.Y. Feng, K. Balasubramanian, Chem. Phys. Lett. 264 (1997) 449. P.Y. Feng, M.Z. Liao, K. Balasubramanian, Chem. Phys. Lett. 296 (1998) 283. K. Balasubramanian, X.L. Zhu, J. Chem. Phys. 115 (2001) 8858. C.S. Wang, K. Balasubramanian, Chem. Phys. Lett. 402 (2005) 294. X.L. Zhu, Spectrochim. Acta Part A 61 (2005) 2730. L.F. Pacios, P.A. Christiansen, J. Chem. Phys. 82 (1985) 2664. L.A. Lajohn, P.A. Christiansen, R.B. Ross, T. Atashroo, W.C. Ermler, J. Chem. Phys. 87 (1987) 2812. K. Balasubramanian, Chem. Phys. Lett. 127 (1986) 324. M.J. Frisch, G.W. Trucks, H.B. Schlegel, et al., Gaussian 03, revision C.02. Gaussian, Inc.: Pittsburgh, PA, 2005. F.W. Froben, W. Schulze, U. Kloss, Chem. Phys. Lett. 99 (1983) 500.
Unusual geometries and spectroscopic properties of electronic states of In2N2 Zhiji Cao a, Krishnan Balasubramanian b
a,b,c,*
a Department of Mathematics and Computer Science, California State University, East Bay, Hayward, CA, United States University of California, Chemistry and Material Science Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, United States c Glenn T Seaborg Center, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, United States
Received 31 January 2007; in final form 22 March 2007 Available online 31 March 2007
Abstract Twenty electronic states of In2N2 are computed using a complete active space multi-configuration self-consistent field followed by multi-reference singles + doubles configuration interaction (MRSDCI) computations. In contrast to other III–V tetramers, In2N2 exhibits nearly degenerate T-shaped triplet states and linear In–In–N–N 3R state. The 1Ag state with a rhombus structure was found to be 0.94 eV higher. Our computations show that anion photodetachment spectra of In2N2 could be substantially different from the spectra of Ga2P2 and related tetramers observed by Neumark and coworkers. The computed vibrational and Raman spectra are provided. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Mixed semi-conductor clusters, especially those of the groups III and V have been the focus of several spectroscopic and theoretical studies [1–27], as these species are used in the fabrication of ultra-fast devices, blue–green lasers and semi-conductor injection lasers. Interestingly these clusters exhibit dramatic variations in properties as a function of cluster size. A detailed study of the properties of such clusters, especially their excited electronic states, could provide significant insight into their spectra and structures. Smalley and coworkers [1] pioneered the spectroscopic study of III–V semi-conductor clusters by demonstrating that laser vaporization of a gallium arsenide foil and subsequent supersonic expansion results in a plethora of GaxAsy clusters of various sizes with dramatic variations in abundance for smaller sizes and culminating into a binomial distribution for larger sizes. Subsequently, a number of * Corresponding author. Address: University of California, Chemistry and Material Science Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, United States. Fax: +1 925 422 6810. E-mail address: [email protected] (K. Balasubramanian).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.03.108
experimental techniques have been employed to probe the low-lying electronic states of group III–V clusters. Neumark and coworkers [2–12] have studied a number of group III–V semi-conductor clusters, especially InxPy, GaxPy, GaxAsy, and AlxPy using anion photodetachment spectroscopy. These experimental studies have yielded the electron affinities, information on the low-lying excited states, and vibrational frequencies of the neutral and anionic clusters. Weltner and coworkers [13–15] have used a matrix-isolation technique to obtain GaX, Ga2X, GaX2, and InX molecules, where X=P, As, and Sb, as well as Ga2As3. They have used electron-spin resonance (ESR) and far-infrared spectroscopic methods to probe the ground states of matrix-isolated clusters. On the basis of the observed hyperfine patterns, the spin multiplicities and the geometries of the ground states of these species could be deduced. Theoretical studies of electronic, structural, and vibrational properties of group III–V clusters have been carried out mostly on the ground states [17–21], although there have been computational studies on the excited states as well [22–27]. Pandey and coworkers [17–20] have carried out systematic theoretical studies of neutral and anionic group III nitride MnNn (M = Al, Ga, and In; n = 1–6)
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
clusters in the ground states within the framework of DFT. Their works were focused on the structural properties, stability, electronic structure, and the changes of these properties upon electron attachment. Our research group [22–26] has carried out systematic theoretical studies of neutral GaxAsy, AlxPy, and InxPy etc., as well as their ions up to 5 atoms using ab initio CASSCF/MRSDCI techniques, focusing on the properties of both the ground and lowlying excited electronic states. Thus a primary focus of our work is predicting spectroscopic properties of the excited states of these clusters. Indium nitride is quite unusual in that as shown here, its bonding characteristics differ substantially from the analogs. For example four-atom mixed clusters like Ga2As2 [27] exhibit a rhombus ground state, whereas, as shown here, In2N2 is very unusual in exhibiting two nearly degenerate T-shaped ground states and a rhombus structure which is 0.94 eV higher in energy. There are very few studies on InxNy clusters up to now. Zhou and Andrews [16] have provided the first infrared spectroscopic evidence for InN, In2N, InN2, In3N, and InN3 species, which are identified from nitrogen and gallium isotopic shifts, mixed isotopic splittings, and density functional theory calculations. Pandey and coworkers [17–20] have studied structures, stabilities, and vibrational properties of neutral and ionized clusters of InxNy up to 12 atoms within the frame of DFT. As demonstrated by our past work, the ground and low-lying electronic states of group III–V clusters could be of multireference in character, and electron correlation effects are significant, especially for energy separations. In this work we consider a systematic study on several low-lying electronic states of the neutral In2N2 using high-level ab initio CASSCF and MRSDCI techniques that included up to 7 million configurations. Both ground and several low-lying excited electronic states are optimized and their energy separations are computed. 2. Computational details We have computed the electronic states of In2N2 with different kinds of geometric arrangements and optimizing each of those geometries. All the computations were carried out in the C2v symmetry with the z-axis chosen as the C2 axis. A complete active space MCSCF (CASSCF) method followed by multi-reference singles + doubles configuration interaction (MRSDCI) is employed. All calculations were carried out using relativistic effective core potentials (RECPs) [28,29] for the core electrons of In and N atoms with the outer 5s25p1 shells for the In atom and the outer 2s22p3 for the N atom retained in the valence space, respectively. The In basis set from Ref. [29] was augmented with the one set of 6-component 5d (ad = 0.2129) and a set of s and p diffuse functions (as = 0.02, ap = 0.0145). The N basis was enhanced with a set of 3d polarization function (ad = 0.8) and a set of s and p diffuse functions (as = 0.1734, ap = 0.1904). The final basis sets for the In atoms were of (4s4p1d) quality, whereas the basis sets
289
for the N atoms are of (4s4p1d) quality. Moreover, for the purpose of comparison, the ground state of In2N2 was also calculated at the MP2 and CCSD(T) levels with relativistic effective core potentials (RECPs) [29] that retained the outer 4d105s25p1 shells for indium. The In basis set from Ref. [29] was augmented with two sets of s and p diffuse functions (as1 = 0.02, as2 = 0.0054, ap1 = 0.0145, ap2 = 0.0045) and a set of 4f function (af = 0.45). The final basis sets for the In atoms were of (5s5p4d1f) quality. In the CASSCF computations the valence 2s and 2p orbitals of N, as well as 5s and 5p orbitals of the In atoms were included in the active space. Among the valence orbitals we chose to include the lowest thirteen orbitals in the CASSCF active space to keep the computations tractable. This resulted in an active space spanning five a1, three b2, three b1, and two a2 orbitals, in C2v, which we label 5332-CAS for the rhombic In2N2. We adopted an equivalent 6331-CAS for a T-shaped In2N2 (labeled InInNN(T)) containing a N–N bond in a horizontal orientation, and a 6331-CAS for another T-shaped In2N2 (labeled InInNN(T2)) containing a In–In bond in the horizontal orientation, a 7330-CAS for the linear InInNN, a 7330CAS for the linear InNInN, and a 5512-CAS for the linear InNNIn, respectively. We ensured that each of these active spaces produced the lowest energy for the lowest state. Sixteen electrons of In2N2 were distributed in all possible ways among these orbitals at the CASSCF level. The MRSDCI calculations included all configurations in the CASSCF with absolute values of coefficients P0.03 as reference configurations. Multireference Davidson corrections to the MRSDCI energies for uncoupled quadruple clusters were calculated and the energy separations thus computed were labeled as MRSDCI + Q results. The MRSDCI included up to 7 million configurations, and geometry optimizations were carried out at the MRSDCI level. The vibrational frequencies were computed at the MP2 level. The CASSCF/ MRSDCI calculations were carried out using a modified version of the ALCHEMY II1 codes to include RECPs [30]. The MP2 and CCSD(T) calculations were made using GAUSSIAN 03 codes [31]. 3. Results and discussion We were able to seek six kinds of structures and twenty electronic states of In2N2 at the CASSCF and MRSDCI levels. Structural parameters along with the energy separations are given in Tables 1 and 2 at the CASSCF and MRSDCI levels, respectively. The geometrical structures are depicted in Fig. 1. As can be seen from both Tables 1 and 2, In2N2 is quite interesting in that unlike heaver group V tetraatomic clusters such as Ga2As2, there are two nearly degenerate states as candidates for the ground electronic
1 The major authors of ALCHEMY II are B. Liu, B. Lengsfiled and M. Yoshimine.
290
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 1 Geometries and energy separations of the electronic states of In2N2 at the CASSCF level System
Symmetry
State
In–In ˚) (A
N–N ˚) (A
In–N ˚) (A
N–In–N (°)
DE (eV)
InInNN(T)
C2v
3
3.091 3.342 2.832 3.209 3.189 2.852 2.906 2.474 4.447 4.361 5.173 3.838 3.831 4.215 3.118
1.100 1.114 1.100 1.101 1.085 1.100 1.103 1.100 1.253 1.313 1.181 1.611 1.599 1.692 2.749 1.189 1.198 1.201 1.215
5.299 4.884 4.088 4.500 4.151 3.932 3.885 4.628 2.310 2.277 2.653 2.081 2.076 2.271 2.079 2.188 2.174 2.391 1.940 1.972, 1.822, 2.024
11.9 13.1 40.5 (In1-N1-In2) 41.8 (In1-N1-In2) 45.2 (In1-N1-In2)
0.00 0.11 0.05 0.12 5.79 0.23 0.96 1.05 1.34 3.30 4.25 5.09 5.28 5.45 6.36 1.98 2.38 3.73 5.45 4.83
B1 A1 3 B1 1 A1 3 A1 3 R 1 + R 3 P 1 Ag 3 B3u 1 B3u 3 B1g 1 Au 3 B3g 3 B1u 1 þ Rg 3 Pu 3 þ Rg 3 Ru 3 R 1
InInNN(T2)
C2v
InInNN
C1v
In2N2
D2h
InNNIn
D1h
InNInN
C1v
Table 2 Geometries and energy separations of the electronic states of In2N2 at the MRSDCI level ˚) ˚) System Symmetry State In–In (A N–N (A InInNN(T)
C2v
3
B1 A1 3 B1 1 A1 3 A1 3 R 1 + R 3 P 1 Ag 3 B3u 1 B3u 3 B1g 1 Au 3 B1u 3 B3g 3 Pu 1 þ Rg 3 þ Rg 3 Ru 3 R 1
InInNN(T2)
C2v
InInNN
C1v
In2N2
D2h
InNNIn
D1h
InNInN In2 ð3 Pu Þ þ N2 ð1 Rþ gÞ In2 ð3 Pu Þ þ N2 ð1 Rþ g Þ (CCSD(T)) In2 ð3 Pu Þ þ N2 ð1 Rþ g Þ (MP2) In2 ð3 Pu Þ þ N2 ð1 Rþ g Þ (CCSD(T)) 2Inð2 PÞ þ N2 ð1 Rþ gÞ 2In(2P) + 2N(4S)
C1v
a b
3.045 3.315 2.785 2.967 3.079 2.802 2.851 2.489 4.362 4.303 5.110 3.825 3.820 3.069 4.202
1.111 1.112 1.110 1.109 1.104 1.122 1.111 1.111 1.266 1.335 1.203 1.574 1.565 2.740 1.685 1.227 1.225 1.244 1.258
31.5 33.5 25.7 45.5 45.3 43.7 82.8
˚) In–N (A
N–In–N (°)
DEa (eV)
5.344 4.912 4.070 4.449 4.113 3.951 3.940 4.610 2.271 2.253 2.625 2.068 2.064 2.057 2.264 2.051 2.128 2.373 1.919 1.968, 1.809, 2.052
11.9 13.0 40.0 (In1-N1-In2) 39.0 (In1-N1-In2) 43.9 (In1-N1-In2)
0.00 (0.00) 0.38 (0.38) 0.09 (0.08) 0.51 (0.53) 4.46 (4.26) 0.33 (0.19) 0.76 (0.68) 0.87 (0.86) 0.94 (0.77) 2.24 (1.89) 3.03 (2.76) 3.86 (3.45) 4.01 (3.59) 4.77 (4.17) 4.73 (4.49) 1.55 (1.24) 1.83 (1.56) 3.37 (3.16) 4.47 (4.03) 4.60 (4.45) 0.03 (0.04) 0.02 0.03b 0.02b 0.94 (1.03) 11.80 (11.04)
32.3 34.5 26.5 44.7 44.5 83.5 43.7
The values in parentheses are the Davidson corrected energies. RECPs retained the outer 4d105s25p1 shells for indium.
state both of 3B1 symmetry, one with T-shaped structure (InInNN(T)), and the other with a T2 shape (see Fig. 1). The T-shaped structure contains an N–N bond in a hori˚ , while zontal orientation with a bond length of 1.111 A ˚ the closest In–N bond distances are 5.344 A. The N–N
˚ is very close to the N2 bond length bond length of 1.111 A 1 þ ˚ of 1.098 A in its Rg ground state. Thus this should be described as a loose complex of In2 with N2. A 1A1 excited state of the same T-geometry is only 0.38 eV above with the ˚ . The other T-shaped strucIn–N bond distance of 4.912 A
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
In2
N2 N1
In1
N1
In1
N2
InInNN(T), C2v
In2
InInNN(T2), C2v
N1 In2
In1
N1
N2
In1
InInNN, C ∞v
In2
N1
N2
InNNIn, D∞h
N2
In2
In 2N2, D2h
In1
In2
N1
In1
N2
InNInN, C∞v
Fig. 1. The geometrical arrangement of the structures of In2N2 clusters.
ture, InInNN(T2), contains a In–In bond in a horizontal orientation and there exists a 1A1 excited state. They are 0.09 eV and 0.13 eV above the corresponding 3B1 and 1A1 states of InInNN(T). A 3R state of linear InInNN geometry was found to be 0.33 eV above the InInNN(T) 3B1 ˚ and the ground state. The In–In bond length is 2.802 A ˚ close to the N2 dimer bond length. N–N length is 1.122 A This suggests that the T-shaped and linear structures are all loose complexes of In2 and N2 where the operation of charge donation and back donation binds the two moieties together. The rhombus structure, which happens to be a low-lying geometry of Ga2As2, exhibits a closed shell 1Ag state with an acute N–In–N bond angle of 32.3 and In–N bond ˚ . But this structure is 0.94 eV above the lengths of 2.271 A 3 InInNN(T) B1 ground state. The rhombic structure of In2N2 is analogous to the corresponding structures of In2 P2 [23] and In2As2 [24] that have been considered before. ˚ is elongated relative to The N–N bond length of 1.266 A ˚ the N2 bond length of 1.098 A in its 1 Rþ g ground state due to the formation of In–N bonds. At the B3LYP level, Kandalm et al. [17] have also found the rhombic state of In2N2 in the D2h symmetry to be a singlet state, which is consistent with our results. However their computed geometrical parameters differ significantly from ours, for ˚ compared to example, their In–N distances are 2.44 A ˚ our MRSDCI result of 2.271 A. There are other significant differences in the computed energy separations between the current work and those in Ref. [17] that we discuss below. As can be seen from both Tables 1 and 2, we have found several excited state for In2N2. Most excited states exhibit rhombus structures. The first excited electronic state is the 3B3u state, which is 1.30 eV above the rhombic 1Ag state. And its geometry is very close to the rhombus 1Ag state. The In–N and N–N bond lengths change by ˚ and 0.069 A ˚ . The lowest state of linear InNNIn 0.018 A was found to be a 3Pu state with the N–N bond length ˚ and the In–N bond length of 2.051 A ˚ . This state of 1.227 A 3 is however 1.55 eV above the InInNN(T) B1 ground state.
291
In addition, a 3R state was found to be the lowest state of linear InNInN. The results shown in Table 2 have been obtained at the MRSDCI level and are thus more accurate than the CASSCF results shown on Table 1. This is because dynamic electron correlation effects are not included at the CASSCF level. By comparing the results in Tables 1 and 2, it is seen that for most low-lying electronic states, higher-order electron correlation effects do not substantially alter the geometries. The In–N bond lengths change ˚ except for the 3Pu state of linear InNat most by 0.06 A NIn. And the N–N bond lengths change at most by ˚. 0.043 A The energy separations are very sensitive to electron correlation effects as seen from Tables 1 and 2. For example, it is seen that the 1Ag state of rhombic In2N2 is 1.34 eV higher than the T-shaped 3B1 state at the CASSCF level, while the value is decreased to 0.94 eV at the MRSDCI level and 0.77 eV at the MRSDCI + Q level. Since the T-shaped and linear InInNN are loose complexes of In2 and N2, electron correlation effects seem to introduce considerable changes. The previous work by Kandalam et al. [17] considers both In2N2 and Ga2N2 at the DFT levels. There are significant differences between our MRSDCI results and Kandalam et al. DFT results. Whereas Kandalm et al. [17] find the ground state of In2N2 to be In–In–N–N triplet state with an unspecified spatial symmetry, we find the 3R In– In–N–N state to be 0.33 eV above the T-shaped triplet ground state of ours. The energy difference between the triplet state with In–In–N–N geometry and the linear InNNIn that Kandam et al. obtain is only 0.35 eV, which differs from our MRSDCI + Q result of 1.22 eV. In addition, in our work T-shaped InInNN(T) and InInNN(T2) structures are found more stable than the linear In–In– N–N structure. The bond lengths calculated in Ref. [17] tend to be uniformly long, for example, in Ref. [17] the ˚ for the In–In–N–N In–N distance is reported as 4.66 A ˚ structure whereas we find the same distance to be 3.951 A at the MRSDCI level. The In–N distances for the 1Ag ˚ in rhombic structure reported in Ref. [17] are 2.44 A ˚ . These subcontrast to our MRSDCI results of 2.271 A stantial differences in bond lengths could also result in greater differences in the computed energy separations. It should be noted that Kandalam et al. [17] have used a smaller basis set and do not appear to include relativistic effects for In, and it has been well established that relativistic effects tend to contract the 5s orbital of In resulting in shorter In–N bonds and hence different energy separations. The dissociation and atomization energies of In2N2 were computed as supermolecular computations at the MRSDCI and MRSDCI + Q levels. As demonstrated in Table 2, the dissociation energy of In2N2 to yield In2 (3Pu) and N2 ð1 Rþ gÞ is computed as 0.03 eV for the 3B1 state of InInNN(T) at the MRSDCI level and 0.04 eV at the MRSDCI + Q level. Moreover, the dissociation energy is computed as 0.03 eV at the MP2 level and 0.02 eV at the CCSD(T) level with RECPs retained the outer 4d105s25p1 shells for indium,
353.67 351.48 382.82 382.82 430.08 426.05
C
56824.3 0 45471.5
B
2157(0.0509, 13.8574)
A
2137(0.1149, 16.6733) 249(139.5168, 349.2182) 1344(0.0000, 7355.9529)
x7
23(0.0625, 0.1595) 125(0.0377, 57.5698) 29(0.1307, 57.5705) 29(0.0718, 217.3589) 447(255.6191, 0.0000) 548(0.0000, 324.2245)
x6 x5
22(0.1015, 0.3915) 29(0.1307, 57.5705) 156(30.8169, 0.0000)
x4
D1h D1h C2v C1v D2h N2 In2 InInNN(T) InInNN In2N2
1
Rþ g 3 Pu 3 B1 3 R 1 Ag
2139(0.0000, 125(0.0000, 2(0.0126, i4(0.0917, 106(2.8896,
9.3382) 61.1256) 13.8276) 7(0.0003, 8.5810) 34.5203) i4(0.0917, 34.5203) 0.0000) 125(0.0000, 519.1183)
x3 x2 x1
Vibrational frequency (IR intensity, Raman activity) State Symmetry System
which are consistent with the MRSDCI and the CCSD(T) results with RECPs retained the outer 5s25p1 shells for indium. It does not change much by involving the 4d orbitals of Indium in the valence space indicating that the RECPs retained the outer 5s25p1 shells for indium are quite reasonable for the low-lying states of In2N2. The small dissociation energy suggests that In2N2 is a weak complex of In2 and N2. The dissociation energy of In2N2 to yield two In atoms and N2 ð1 Rþ g Þ ground state is computed as 1.03 eV. The difference between the two dissociation energies gives the De (dissociation energy) of In2, which is obtained as 0.99 eV at the MRSDCI + Q level. It is close to the 0.87 eV deduced by Froben et al. [32]. The atomization energy to fully separate In2N2 into two In (2P) and two nitrogen atoms (4S) is calculated to be 11.04 eV for the InInNN(T) and 10.27 eV for rhombic In2N2, respectively. This is consistent with our anticipation that the N–N bonding is considerably stronger than that of the In–In bond in In2N2, and plays a more important role in the properties for the electronic states of In2N2. Moreover the difference between the energies of products 2In + N2 and 2In + 2N in Table 2 is De of N2 (=10.01 eV), which agrees reasonably with the experimental D0 value of N2 (9.75 eV). The zero-point corrected result is much closer. Although there are no spectroscopic studies on the In2N2 clusters, Neumark and co-workers [3,5] have obtained the anion photoelectron spectroscopy of indium phosphide clusters of up to 27 atoms. Among the various clusters, the In2P2 cluster exhibits a well-resolved spectrum with five peaks. Relative to the lowest energy peak, the energy separations are 0.70, 1.02, 1.73, and 2.42 eV, respectively. In a previous study on the In2P2 cluster, Feng et al. [23] found the 1Ag state with a rhombus structure as the ground state. The first excited state is the 3B2g state which was computed at 1.26 eV above the ground state. It is evident that the first peak of the photoelectron 1 spectrum of In2 P 2 is due to the Ag ground state of In2P2. The second and third peaks correspond to the other kind of structures instead of rhombus structure. There are two electronic states near the 1.7 eV region, namely, 1Au and 1 B2g states which were computed at 1.650 and 1.659 eV above the ground state, respectively. In addition, the fifth peak of photoelectron spectrum of In2 P 2 corresponds to the 3B3u excited state of In2P2 which was computed at 2.425 eV. The spectra of In2N2 are likely to differ substantially from the spectra of In2P2 primarily due to the T-shaped and T2-shaped ground states and the rhombic structure is 0.94 eV higher than the InInNN(T) 3B1 ground state. It is very clear that the competition of four different geometries for the lowest lying excited states of In2N2 would complicate the spectra. Moreover in contrast to In2P2 the energy separations of even the rhombic excited states of In2N2 are larger and thus all of the excited rhombic states of rhombic geometry may not be accessible in the PES spectra of the anions for In2N2.
Rotational constant
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 3 Harmonic vibrational frequencies (cm1) and rotational constants (MHz) of In2N2 with IR intensity and Raman activity in the parentheses at the MP2 level
292
System
Symmetry
State
Total
Gross population
In
N
In
4.994 4.993 4.994, 4.997, 5.012, 4.988, 4.989, 4.988, 5.410 5.492 5.284 5.566 5.574 5.546 5.459 5.443 5.367 5.339 5.528 6.069,
1.753, 1.797, 1.740 1.800 1.656 1.711, 1.678, 1.723, 1.785 1.764 1.808 1.500 1.472 1.349 1.766 1.797 1.807 1.815 1.402 1.783,
s InInNN(T)
C2v
InInNN(T2)
C2v
InInNN
C1v
In2N2
D2h
InNNIn
D1h
InNInN
C1v
3
B1 1 A1 3 B1 1 A1 3 A1 3 R 1 + R 3 P 1 Ag 3 B3u 1 B3u 3 B1g 1 Au 3 B1u 3 B3g 3 Pu 1 þ Rg 3 þ Rg 3 Ru 3 R
3.015, 3.016, 3.007 3.005 3.007 3.013, 3.011, 3.027, 2.590 2.508 2.716 2.434 2.426 2.454 2.541 2.557 2.633 2.661 2.472 2.537,
2.997 2.998
3.007 3.007 2.986
2.136
4.992 4.992 4.974 4.991 4.993 4.998
5.257
Overlap In–N
Dipole moment (D)
0.009 0.007 0.007 0.007 0.007 0.015 0.012 0.005 0.282 0.292 0.019 0.542 0.563 0.724 0.273 0.094 0.113 0.040 0.195 0.373 (In1-N1)
0.008 0.022 0.073 0.027 0.201 0.153 0.143 0.049
N p 1.756 1.796
1.734 1.712 1.763
0.890
1.121, 1.087, 1.120 1.058 1.143 1.146, 1.172, 1.155, 0.671 0.594 0.752 0.812 0.836 0.961 0.634 0.687 0.737 0.721 1.046 0.699,
d 1.099 1.068
1.120 1.141 1.073
1.102
0.142, 0.132, 0.146 0.148 0.208 0.155, 0.160, 0.150, 0.133 0.150 0.156 0.122 0.118 0.143 0.140 0.073 0.089 0.125 0.025 0.055,
0.142 0.134
0.154 0.155 0.149
0.144
s
p
1.778 1.775 1.751, 1.759, 1.727, 1.763, 1.757, 1.785, 1.819 1.825 1.821 1.823 1.820 1.860 1.880 1.498 1.532 1.624 1.473 1.707,
3.130 3.131 3.158, 3.153, 3.202, 3.144, 3.148, 3.118, 3.525 3.605 3.383 3.703 3.713 3.667 3.552 3.977 3.770 3.651 3.985 4.341,
1.791 1.788 1.796 1.791 1.786 1.778
1.890
3.114 3.116 3.093 3.114 3.120 3.133
3.341
0.404
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 4 The Mulliken population analyses for the low-lying electronic states of In2N2
293
294
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
Table 3 shows vibrational frequencies and rotational constants of lowest states of T-shaped, linear, and rhombus In2N2 together with In2 and N2 for comparison. At the MP2 level the 3R state of linear In2N2 is a genuine minimum structure, while it has two degenerate soft imaginary frequencies (i4 cm1). As seen from Table 3, the In–In stretching vibrational frequencies are 125 cm1 for InInNN(T), and 125 cm1 for rhombus In2N2, respectively, which are very close to the 125 cm1 of free In2. The N–N stretching frequencies obtained at 2137 cm1 for InInNN(T) and 2157 cm1 for linear InInNN are close to 2139 cm1 of free N2, which confirms the weak interaction between In2 and N2 in the T-shaped and linear In2N2. Moreover, the N–N stretching frequency of rhombus structure is obtained at 1344 cm1 which is consistent with the longer N–N bond. The contributions of the leading configurations of most of the electronic states are below 82% indicating the significance of electron correlation effects from multiple references. The leading configurations of the 3B1 states of the InInNN(T) and InInNN(T2) are 1a21 2a21 3a21 4a21 5a21 6a11 1b22 1b21 2b11 and 1a21 2a21 3a21 4a21 5a11 1b22 2b22 1b21 2b11 , respectively, which contribute up to 81%. The 1A1 excited states of these geometries are obtained by the promotion of an electron from the 2b1 orbital to the single-occupied a1 orbital. The 3 R state of linear InInNN is predominantly composed of the 1r22r23r24r25r21p42p2 configuration. The 1R+ excited state has the same leading configuration but this configuration contributes only 41% indicating substantial multi-reference character. The 1a2g 2a2g 1b21u 1b22u 1b23u portion of the electronic configuration is common for the low-lying electronic states of rhombic In2N2. The differences arise from the occupancies for the 3ag, 2b2u, 2b3u, 1b1g, and 1b3g orbitals. Consequently, analysis of the compositions of these orbitals could provide insight into the nature of the low-lying electronic states. The 3ag orbital is composed of [N1(2py)– N2(2py)]–[In1(5s) + In2(5s)], which is a bonding r orbital. The 2b2u orbital is an antibonding [N1(2s)–N2(2s)] orbital. The 2b3u orbital is composed of [N1(2px) + N2(2px)] + [In1(5px) + In2(5px)], which contains a p bonding interaction between two N atoms and r antibonding interactions between In and N. The 1b1g orbital is mainly [N1(2px)– N2(2px)] + [In1(5py)–In2(5py)], which contains a p antibonding interaction between two N atoms and p bonding interactions between In and N. The 1b3g orbital is made of [N1(2pz)–N2(2pz)], and it is an antibonding orbital. The leading configuration of the rhombic 1Ag state is 2 1ag 2a2g 3a2g 1b21u 1b22u 1b23u 2b23u 1b21g which makes an 81% contribution. All the excited states arise from transfer of electrons from the bonding to the antibonding orbitals, resulting in energies above the 1Ag state. For example, the 3B3u and 1B3u excited states are obtained by the promotion of an electron from the 1b1g HOMO to the 2b2u LUMO. The 3B1g excited state is formed by the promotion of an electron from the 2b3u orbital to the 2b2u orbital.
Table 4 shows the Mulliken population distributions. As seen from Table 4, all of the electronic states in In2N2 exhibit charge transfers from In to N resulting in In+N ionic bonds. In the case of two T-shaped structures the charge transfers between N2 and In2 are approximately equal so that the overall gross populations of In and N are closest to their atomic values. A critical examination of the individual atomic populations reveals that the N transfers 0.22 e from its 2s orbital to In(5p) whereas In(5s) transfers about 0.25e to N(2p). This dative exchange of charges facilitates the formation of a loose complex between the species resulting in T-shaped structures. A similar feature is seen in the triplet state of the linear In–In–N–N isomer. The In(d) population suggests charge polarization in these structures. All electronic states exhibit reduced s populations compared to atomic populations, consistent with the anticipated hybridization with the p orbitals. The N(2p) populations in all of the electronic states of In2N2 are uniformly larger than 3, which suggests that most of the charge transfers from the In atoms is received by the N(2p) orbitals. In addition, the d populations of the In atoms are noticeably larger than 0, and thus the participation of the 5d polarization is quite significant. In comparing the populations of the ground state with the low-lying excited electronic states, it is seen that the excited states exhibit larger In(5p) populations and smaller In(5s) populations, suggesting 5s to 5p promotions on In in the excited states. These features result in the enhancement of the In–N bonding, as seen from the larger In–N overlap populations and decrease in the N–N bonding in the excited electronic states. 4. Conclusions Twenty electronic states of the In2N2 cluster are computed using the CASSCF/MRSDCI technique. Results show that in contrast to other III–V tetramers, In2N2 exhibits two nearly degenerate T-shaped 3B1 states that are found to be the ground state candidates followed by a low-lying linear In–In–N–N 3R state. The 1Ag state with a rhombus structure was found to be 0.94 eV higher. A number of other excited states with rhombus and other geometries are found. We have computed the various dissociation and atomization energies. Our computations show that the anion photodetachment spectra of In2N2 would be substantially different from the corresponding spectra of Ga2P2 and related tetramers observed by Neumark and coworkers. Acknowledgement This research was supported by the US National Science Foundation under Grant No. CHE-0540251. The work at Lawrence Livermore National Laboratory was performed under the auspices of US Department of Energy by the University of California under Contract No. W-7405Eng-48.
Z. Cao, K. Balasubramanian / Chemical Physics Letters 439 (2007) 288–295
References [1] S.C. Obrien, Y. Liu, Q. Zhang, J.R. Heath, F.K. Tittel, R.F. Curl, R.E. Smalley, J. Chem. Phys. 84 (1986) 4074. [2] C.C. Arnold, D.M. Neumark, Can. J. Phys. 72 (1994) 1322. [3] C.S. Xu, E. Debeer, D.W. Arnold, C.C. Arnold, D.M. Neumark, J. Chem. Phys. 101 (1994) 5406. [4] T.R. Taylor, K.R. Asmis, C.S. Xu, D.M. Neumark, Chem. Phys. Lett. 297 (1998) 133. [5] K.R. Asmis, T.R. Taylor, D.M. Neumark, Chem. Phys. Lett. 308 (1999) 347. [6] T.R. Taylor, K.R. Asmis, H. Gomez, D.M. Neumark, Eur. Phys. J.D 9 (1999) 317. [7] H. Gomez, T.R. Taylor, D.M. Neumark, J. Phys. Chem. A 105 (2001) 6886. [8] T.R. Taylor, H. Gomez, K.R. Asmis, D.M. Neumark, J. Chem. Phys. 115 (2001) 4620. [9] H. Gomez, T.R. Taylor, Y. Zhao, D.M. Neumark, J. Chem. Phys. 117 (2002) 8644. [10] G. Meloni, M.J. Ferguson, S.M. Sheehan, H. Gomez, Z. Liu, D.M. Neumark, Chem. Phys. Lett. 392 (2004) 90. [11] G. Meloni, S.M. Sheehan, B.F. Parsons, D.M. Neumark, J. Phys. Chem. A 110 (2006) 3527. [12] S.M. Sheehan, G. Meloni, B.F. Parsons, N. Wehres, D.M. Neumark, J. Chem. Phys. 124 (2006). [13] S. Li, R.J. Vanzee, W. Weltner, J. Phys. Chem. 97 (1993) 11393.
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
295
R.J. Vanzee, S. Li, W. Weltner, J. Chem. Phys. 98 (1993) 4335. S. Li, R.J. Vanzee, W. Weltner, J. Phys. Chem. 98 (1994) 2275. M.F. Zhou, L. Andrews, J. Phys. Chem. A 104 (2000) 1648. A.K. Kandalam, R. Pandey, M.A. Blanco, A. Costales, J.M. Recio, J. Phys. Chem. B 104 (2000) 4361. A. Costales, A.K. Kandalam, A.M. Pendas, M.A. Blanco, J.M. Recio, R. Pandey, J. Phys. Chem. B 104 (2000) 4368. A. Costales, M.A. Blanco, A.M. Pendas, A.K. Kandalam, R. Pandey, J. Am. Chem. Soc. 124 (2002) 4116. A. Costales, R. Pandey, J. Phys. Chem. A 107 (2003) 191. C.J. Zhang, J. Chem. Phys. 124 (2006) 184316. K. Balasubramanian, J. Chem. Phys. 87 (1987) 3518. P.Y. Feng, K. Balasubramanian, Chem. Phys. Lett. 264 (1997) 449. P.Y. Feng, M.Z. Liao, K. Balasubramanian, Chem. Phys. Lett. 296 (1998) 283. K. Balasubramanian, X.L. Zhu, J. Chem. Phys. 115 (2001) 8858. C.S. Wang, K. Balasubramanian, Chem. Phys. Lett. 402 (2005) 294. X.L. Zhu, Spectrochim. Acta Part A 61 (2005) 2730. L.F. Pacios, P.A. Christiansen, J. Chem. Phys. 82 (1985) 2664. L.A. Lajohn, P.A. Christiansen, R.B. Ross, T. Atashroo, W.C. Ermler, J. Chem. Phys. 87 (1987) 2812. K. Balasubramanian, Chem. Phys. Lett. 127 (1986) 324. M.J. Frisch, G.W. Trucks, H.B. Schlegel, et al., Gaussian 03, revision C.02. Gaussian, Inc.: Pittsburgh, PA, 2005. F.W. Froben, W. Schulze, U. Kloss, Chem. Phys. Lett. 99 (1983) 500.