Energetic Properties and Electronic Structure of [Si,N,S] and [Si,P,S

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Energetic Properties and Electronic Structure of [Si,N,S] and [Si,P,S] Isomers Brian Finney, Zongtang Fang, Joseph S. Francisco, and David A Dixon J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b00918 • Publication Date (Web): 25 Feb 2016 Downloaded from http://pubs.acs.org on February 28, 2016

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The Journal of Physical Chemistry

Energetic Properties and Electronic Structure of [Si,N,S] and [Si,P,S] Isomers Brian Finney,a Zongtang Fang, b Joseph S. Francisco, a,c and David A. Dixon b, *,† a

Department of Chemistry, Purdue University, West Lafayette, IN

b

Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa, Alabama

35487-0336, USA c

Department of Chemistry and Office of the Dean, University of Nebraska-Lincoln, Lincoln, NE

Abstract Correlated molecular orbital theory at the coupled cluster CCSD(T) level with augmented correlation consistent basis sets has been used to predict the structure and energetic properties of the isomers of [Si,N,S] and [Si,P,S]. The predicted ground states are linear 2SNSi and cyclic 2

SPSi. The other two isomers are predicted to be ~ 20 to 50 kcal/mol less stable than the ground

state. The excess spin is mainly on S for 2SNSi and on P for 2SPSi. The calculated total atomization energies with the CBS limits derived from different methods differ by ~ 2 kcal/mol. The results provide the best available heats of formation for these species. The bond dissociation energies (BDEs) in 2SNSi are comparable to those in the corresponding diatomic molecules. For cyclic 2SPSi, the formation of 4P + 2SSi requires less energy than the other bond dissociation processes. The BDEs in the higher energy isomers are substantially smaller than the corresponding diatomic species.

†

Email: [email protected] 1 ACS Paragon Plus Environment


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Introduction Of the over 180 molecules that have been detected in the interstellar medium or circumstellar envelopes,1,2 over sixty contain either nitrogen or phosphorus. Molecules of interest include: NS, 3 , 4 , 5 , 6 , 7 SiN, 8 , 9 PO, 10 SiCN, 11 SiNC, 12 HNCS, 13 HSCN, 14 HOCN, 15 , 16 HCNO, 17 HNCO,13,18,19,20 and SiS. 21,22,23,24,25,26,27,28,29,30 Additional molecules containing nitrogen and phosphorus may also be present, generated by addition to these molecules, for example, the SiNS and SiPS molecules. Only one computational study has been reported for SiPS31 and its isomers and none for SiNS. The global minimum for [Si,P,S] was found to be the trigonal cyclic structure with the SSiP, SiPS, and SiSP linear structures 16.3, 34.5, and 48.1 kcal/mol higher in energy, respectively at the CCSD(T)/6-311+G(2df)//QCISD/6-311G(d) level. Activation energies for conversion of the cyclic isomer to linear isomers were predicted to be 41.0, 40.8, and 53.5 kcal/mol, respectively. The bond dissociation energy (BDE) of SSiP to 4P and 1SSi was predicted to be 43.0 kcal/mol. Among the [X, Y, Z] (X=C, Si; Y=N,P; Z=O,S) group of isomers, the trigonal cyclic minimum seems to be unique among only the phosphorus and silicon containing molecules. The same study found that the trigonal cyclic structure for the [P,Si,O] isomer group was again the global minimum with the O-Si-P linear arrangement 10.4 kcal/mol higher in energy and the Si-P-O isomer is 30.8 kcal/mol higher in energy. The [P,C,O] and [P,C,S] isomers were also studied at the same computational level. Linear PCO and PCS are the minima and the bent trigonal structures are 51.1 and 36.7 kcal/mol higher in energy, respectively. The isovalent [C,N,O], 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41

, 42

[C,N,S],41,42, 43 , 44 , 45 , 46 , 47 and

[Si,N,O]39,48,49,50,51 isomers have also been investigated computationally. The predicted trends do not depend on the level of theory. For the [C,N,O] isomers, linear OCN is the global minimum

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with linear ONC and the OCN trigonal structure higher in energy by 61.5 and 73.8 kcal/mol, respectively at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G(d) level.32 These differences are smaller for the [C,N,S] isomers with SCN the global minimum and SNC and the trigonal structure 29.9 and 42.7 kcal/mol higher in energy, respectively, at the CCSD(T)/aug-ccpVDZ//B3LYP/6-31+G(d) level.43 Both of the [C,N,O] and [C,N,S] studies were accompanied by mass spectrometry experiments. Three barriers for the different isomers were observed in an infrared matrix isolation study of the [Si,N,O] isomers.48 The global minimum is predicted to be linear 2Π ONSi with the trigonal structure and linear OSiN 7.1 and 9.2 kcal/mol higher in energy, respectively, at the B3LYP/6-311+G(d) level. We have re-examined the structures and vibrational spectra of the [Si,P,S] isomers at much higher levels of theory, CCSD(T) and CCSD(T)-F12. We have then used the FellerPeterson-Dixon approach to predict the heats of formation of these isomers. We have extended this study to the isomers of [Si,N,S] using the same computational approaches. Computational Approaches Geometry optimizations were carried out at the molecular orbital theory coupled cluster CCSD(T) 52,53,54,55 level. Harmonic vibrational frequencies were calculated to characterize the stationary points located on the potential energy surface and to obtain zero−point energy corrections (ZPEs). The electronic structures of the open-shell molecules were calculated with the R/UCCSD(T) approach where a restricted open shell Hartree-Fock (ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation.56,57 The optimizations were calculated using the correlation consistent aug-cc-pVnZ (n= D, T, Q, 5) basis sets58 for Si, N, S and P and the aug-cc-pV(n+d)Z basis sets (n= D, T, Q, 5) including the extra d function59 for the second row atoms. These basis sets are denoted aVnZ and aV(n+d)Z



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respectively. In addition, the explicitly correlated CCSD(T)-F1260,61 method was also employed for geometry optimization using the cc-pVnZ-F12 (n = T, Q) basis sets. 62 The calculated electronic energies with n= D, T, and Q were extrapolated to the complete basis set (CBS) limit using a mixed Gaussian/exponential equation (1).63 E(n) = ECBS + A exp[−(n − 1)] + B exp[−(n − 1)2]

(1)

The electronic energies calculated with n = Q and 5 were extrapolated to the CBS limit with equation (2).64,65,66 E(lmax) = ECBS + B/lmax3

(2)

with an lmax = n. The energies with the CCSD(T)-F12 method were extrapolated to the CBS limit with equation 2. The composite thermochemistry approach of Feller-Peterson-Dixon67,68,69,70 was used to calculate the total atomization energies (ΣD0,0K, TAE) as shown in equation (3). ΣD0,0K = ∆EZPE + ∆ECBS + ∆ECV +∆ESR + ∆ESO

(3)

The core-valence (CV) correlation corrections for the 1s2 electrons on C and N and 2s22p6 electrons for Si and P were calculated at the CCSD(T) level with the aug-cc-pwCVnZ basis sets (n =D, T, Q); these combined basis sets will be denoted as awCVnZ. Scalar relativistic (SR) corrections were calculated with the second-order Douglas-Kroll-Hess Hamiltonian71,72,73 and the all-electron aug-cc-pVTZ-DK basis set;74 these basis sets will be collectively denoted as aVTZDK. The spin orbit corrections (∆ESO) for the atoms were taken from the experiment.75 (The spin-orbit corrections for the atoms are calculated as (ΣJ(J(2J + 1)·E(J)))/(ΣJJ(2J + 1)).) The spin orbit correction for N and P is zero. The ground state atomic spin-orbit corrections are ∆ESO(Si) = -0.43 and ∆ESO(S) = -0.56 kcal/mol. By using the heats of formation at 0 K for the elements:76 ∆Hf,0K (Si) = 107.40 ± 0.6 kcal/mol, ∆Hf,0K (S) = 65.66 ± 0.06 kcal/mol, ∆Hf,0K (N) = 112.53±


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0.02 kcal/mol and ∆Hf,0K (P) = 75.42 ± 0.24 kcal/mol, we can derive the heats of formation of the studied molecules. The heats of formation at 298 K can then be calculated using the approach described by Curtiss et al.77 The CCSD(T) calculations were done with the MOLPRO program. 78 , 79 Orbital occupancies were determined using NBO6 80 , 81 for the natural bond orbital (NBO) 82 , 83 , 84 , 85 population analysis. The NBO calculations were carried out using the B3LYP hybrid functional86,87 with the DZVP2 basis set88 for Si, N, S, and P. The open shell DFT calculations were all done in the spin unrestricted formalism. The density functional theory calculations were done using Gaussian 09.89 Results and Discussions The geometries optimized at the CCSD(T)/aV(T+d)Z level are shown in Figure 1. The NBO population (NPA) analysis is shown in Table 1 and the calculated vibrational frequencies at the CCSD(T)/aV(T+d)Z level are shown in Table 2. The heats of formation with different basis sets and the BDEs are summarized in Table 3 and Table 4 respectively. The geometries and vibrational frequencies for both the doublet and quartet states calculated with other basis sets are shown in the Supporting Information (SI). The relative energies for both doublet and quartet states are shown in Figure S1 (SI). All of the doublet isomers are predicted to be more stable than the corresponding quartet states except for linear SiSP where the quartet is ~ 2 kcal/mol lower than the doublet in energy. For comparison, 2SiSN is ~ 2 kcal/mol more stable than the 4

SiSN.

Geometries and Atomic Populations The geometries for the [Si,N,S] and [Si,P,S] species are linear except for 2SPSi and 4SiSP shown in Figure 1. The ground state for the [Si,N,S] isomers is



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Figure 1. Optimized Geometries with bond distance in Å and bond angle in degree at the CCSD(T)/av(T+d)Z level. The relative energies in kcal/mol are calculated at the CCSD(T)/CBS limit extrapolated using the aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets. Atoms: S = Yellow, N = Blue, Si = Grey, P = Red.

2

SNSi in the 2Π state and the ground state for the [Si,P,S] isomers is the cyclic 2SPSi in the 2A´´

state. The difference is due in part to the much shorter S-N and N-Si bonds as compared to the longer S-P and P-Si bonds. An S-Si bond can form in the P case as all the bond distances are about the same. This is not possible for the nitrogen case. For the [Si,N,S] isomers, the S-N bond distance is slightly longer for the S in the terminal position than in the middle position. The S-Si bond length is slightly shorter for S lying in the terminal position than in the middle position, and the N-Si bond length is shorter when N is bonded to a terminal Si rather than in the middle position. For the [Si,P,S] isomers, the bond distances of the S-P, S-Si and P-Si bonds in cyclic 2SPSi are longer than for the linear structures. The S-Si bond distance in 2SSiP is 0.18 Å shorter than in 4SiSP. The optimized bond distances using various basis sets differ by up to 0.06 6 ACS Paragon Plus Environment

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Å. The ∠S-P-Si bond angle in cyclic 2SPSi ranges from 59.4º to 59.7º (Table S2, SI). The rotational constants to aid in identifying these species experimentally are given in the Supporting Information together with the dipole moments calculated at the MP2/aug-cc-pV(T+d)Z level.

Table 1. NPA Population Analysis with the B3LYP Functionala molecule

a

state

2

SNSi

2

Π

2

SSiN

2

Π

2

SiSN

2

Π

2

SPSi

2

SSiP

4

SiSP

2

A´´

2

4

Π

A´´

atom N S Si N S Si N S Si P S Si P S Si P S Si

pop 2s 2p4.69 3s1.783p3.82 3s1.743p1.25 2s1.842p3.97 3s1.863p4.64 3s0.913p1.68 2s1.812p3.70 3s1.563p4.20 3s1.853p1.74 3s1.843p3.21 3s1.853p4.50 3s1.823p1.64 3s1.843p3.38 3s1.833p4.63 3s1.133p2.10 3s1.893p2.88 3s1.823p4.73 3s1.893p1.69 1.60

charge -1.31 0.34 0.97 -0.82 -0.52 1.35 -0.54 0.16 0.38 -0.10 -0.39 0.48 -0.24 -0.48 0.72 0.20 -0.59 0.39

α (s) 0.80 0.89 0.88 0.93 0.93 0.45 0.91 0.78 0.93 0.93 0.93 0.91 0.91 0.92 0.56 0.95 0.92 0.95

α (p) 2.40 2.27 0.70 2.43 2.41 0.80 2.26 2.09 0.95 1.95 2.42 0.80 2.10 2.41 1.04 2.37 2.36 1.37

α-β (p) 0.11 0.72 0.15 0.89 0.18 -0.08 0.82 -0.02 0.16 0.69 0.34 -0.04 0.82 0.19 -0.02 1.87 0 1.06

α-β = 0 for s pop.

The NPA analysis is summarized in Table 1. For 2SNSi, there is 0.72e excess spin in the S 3p orbital and the remaining 0.28 e is approximately averaged over the N 2p and Si 3p orbitals. N has a negative charge and the S and Si have positive charges. In 2SNSi, there is modest backbonding to the S from the N. 2SSiN has most of the excess spin in the N 2p orbital and there is 0.18e excess spin in the S 3p orbital. Both N and S have negative charges. There is backbonding into the Si 3p orbital with 1.7e spin paired from S and N. Most of the excess spin in 7 ACS Paragon Plus Environment


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2

SiSN is also on the N with a small excess spin of 0.16e on the Si. Only N has a negative charge

in 2SiSN. Some 3p electrons move from Si into the S 3p orbital. For the [S,P,Si] isomers, S has a negative charge in all three isomers whereas only one isomer has a negative charge on the S for the [S,N,Si] isomers. In 2SPSi, the excess spin is split between the 3p orbitals on P (0.7e) and S (0.3e). The P and S have negative charges of -0.10e and -0.39e respectively. Significant backbonding is predicted from Si to S and P. The population of S and Si in 2SSiP behaves like that in 2SSiN. The S is more electronegative than P in 2SSiP, whereas the N is more electronegative than S in 2SSiN. There is clear evidence of backbonding from P and S to Si 2p orbitals. For 4SiSP, one excess spin is approximately localized in a Si 2p orbital and the other two excess spins are localized in P 2p orbitals. There is ~0.7e backbonding from Si to S. Vibrational Frequencies The calculated vibrational frequencies at the CCSD(T)/aV(T+d)Z level are summarized in Table 2. The Si-N and N-S stretches are significantly mixed in 2SNSi so there are effectively an asymmetric combination and a symmetric combination with the symmetric combination much higher in energy. The Si-S stretching mode in 2SSiN is predicted to be ~100 cm-1 blue-shifted compared to 2SiSN. The Si-S stretching modes in 4SiSP and 2SSiP species are red-shifted by 30 cm-1 and blue-shifted by 200 cm-1 respectively in comparison to 2SiSN and 2SSiN. The N-S stretch is redshifted from the diatomic by ~ 200 cm-1 for 2SiSN.90 Compared to the diatomic SiS, 91 the Si-S stretch is predicted to be red-shifted for 2SSiN, 2SiSN and 2SiSP by ~ 140 cm-1 to 260 cm-1. For 2

SSiP, the Si-S stretch is ~ 50 cm-1 blue-shifted due to the slight mixing between Si-P and Si-S

stretches. The vibrational frequencies calculated with various basis sets are shown in SI Table S4. For the [Si,N,S] species, the N-S stretching bands differ by up to 100 cm-1 with different


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Table 2. Calculated Harmonic Vibrational Frequencies in cm-1 at the CCSD(T)/av(T+d)Z Level. Molecule 2

2

2

SNSi

SSiN

SiSN

2

SPSi

CCSD(T) (cm-1) 238a

assignment π bend

607

asymmetric stretch

1230

symmetric stretch

178b

π bend

618

Si-S stretch

1056

Si-N stretch

124c

π bend

512

Si-S stretch

1006

N-S stretch

355

bend

444

asymmetric stretch

583

symmetric stretch

150 2

4

a

SSiP

SiSP

d

π bend

453

Si-P stretch

816

Si-S stretch

159

bend

437

P-S stretch

484

Si-S stretch

average of 215 and 265 cm-1. b average of 167 and 190 cm-1. c average of 110 and 139 cm-1.

d

average of 145 and 156 cm-1.

basis sets. The differences for Si-N and Si-S stretching are within 30 and 40 cm-1. The predicted results with F12 basis sets are comparable to the others. For the [Si,P,S] species, the predicted results with the various basis sets for Si-S stretching differ by up to 30 kcal/mol. A smaller difference of 15 cm-1 is predicted for P-S stretches. For the Si-P stretches, the difference is less



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than 40 cm-1. In cyclic 2SPSi, both symmetric and asymmetric stretching modes predicted by various basis sets differ by up to 40 cm-1. Heats of formation The different energy contributions to the total atomization energies (TAE) for the [Si,N,S] and [Si,P,S] species are shown in Table 3. The calculated total dissociation energies and heats of formation are given in Table 4. The valence electron contributions with the limits derived from different methods differ by ~ 2 kcal/mol. The contributions calculated with extra core d function are less than 1.0 kcal/mol larger than those without extra core d function from the energies derived by extrapolating D, T, Q. For the results extrapolated from Q and 5, the extra core d function is predicted to decrease the contribution by ~ 1 kcal/mol. The contributions predicted by the explicitly correlated CCSD(T)-F12 method are consistent with that extrapolated from Q and 5 with the extra core d functions. The core-valence corrections are predicted to increase the TAE by 0.5 to 1.3 kcal/mol for the [S,N,Si] species and by 0.5 to 1.0 kcal/mol for the [S,P,Si] species. The scalar relativistic effects are predicted to decrease the TAEs by ~ 0.5 kcal/mol. The ground state linear 2SNSi for the [Si,N,S] species is ~ 23 and 56 kcal/mol more stable than the other two linear isomers, 2SSiN and 2SiSN respectively. For the [Si,P,S] isomers, the two isomers, 2SSiP and 4SiSP are ~ 19 and 51 higher in energy than the ground state cyclic 2SPSi . The relative energies for [Si,P,S] species are slightly larger than previous reported values at the CCSD(T)/B3LYP level, where the linear 2SSiP and 2SiSP species are ~ 16 and 48 kcal/mol less stable than the ground state cyclic 2SPSiP.31 All of these molecules, except for 2SiSN, the least stable isomer of the [Si,N,S] species, have little if any multi-reference character as shown by the largest double amplitudes and the T1 diagnostic. 92 A list of the T1 diagnostics is given in the Supporting Information. Except for 2

SiSN, the spin contamination at the CCSD level is

Energetic Properties and Electronic Structure of [Si,N,S] and [Si,P,S

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