Calculated Dipole Moments and Dipole Polarizabilities of Observed

Calculated Dipole Moments and Dipole Polarizabilities of Observed and Candidate Astromolecules Containing Silicon and Phosphorus David E. Woon & Holger S. P. Mller Overview of Talk Motivation & Background Computational Approach to Calculating Response Properties Basis Set Dependence & Complete Basis Set Extrapolations RCCSD(T)/CBS Results for ~80 Si/P Species Theory vs. Experiment RCCSD(T)/AVXZ, B3LYP, & MP2 vs. RCCSD(T)/CBS B3LYP Motivation & Background The availability of ALMA increases the likelihood of detecting exotic species in the interstellar and circumstellar media, assuming sufficient data is available for candidate molecules. Since the intensity of rotational transitions scales as the square of the dipole moment, values of dipole moments are one useful factor for deciding which species to focus on. ESO / C. Malin - http://www.eso.org/public/images/ann13016a/ Motivation & Background 11 species containing silicon have been detected or tentatively (?) detected to date in the ISM/CSM: SiH4 c-SiC2

SiO SiS SiC 1974 SiN 1992 1974 c1-SiC3 1999 1984 SiC4 1989 1984 1989 SiCN SiH (?) SiNC 2000 2001 2004 H C

6 species containing phosphorus have been detected or tentatively (?) detected to date in the ISM/CSM: PN CP HCP PO C2P N O Si PH3 (?) P S 1987 1990 2007 2007 2008 2008 Motivation & Background 11 species containing silicon have been detected or tentatively (?) detected to date in the ISM/CSM:

SiH4 c-SiC2 SiO SiS SiC 3.1 SiN 2.6 1.7 c1-SiC3 0.0 1.6 2.3 SiCN 6.5 SiH (?) 3.1 4.0 SiC4 m in D SiNC 0.1

2.6 CW Leo (IRC +10216) 6 species containing phosphorus have been detected or tentatively (?) detected to date in the ISM/CSM: PN CP HCP PO C2P H C N O Si PH3 (?) P S 2.8 0.9 0.4 2.0

3.2 0.6 Motivation & Background The availability of ALMA increases the likelihood of detecting exotic species in the interstellar and circumstellar media, assuming sufficient data is available for candidate molecules. Since the intensity of rotational transitions scales as the square of the dipole moment, values of dipole moments are one useful factor for deciding which species to focus on. ESO / C. Malin - http://www.eso.org/public/images/ann13016a/ We calculated dipole moments and dipole polarizabilities of ~80 Si & P compounds and compared RCCSD(T) against B3LYP and MP2. Computational Overview Response properties can be calculated as expectation values (B3LYP, MP2) or with the finite field approximation [RCCSD(T)] (with Gaussian and Molpro, respectively). Extrapolations to the estimated complete basis set (CBS) limit were performed for most of the molecules at the RCCSD(T) level; energies rather than properties were extrapolated. The accuracy of RCCSD(T)/CBS results were compared against the few (11) available experimental values (me vs m0). Average deviations between finite basis set results and the CBS limits were performed for RCCSD(T); B3LYP and MP2 were

benchmarked against the RCCSD(T) and large basis set results. Finite Field Approximation The energy of a molecule changes in response to an applied electric field as E(Fx,Fy,Fz) = E0 mi Fi aij Fi Fj + i=1-3 i,j=1-3 The dipole moment (mi ) is a vector that scales linearly with the applied field strength. The dipole polarizability (aij) is a tensor that scales with the square of the field strength. NOTE: Dipole moments of ions were calculated at the center of mass (values for neutrals are origin-independent). Finite Field Approximation Energies of HCP for field strength increments of 0.0002 au. Fx Fz m Calculate mz and axx/azz for each pair of Fx and Fz. Finite Field Approximation The behavior is quite flat across the range of field strengths. Good approximations for mi and aii can be determined with electric fields of 0.001 au applied parallel to each of the principal axes of a molecule, which means

no more than 7 energy calculations per molecule are needed (and symmetry often reduces the count). Basis Set Dependence: Properties vs. Energies We calculated mi and aij with different correlation consistent basis sets: aug-cc-pVXZ {H, C, N, O} and aug-cc-pV(X+d)Z {Si, P, S} for X = {D, T, Q, 5, 6}. Diffuse basis functions (aug-) are always included. Short form: AVXZ. We uses SiO for benchmarking. With a 1S+ ground state, only 4 energies need to be calculated: F(0); Fx(0.001) = Fy( 0.001), Fz(+0.001), and Fz(-0.001). Basis Set Dependence: Properties vs. Energies SiO The dipole moment is flat but erratic in this case. The dipole polarizabilities are largely insensitive to basis set beyond AVDZ in this case. Basis Set Dependence: Properties vs. Energies The total energies at any field strength converge exponentially. SiO Fit with: E(X) = A + B e-Cx SETS mz

axx azz DTQ DTQ5 TQ5 TQ56 Q56 3.124 3.112 3.099 3.104 3.109 4.060 4.064 4.070 4.071 4.073 5.137 5.121 5.103 5.107 5.112 Basis Set Dependence: Properties vs. Energies The total energies at any field strength converge exponentially. Fit with: E(X) = A + B e-Cx SETS mz

axx azz DTQ DTQ5 TQ5 TQ56 Q56 3.124 3.112 3.099 3.104 3.109 4.060 4.064 4.070 4.071 4.073 5.137 5.121 5.103 5.107 5.112 Not much variation: use TZ, QZ, and 5Z RCCSD(T)/CBS: 2.6 D < mz < 6.5 D SiC4 HCCNSi

C3P- C 3P 6.47 5.79 5.91 3.91 SiO+ HSiN 4.41 4.38 c1-SiC3 H3PS PO+ 3.30 4.04 H2SiO H3PO 3.70 3.63

SiO SiCN C 2P CP- 3.10 3.09 3.24 3.01 3.76 H2SiS SiN SiNC PCN PN H C N O Si 2.63 2.72

2.61 2.80 2.77 P S RCCSD(T)/CBS: 1.4 D < mz < 2.5 D SiN- c-SiC2 c2-SiC3 2.52 PNC C-C2P 2.24 2.48 2.34 SPN 2.30 2.08 SiS SiP+ SiC

PO PNO P2O 1.70 1.68 1.58 1.95 1.89 1.80 OSiS HCCNSi PNS 1.52 1.49 1.56 HCCP+ 1.48 CH3CP 1.52

PO2 H C N O Si 1.43 P S RCCSD(T)/CBS: 0.6 D < mz < 1.4 D c-H2C2Si 1.04 SiCCH 0.98 c-P2O 1.41 0.74 CP 0.92 1.09 1.16 1.13 H2CP

0.90 SiP PH+ 0.89 0.86 OPN CPN 0.81 0.65 0.64 PH3 0.62 HCCP HC3P 0.92 H2CSiH2 PS+ 1.26 PH2+

H2CCSi c-P2S PS2 PH2 PS 0.57 N O 0.57 0.60 H C Si P S RCCSD(T)/CBS: 0.1 D < mz < 0.5 D H2Si2 SiC2 SiH+ PH 0.47 0.45

0.44 0.48 c-Si3 SiP- HNSi HCP 0.30 0.25 0.43 0.43 SiH3- H2SiSi H2CSi PS2 0.23 0.20 0.18 0.26

H C SiH2 HCSi SiH PH- N 0.15 0.12 0.10 0.16 O Si P S Accuracy Data Set RCCSD(T)/CBS B3LYP/ACVQZ MP2/ACVTZ Reference experiment experiment experiment

n 11 11 10 RMSD 0.0454 D 0.0915 0.2570 RCCSD(T)/AVTZ RCCSD(T)/AVQZ RCCSD(T)/AV5Z RCCSD(T)/CBS RCCSD(T)/CBS RCCSD(T)/CBS 78 78 78 0.0134 D 0.0048 0.0019 B3LYP/VTZ B3LYP/AVTZ B3LYP/ACVTZ B3LYP/ACVQZ B3LYP/ACVQZ B3LYP/ACVQZ 79 79 79

0.0467 D 0.0133 0.0112 Conclusions Benchmark quality values of dipole moments and dipole polarizabilities were computed for about 80 compounds that contain silicon and/or phosphorus. See Mller & Woon, J. Chem. Phys. A 117, 13868-13877 (2013) for the full tables of results. RCCSD(T)/AVTZ results reproduce estimated CBS limits to within about 0.01 D. B3LYP/AVTZ offers reasonable results, to within about 0.1 D of experiment, which may be sufficient for molecules that are too large to be treated with RCCSD(T). The calculated values of m and a can also be used to estimate reaction rates; see Woon & Herbst, ApJS 185, 273-288 (2009) for details. Acknowledgment DEW acknowledges the support of NASA Exobiology grant NNX 10AR82G. HSPM acknowledges support for the CDMS via the Bundesministerium fr Bildung und Forschung through project FKZ 50OF0901 (ICC HIFI Herschel) and project ALMA ARC 5A11PK3. Thank you for sticking around until (nearly) the end!

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