(MO)2 and Related Hydrides for M = Mg, Al, Si, P, S, Ca, and Ti and Heuristics for Predicting Anharmonic Corrections of Inorganic Oxides Brent R
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pubs.acs.org/JPCA Article Anharmonic Frequencies of (MO)2 and Related Hydrides for M = Mg, Al, Si, P, S, Ca, and Ti and Heuristics for Predicting Anharmonic Corrections of Inorganic Oxides Brent R. Westbrook and Ryan C. Fortenberry* Cite This: J. Phys. Chem. A 2020, 124, 3191−3204 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information ABSTRACT: The low-frequency vibrational fundamentals of D2h inorganic oxides are readily modeled by heuristic scaling factors at fractions of the computational cost compared to explicit anharmonic frequency computations. Oxygen and the other elements in the present study are abundant in geochemical environments and have the potential to aggregate into minerals in planet-forming regions or in the remnants of supernovae. Explicit quartic force field computations at the CCSD(T)-F12b/cc- pVTZ-F12 level of theory generate scaling factors that accurately predict the anharmonic frequencies with an average error of less than 1.0 cm−1 for both the metal−oxygen stretching frequencies and the torsion and antisymmetric stretching frequencies. Inclusion of hydrogen motions is less absolutely accurate but is similarly relatively predictive. The fundamental vibrational frequencies for the seven tetra-atomic inorganic oxides examined presently fall below 876 cm−1 and most of the hydrogenated species do as well. Additionally, ν −1 6 for the SiO dimer is shown to have an intensity of 562 km mol , with each of the other molecules having one or more frequencies with intensities greater than 80 km mol−1, again with most in the low-frequency infrared range. These intensities and the frequencies computed in the present study should assist in laboratory characterization and potential interstellar or circumstellar observation. ■ INTRODUCTION experimentally; their lack of a permanent dipole moment 1 makes them invisible to rotational spectroscopy. Previous Oxygen is the third most abundant element in the universe 27,28 2 computational studies show that the lowest-energy isomer and the most abundant element in the earth’s crust, making it of both (AlO) and (SiO) is the cyclic D form, giving a basis a likely component in molecules for novel astrochemical 2 2 2h for treating the other systems in the same way. Vibrational searches. Previous work has shown that it behaves like a mortar − frequency data for the cyclic AlO29 and SiO30 32 dimers have holding inorganic elements together to form mineralogical been obtained previously in the laboratory. In the case of compounds.3,4 These mineral precursors may represent the (SiO)2, there is some inconsistency between the spectrum and early stages of planet formation or the remnants of planetary 30 − the predicted features for the cyclic structure. Consequently, disintegration.5 17 In either case, their detection aids in the Downloaded via UNIV OF MISSISSIPPI on April 23, 2020 at 13:34:11 (UTC). a goal of the present work is to provide reliable spectroscopic understanding of planetary and stellar lifecycles. Many of these data for these dimers in an effort to aid their detection in the precursors are difficult to synthesize or to separate under interstellar medium, protoplanetary disks, or the outgassing of laboratory conditions. Such species are perfectly suited to See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. evolved stars. computational investigation. The current state-of-the-art quantum chemical ap- Like oxygen, the other elements in the current study are 33−43 proach for the production of accurate vibrational abundant in space and contribute to the formation of frequencies relies on a fourth-order Taylor series approx- interstellar dust grains1 that could precede mineral formation. imation to the internuclear potential. This method produces Of these compounds, (MgO)2, (AlO)2, (SiO)2, (PO)2, (SO)2, vibrational frequencies within 1.0 cm−1 of the gas-phase (CaO)2, and (TiO)2, several of the monomeric versions have experiment in many cases. However, its high computational been previously detected in circumstellar or interstellar 18 19,20 21 22 cost and use of symmetry-internal coordinates that can be environments, including AlO, SiO, PO, SO, and ffi 23 24 di cult to determine for cyclic molecules limit the size and TiO. Additionally, closely related molecules such as SO2, + 25 23 shape of the systems that can be analyzed. Nevertheless, SO , and TiO2 have also been detected in these regions, suggesting that there are more molecules composed of the same elements to be found in places such as VY Canis Majoris, Received: February 24, 2020 Sagittarius B2, and Orion A, where these previous detections Revised: March 20, 2020 took place. In particular, the dimeric forms of the Published: March 26, 2020 aforementioned monomers would likely occur wherever the monomers do, based on the strong dimerization energy of 26 ffi (MgO)2. However, they are more di cult to examine © 2020 American Chemical Society https://dx.doi.org/10.1021/acs.jpca.0c01609 3191 J. Phys. Chem. A 2020, 124, 3191−3204 The Journal of Physical Chemistry A pubs.acs.org/JPCA Article previous computational work26 has elucidated the spectro- scopic constants of the cyclic MgO dimer at this state-of-the- art level, providing a baseline comparison for the present work. A slightly less accurate but more computationally tractable method involving explicit correlation with only a triple-zeta − basis set44 47 is also often employed, which typically still gives vibrational frequencies within 7.0 cm−1 of the gas-phase experiment. The decreased computational requirements for this method generally make it worth the reduced accuracy, but greater improvements are highly desirable. As a result of the computational demands required for these Figure 1. Visual depiction of the (MO)2 molecule. higher level procedures, the present study investigates the use 1 of heuristic scaling factors to obtain usable anharmonic S (a ) =[−+rr(O O ) (M − M )] vibrational frequencies without the burden of computing 1g 2 1 2 1 2 (1) them directly for inorganic oxides. Scaling factors have often been employed to bring computed harmonic frequencies inline 1 − S2g(a ) =[−−rr(O1 O 2 ) (M 1 − M 2 )] with experimental results.48 69 The generation of scaling 2 (2) factors based on a small series of molecules could aid in rapid 1 generation of large amounts of accurate spectroscopic data that Sr31g(b ) =[(O1 − M 1 ) − r (O 1 − M 2 ) − r (O 2 − M 1 ) would allow for the characterization of experimental spectra in 2 a way that would not be feasible using the aforementioned +−]r(O22 M ) (3) methods. Such data will be invaluable in analyzing the observations of new astronomical observatories such as the S41u(b )=[τ O 2 − M 2 − M 1 − O 1] (4) forthcoming James Webb Space Telescope. 1 Sr53u(b ) =[(O 1 − M 1 ) + r (O 1 − M 2 ) − r (O 2 − M 1 ) ■ COMPUTATIONAL DETAILS 2 Optimized geometries, harmonic frequencies, and dipole −−]r(O22 M ) (5) moments are computed using the Molpro 2015.1 software package70 along with coupled cluster theory at the singles, 1 Sr62u(b ) =[(O 1 − M 1 ) − r (O 1 − M 2 ) + r (O 2 − M 1 ) doubles, and perturbative triples71 level within the F12 2 explicitly correlated construction72,73 (CCSD(T)-F12b). The −−]r(O22 M ) (6) cc-pVTZ-F1244,74,75 basis set is used in all of these computations, with the exception of those involving calcium Similarly, the symmetry-internal coordinates for (SO)2 are and titanium. For these, a default cc-pVTZ76,77 basis is used, given by interchanging the third and fourth coordinates 78 with a def2-TZVPP/jkfit basis for the JK and RI portions of 1 the energy computations. Furthermore, titanium requires an S11(a ) =[−+−rr(O1 O 2 ) (S 1 S 2 )] 2 (7) aug-cc-pVTZ77 basis set for the DF portion, while calcium requires a def2-TZVPP/mp2fit78 basis for the same, in a 1 S (a ) =[−−−rr(O O ) (S S )] scheme previously demonstrated to give accurate results for 21 2 1 2 1 2 (8) other transition metals.79 This scheme is abbreviated as F12- TZ in the following. Double-harmonic IR intensities utilize the S31(a )=[τ O 2 − S 2 − S 1 − O 1] (9) Gaussian 16 program at the MP2/6-31+G* and B3LYP/cc- 80−84 fi 1 pVTZ levels of theory. The rst of these has been shown Sr(a ) =[(O − S ) − r (O − S ) − r (O − S ) to agree semiquantitatively with more expensive levels of 422 1 1 1 2 2 1 theory without commensurate computational require- +−]r(O S ) (10) ments.85,86 22 The explicit anharmonic vibrational frequencies are 1 fi Sr51(b ) =[(O 1 − S 1 ) + r O 1 − S 2 ) − r (O 2 − S 1 ) computed using a quartic force eld (QFF) approach at this 2 F12-TZ level. The QFF method utilizes a fourth-order Taylor series expansion of the potential energy portion of the −−]r(O22 S ) (11) 87 internuclear Watson Hamiltonian. This involves optimization 1 of the geometry to generate a reference configuration followed Sr62(b ) =[(O 1 − S 1 ) − r (O 1 − S 2 ) + r (O 2 − S 1 ) by 233 single-point energy computations for displacements of 2 symmetry-internal coordinates of 0.005 Å and 0.005 radians in −−]r(O22 S ) (12) ’ the case of the tetra-atomic D2h molecules. Sulfur s deviation fi from the planar structure of the other molecules changes the The analogous coordinates for the ve-atom C2v molecules, with labels being given in Figure 2, are symmetry from D2h to C2v and adds 120 more points for a total fi of 353. The additional atoms in the ve- and six-atom hydride S11(a )=−r (M 1 M 2 ) (13) molecules increase these requirements to 1613 and 4565 points, respectively.