Rovibrational Considerations for the Monomers and Dimers of

Article Cite This: J. Phys. Chem. A 2018, 122, 7079−7088

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Rovibrational Considerations for the Monomers and Dimers of Magnesium Hydride and Magnesium Fluoride C. Zachary Palmer† and Ryan C. Fortenberry*,‡,† †

Department of Chemistry & Biochemistry, Georgia Southern University, Statesboro, Georgia 30460, United States Department of Chemistry & Biochemistry, University of Mississippi, University, Mississippi 38677, United States

‡

J. Phys. Chem. A 2018.122:7079-7088. Downloaded from pubs.acs.org by UNIV OF CONNECTICUT on 09/17/18. For personal use only.

S Supporting Information *

ABSTRACT: Magnesium is an understudied chemical element that is quite useful in materials science and may be an essential astrochemical building block for grain formation in proto-planetary disks. This work provides quantum chemical prediction for the vibrational and rovibrational spectra of the structurally similar magnesium hydride and magnesium fluoride monomers and dimers. Magnesium fluoride is commonly utilized in infrared-observing windows and is a known terrestrial mineral, sellaite. Magnesium hydride is likely to exist in various astrophysical environments. Comparison of the anharmonic quantum chemical spectral data computed in this work to known gas phase values for MgH2 is excellent with the computed 1584.1 cm−1 antisymmetric Mg−H stretch less than 5 cm−1 below experiment for example. The condensed phase vibrational attributions of the dimer, however, are less comparable with the present results potentially indicating that some of the previous assignments may need to be revisited. The magnesium fluoride monomer and dimer have no previous vibrational experimental results reported, and the work here should be solid predictions as to their spectral features for comparison either to laboratory work or potentially even to interstellar observations.

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One common Mg-bearing material is magnesium fluoride, often used in high-perfomance optics as a near-infrared window surface9 in applications ranging from coverings for missile sensors to, ironically enough, telescope optics and pressure chamber windows. Magnesium fluoride is stable, strong, and absorbs very little light across the near- to midinfrared. Magnesium fluoride is also a known, naturally occurring mineral referred to as sellaite. While rare, this mineral is most often found as an inclusion in heterogeneous rock structure. Magnesium hydride is not a naturally occurring terrestrial material, but it has the same topology and gross crystalline structure as magnesium fluoride10,11 making analysis of these Mg-bearing structures a natural pairing. Additionally, MgH2 is likely to be present in the interstellar medium (ISM), and there exist some spectral data for the MgH2 monomer, making benchmarking for these Mg-bearing species possible.10,12,13 While aggregration of larger monomer units leading to the crytalline forms necessarily takes place, controlling the observation of such steps in the laboratory would be exceedingly difficult. However, quantum chemistry can analyze any species as isolated molecules in order to provide novel insights into any spectral readings. The use of fourth-order Taylor series expansions of the potential within the Watson

INTRODUCTION The seemingly disparate disciplines of materials chemistry and planetary science find common ground in the analysis of molecules containing the element magnesium. While little synthetic chemistry involves element 12 beyond Grignard reactions, where the often instrinsically weak bonds make them a favorite starting material, magnesium is quite common in inorganic crystalline materials like those found in the Earth’s crust and mantle or those found in refractory and thermally stable modern materials. Magnesium is strongly believed to be necessary in the nucleation of dust grains that ultimately lead to planets1 and has been detected in known interstellar molecules2−4 with others speculated to exist.5 Recent work has even shown a seeming correlation between higher abundances of magnesium in the spectra of stars known to host planets and lower abundances in stars known not to host planets.6,7 Hence, the presence of small molecules containing magnesium such as small clusters of the same stoichiometric ratio as the larger crystalline minerals may be an early indication of planet formation.8 Remote sensing of stellar nurseries or protoplanetary disks requires spectral reference data for such small, Mg-bearing molecules. Additionally, directly observing the intermediates of such nucleation in the gas phase in the laboratory could also lead to novel synthetic steps for the creation of materials with novel properties. However, little spectral data for these inorganic species has been previously provided. © 2018 American Chemical Society

Received: July 10, 2018 Revised: August 9, 2018 Published: August 10, 2018 7079

DOI: 10.1021/acs.jpca.8b06611 J. Phys. Chem. A 2018, 122, 7079−7088

Article

The Journal of Physical Chemistry A

Figure 1. Magnesium fluoride dimer CCSD(T)-F12/aug-cc-pVTZ equilibrium geometry.

Hamlitonian, most often called quartic force fields (QFFs), based on composite potential energy surfaces14−16 has provided exceptional accuracy for infrared and microwave/ submillimeter spectra when compared to gas phase experiment. Often, the vibrational frequencies can be as good as within 1.0 cm−1 of experiment and rotational contants within 20 MHz, especially for the B and C constants.17−24 Application to Mgbearing molecules has shown promise,25 especially for magnesium oxide monomer, dimer, and trimer.8 In order to further explore the spectra of small, magnesium species for applications to both materials science and planet formation, this work will utilize these trusted techniques for the provision of rovibrational data for monomers and dimers of magnesium hydride and magnesium fluoride.

computed from the cc-pVTZ-DK basis set with such corrections turned on and then off. This creates the so-called CcCR QFF:35 for CBS, “C”; core correlation, “cC”; and relativity, “R”. The D2h dimers have more atoms and more total points (1973) precluding the use of the CcCR QFF. However, the CCSD(T)-F12/aug-cc-pVTZ level of theory36−40 has shown promise in computing QFFs.41 Hence, this level of theory will be employed for both the monomers and dimers in the determination of the reference geometries and the points that define the QFF. The monomers follow the same coordinates as that given above. The dimers have the atom numbering pattern given in Figure 1 for (MgF2)2. Their coordinates are

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COMPUTATIONAL DETAILS The standard approach employed by our group for computing QFFs with composite energy potential surfaces begins with coupled cluster singles, doubles, and perturbative triples [CCSD(T)]26−28 geometry optimiztions with the aug-ccpV5Z basis set.29−32 This geometry is then appended with a correction for core correlation through adding the difference between CCSD(T) geometry optimizations for the Martin− Taylor (MT) core correlating basis set33 with and without core electrons included. From this, 57 total geometry displacements of the internal coordinates up to fourth order are constructed with magnitudes of 0.005 Å for bond lengths and 0.005 radians for bond angles and torsions. The D∞h monomer molecule QFFs are defined with internal coordinates of 1 S1(σ +) = [(X1−Mg) + (X 2− Mg)] (1) 2 S2(σ −) =

1 [(X1−Mg) − (X 2−Mg)] 2

S1(ag ) =

1 [(X1−X 2) + (Mg1− Mg 2)] 2

(5)

S2(ag ) =

1 [(X1−X 2) − (Mg1− Mg 2)] 2

(6)

S3(ag ) =

1 [(Mg1−X3) + (Mg 2−X4)] 2

(7)

S4(b1u) =

1 [(X1−Mg1) − (X1−Mg 2) − (X 2−Mg1) 2 + (X 2−Mg 2)]

S5(b1u) =

(3)

S4(π ) = ∠(X1−Mg−X 2)yz

(4)

1 [(X3−Mg1−X1) − (X3−Mg 2−X 2) 2 − (X4 −Mg 2−X1) + (X4 −Mg 2−X 2)]

S6(b2u) =

S7(b2u) =

(10)

1 [(X3−Mg1−X1) + (X3−Mg 2−X 2) 2 − (X4 −Mg 2−X1) − (X4 −Mg 2−X 2)]

where X = H, F. At each point, CCSD(T) energies with aug-cc-pVTZ, augcc-pVQZ, and aug-cc-pV5Z basis sets are extrapolated to the complete basis set (CBS) limit via a three-point formula.34 The MT basis sets are again used to compute the effect of core correlation but for the energy this time. Futhermore, the Douglas−Kroll scalar relativistic energy corrections are also

S8(b3g ) =

S9(b3g ) =

1 [(Mg1−X3) − (Mg 2−X4)] 2

(11)

(12)

1 [(X1−Mg1) − (X1−Mg 2) + (X 2−Mg1) 2 − (X 2−Mg 2)]

7080

(9)

1 [(X1−Mg1) + (X1−Mg 2) − (X 2−Mg1) 2 − (X 2−Mg 2)]

(2)

S3(π ) = ∠(X1−Mg−X 2)xz

(8)

(13) DOI: 10.1021/acs.jpca.8b06611 J. Phys. Chem. A 2018, 122, 7079−7088

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Table 1. MgH2 CcCR and CCSD(T)-F12/aug-cc-pVTZ QFF Rotational Constants (in MHz) and VPT2 Frequencies (in cm−1) with MP2/6-31+G* Double Harmonic Intensities (in km/mol in Parentheses) MgH2 experiment gas-phasea Be B0 B1 B2 B3 De He (Hz) ω1(σ+u ) ω2(πg) ω3(σ+g ) ν1(σ+u ) ν2(πg) ν3(σ+g ) zero-point

CcCR

Ne matrixb

86418.38 85400.89 86686.70 1.1745 19.5

1588.67157

1576.8 450.4

24

87096.7 86363.8 85348.8 86650.0 85340.3 1.131 13.422 1636.1 (362) 434.0 (489) 1612.6 1584.1 426.0 1560.5 2040.0

MgHD experiment gas-phasea

Ne matrixb

Be B0 B1 B2 B3 De He (Hz) ω1(σ+u ) ω2(πg) ω3(σ+g ) ν1(σ+u ) ν2(πg) ν3(σ+g ) zero-point

1569.3 1140.7

Ne matrixb

Be B0 B1 B2 B3 De He (Hz) ω1(σ+u ) ω2(πg) ω3(σ+g ) ν1(σ+u ) ν2(πg) ν3(σ+g ) zero-point

1163.2

CCSD(T)-F12

MgH2

26

24

87096.7 86362.9 85357.1 86643.8 85339.5 1.131 13.422 1631.2 432.7 1612.6 1579.6 424.8 1560.4 2036.3

86899.5 86163.1 85163.5 86429.3 85157.6 1.142 14.065 1623.5 437.9 1599.3 1572.8 435.5 1551.9 2034.9

MgH2

87096.7 86363.3 85353.2 86646.8 85339.9 1.131 13.422 1633.6 433.4 1612.6 1581.8 425.4 1560.5 2038.1 CcCR 25

26

24

58825.9 58422.2 57936.6 58588.4 57768.2 0.565 3.724 1625.1 380.8 1170.5 1572.9 374.7 1143.5 1764.2

58799.5 58395.8 57913.3 58559.6 57743.2 0.565 3.716 1623.7 380.0 1168.9 1571.6 374.0 1142.0 1762.0 CcCR

58775.0 58371.3 57891.5 58533.0 57720.0 0.564 3.708 1622.4 379.3 1167.4 1570.4 373.3 1140.5 1759.9

58692.7 58287.1 57809.3 58442.1 57643.7 0.570 3.938 1612.2 384.1 1161.2 1562.6 382.4 1136.0 1759.5

24

25

26

24

43584.0 43328.2 42928.3 43453.4 42965.9 0.283 1.682 1201.3 318.7 1140.8 1173.1 314.4 1115.1 1480.0

43584.0 43327.9 42931.2 43451.3 42965.6 0.283 1.682 1197.9 317.8 1140.8 1169.8 313.5 1115.0 1477.4

MgHD

MgHD

MgD2

MgD2

MgHD

MgD2

43584.0 43327.6 42933.8 43449.3 42965.4 0.283 1.682 1194.7 316.9 1140.8 1166.7 312.7 1115.0 1475.0

25

MgH2

24

MgD2 experiment gas-phasea

25

MgH2

MgHD

MgD2

43485.3 43227.9 42833.5 43345.7 42872.0 0.286 1.762 1192.1 321.5 1131.3 1164.5 320.2 1108.1 1475.7

MgH2

86899.5 86162.7 85167.9 86426.1 85157.2 1.142 14.065 1621.0 437.2 1599.3 1570.5 434.8 1551.8 2033.0 CCSD(T)-F12 25

MgHD

58666.4 58260.7 57786.0 58413.5 57618.7 0.570 3.929 1610.8 383.4 1159.6 1561.3 381.6 1134.5 1757.3 CCSD(T)-F12 25

MgD2

43485.3 43227.7 42836.4 43343.6 42871.7 0.286 1.762 1188.7 320.6 1131.3 1161.2 319.3 1108.0 1473.0

26

MgH2

86899.5 86162.4 85171.9 86423.2 85156.9 1.142 14.065 1618.7 436.6 1599.3 1568.3 434.2 1551.8 2031.3 26

MgHD

58642.0 58236.3 57764.4 58386.9 57595.6 0.570 3.921 1609.5 382.7 1158.1 1560.1 380.9 1133.0 1755.2 26

MgD2

43485.3 43227.4 42839.1 43341.7 42871.5 0.286 1.762 1185.5 319.8 1131.3 1158.2 318.4 1108.0 1470.6

a

Reference 13. bReference 10.

S10(b3u) =

S11(b3u) =

S12(b2u) =

1 [(X3)z + (X4)z ] 2 1 [(X1)z + (X 2)z − (Mg1)z − (Mg 2)z ] 2

1 [(X3)z − (X4)z ] 2

All computations in this work utilize the MOLPRO2015.1 quantum chemistry package42 except for the MP2/6-31+G* double-harmonic vibrational intensities computed with Gaussian09,43−45 which are shown to correlate well with semiglobal CCSD(T)/aug-cc-pVTZ values.46,47 Regardless of the electronic structure method utilized, fitting of the points is done with a least-squares approach where the sum of the residuals squared is on the order of 10−17 au2 or even less. Refitting the points generates numerically zero

(14)

(15)

(16) 7081


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exhibit a Darling−Denison resonance since they fall so close together. The difference between CcCR and CCSD(T)-F12/aug-ccpVTZ is most notable in the rotational constants. The longer bond lengths of the explicitly correlated method create lower frequency rotational constants. While this leads to errors on the order of 200 MHz, the rotational spectra of MgH2 and the other species in this study are likely not of significance for astrochemistry or laboratory analysis anyway. However, the vibrational frequencies are much more consistent between these methods. The two CCSD(T)-F12/aug-cc-pVTZ hydride stretches fall about 10 cm−1 below the CcCR while the bend is about this same magnitude above. As a result, the vibrational frequencies for the dimer should expect to be within about 1% of gas phase experiment. By happenstance, the CCSD(T)-F12/ aug-cc-pVTZ QFF anharmonic frequencies are actually quite close to the Ne matrix results typically within 5.0 cm−1 or less. Regardless, a more clear comparison between the methods comes in the force constants given in Table 2. The CCSD(T)-

gradients at the equilibrium geometry. The force constants are then transformed from the above symmetry-internal coordinates into Cartesian coordinates with the INTDER48 program. Second-order rotational and vibrational perturbation theory (VPT2)49−51 are utilized to computed the vibrationally averaged (Rα) geometries, rotational constants, and vibrational frequencies.

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RESULTS AND DISCUSSION Magnesium Hydride. MgH2 Monomer. MgH2 has a (1σ2g )(2σ2g )(1π4u)(1σ2u)(3σ2g )(2σ2u) orbital occupation and a T1 diagnostic of less than 0.01. The first four orbitals correspond to the 1s, 2s, 2px/y, and 2pz core orbitals on the magnesium atom. While the last two molecular orbitals in the previous list are mostly the bonding and antibonding hydrogen 1s orbital pairs, the 3s magnesium orbital exhibits bonding character in the (3σ2g ), and the 2pz also contributes to bonding in the (2σ2u) indicating adequate bonding for a stable structure. The CcCR MgH2 computed values are in excellent agreement with experiment when such data are present and are likely providing accurate predictions of other values where not present. First, the CcCR Mg−H Rα vibrationally averaged bond length in the magnesium hydride dimer is 1.705 984 Å and CCSD(T)-F12/aug-cc-pVTZ is 1.708 059 Å while that determined from gas-phase experiment is 1.703 326 7 Å.13 These all compare well with the nearly full-configuration interaction equilibrium distance of 1.711 Å.12 The other spectroscopic values for MgH2 are given in Table 1. Further excellent corroboration with experiment continues. The CcCR B0 value of 86363.8 MHz differs from experiment by 54.6 MHz, and the vibrationally excited B1 and B2 values differ by roughly the same amount and are always lower. Even the D and H values give good comparison between theory and experiment where the QFF-derived H values have been known to present problems in the past.52−55 The ν1 antisymmetric Mg−H stretching fundamental vibrational frequency in Table 1 has been observed to be 1588.7 cm−1 while the CcCR value for the standard 24 Mg isotope is computed via VPT2 to be 1584.1 cm−1, a difference of only 4.6 cm−1. The Ne matrix result10 of 1576.8 cm−1 is below the CcCR value. Furthermore, the Ne matrix experiments done with HD and D2 produce ν1 vibrational frequencies of 1569.3 and 1163.2 cm−1 which are within 10.0 cm−1 of the 1572.9 and 1173.1 cm−1, respectively, frequencies computed with VPT2 and the CcCR QFF. The visible ν3 stretch of 24 MgHD for the Ne matrix is 1140.7 cm−1 and is 1143.5 cm−1 for CcCR, a difference of 2.8 cm−1. The CcCR QFF VPT2 results are always greater in magnitude than the condensed phase results for the stretches indicating consistency for the matrix shifts and that the computed frequencies may be closer to the gas-phase results. These excellent comparisons with previous gas-phase and Ne matrix experimental results bode well for further quantum chemical rovibrational analysis of these Mg-bearing species. The other vibrational frequencies are well-behaved with expected anharmonicities and comparison to earlier computations.12 Interestingly, the antisymmetric stretch is actually not the brightest vibrational mode while its 362 km/mol intensity is still rather large. The π-bending mode actually is, but the 426.0 cm−1 fundamental frequency likely will make this transition more difficult to observe. The symmetric stretch, naturally, has no intensity, but the ν1 and ν3 fundamentals

Table 2. MgH2 CcCR and CCSD(T)-F12/aug-cc-pVTZ Force Constants (in mdyne/Ånradm) CcCR F11 F22 F33 F44 F441 F331 F221 F111

1.544227 1.466294 0.148532 0.148535 −0.0361 −0.0363 −3.9088 −4.0297

F11 F22 F33 F44 F441 F331 F221 F111

1.518793 1.443850 0.151528 0.151528 −0.0386 −0.0385 −3.9149 −3.8115

F4444 F4433 F3333 F4422 F3322 F2222 F4411 F3311 F2211 F1111

−0.05 0.04 0.08 −0.07 −0.05 9.26 −0.25 −0.13 9.10 9.14

F4444 F4433 F3333 F4422 F3322 F2222 F4411 F3311 F2211 F1111

0.09 0.24 0.10 −0.05 −0.05 8.92 −0.03 −0.03 8.83 8.85

CCSD(T)-F12

F12 bond length quadratic force constants for coordinates F11 and F22 are lower than those for CcCR while the bend is higher. However, none of the differences, again, are greater than 0.1 mdyne/Å2 making for useful predictions of vibrational behavior in larger molecules with the less-costly CCSD(T)F12/aug-cc-pVTZ level of theory for the definition of the QFF energies. Magnesium exists as roughly 79% 24 Mg, 10% 25 Mg, and 11% 26 Mg. Hence, the isotopes are important for analysis and are also given in Table 1. The heavy atom isotopic shifts are not that great, on the order of ∼3 cm−1 for the antisymmetric stretch, ∼ 1 cm−1 for the bend, and none, by symmetry, for the symmetric stretch. However, the addition of a single deuterium or pair have a more marked effect as is known for deuteration. MgH2 Dimer. The correlation between theory and the Ne Matrix experiment is not as strong for the magnesium hydride dimer as it is for the monomer based on the currently assigned 7082


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Table 3. MgH2 Dimer CCSD(T)-F12/aug-cc-pVTZ QFF VPT2 Frequencies (in cm−1) with MP2/6-31+G* Double Harmonic Intensities (in km/mol in Parentheses) 24

Mg2H4

a

expt ω1(ag) ω2(b3u) ω3(ag) ω4(b3u) ω5(b3g) ω6(b2u) ω7(b1u) ω8(b2u) ω9(ag) ω10(b2g) ω11(b3g) ω12(b1u) ν1(ag) ν2(b3u) ν3(ag) ν4(b3u) ν5(b3g) ν6(b2u) ν7(b1u)b ν8(b2u) ν9(ag) ν10(b2g) ν11(b3g)b ν12(b1u)b zero-point

1583.7 1169.9 1058.9 665.9

theory 1623.4 1616.0 1309.2 1261.0 1125.3 1085.5 670.4 368.6 332.5 315.1 296.6 221.0 1535.1 1533.5 1354.0 1130.9 939.8 972.0 646.3 318.3 311.6 231.2 285.9 213.1 5016.7

(407) (1231) (588) (553) (369)

(261)

24

Mg25MgH4

24

1623.4 1615.4 1309.1 1260.4 1125.2 1085.0 668.2 368.5 329.3 314.6 272.7 217.8 1534.5 1533.0 1354.5 1130.0 937.9 972.7 644.1 318.7 308.8 231.0 262.0 209.8 5014.1

Mg26MgH4 1622.9 1614.7 1309.1 1259.9 1125.0 1084.5 668.0 368.4 326.3 314.0 273.1 217.7 1534.1 1532.4 1355.0 1129.3 936.5 973.3 644.8 319.1 306.8 230.8 262.4 209.7 5054.9

D(ring)Mg2H3

D(out)Mg2H3

Mg2D4

1624.0 1615.7 1220.3 1203.3 849.5 836.5 574.5 367.0 332.0 314.6 273.1 218.0 1537.8 1532.6 1230.8 1091.5 729.5 797.5 556.0 313.2 307.2 224.8 262.0 210.0 4630.6

1620.1 1261.1 1309.2 1169.0 1122.6 1084.4 661.9 345.8 323.0 250.4 250.0 169.4 1536.9 1136.9 1309.9 1119.6 938.5 988.5 637.8 297.6 310.1 221.7 239.3 172.7 4704.0

1173.6 1164.9 928.1 908.6 801.5 785.9 446.5 324.7 264.5 241.9 187.1 160.1 1127.0 1121.4 950.2 841.9 707.2 726.3 424.5 328.2 234.7 187.4 176.0 152.3 3662.6

a

Ne matrix results from ref 10. bProblems in the out-of-plane coordinates preclude a full QFF treatment. These anharmonic values are scaled by 0.9641. This is dicussed in the text.

lines from ref 10. There are no currently available gas phase data for the dimer, Mg2H4. All of the anharmonic CCSD(T)F12/aug-cc-pVTZ data are below that from the Ne matrix data as shown in Table 3. The ν2 (b3u) antisymmetric, exterior Mg− H stretch is 1533.5 cm−1 from the current computations and is 1583.7 cm−1 in the condensed phase experiment. The similar experiment done in excess H2 instead of the Ne matrix yields similar results.10 The ν4 (b3u) H1/H2 shuttle fundamental is computed to have a much brighter intensity by a factor of 3 compared to the monomer, and its CCSD(T)-F12/aug-ccpVTZ anharmonic frequency is 1130.9 cm−1, 39.9 cm−1 less than the assigned Ne matrix value. The other observable fundamental in this frequency range is the ν6 (b 2u) fundamental where H1 and H2 are moving perpendicular to the H3−Mg1−Mg2−H4 axis. The current computations put this value at 972.0 cm−1 which is significantly less than the 1058.9 cm−1 assigned in the Ne matrix. The excellent gas and condensed phase data comparison for the monomer implies either misassignment in the spectrum, improper computations, or both. The current computations suffer from an improper treatment of the out-of-plane bends in this highly symmetric system. Hence, the anharmonic values in Table 3 for ν7, ν11, and ν12 are scaled from the harmonic by a fairly standard 0.9641 value. Hence, these are only estimates. However, the QFF does not include cubic or quartic terms for the force constants associated with the out-of-plane mode so errors brought about by their inclusion should be minimized. The current harmonic frequencies have been computed from both the current approach as well as the standard means available in MOLPRO, and they both agree to within 0.3 cm−1

of one another. Additionally, the assignments in the experimental paper are largely based upon B3LYP/6-311+ +G(3df,3pd) harmonic computations and corroborative MP2 computations with the same basis set. Those B3LYP frequencies computed in ref 10. agree to within 22.0 cm−1 of the CCSD(T)-F12/aug-cc-pVTZ harmonic frequencies in all cases with some agreeing to within 1.0 cm−1. Consequently, the real question for the assignment of the dimer is what the anharmonic shifts are expected to be. The shifts for the hydride stretches of the monomer are basically 50 cm−1, and the CCSD(T)-F12/aug-cc-pVTZ anharmonic shift for the dimer is on the order of double this: 82.5 cm−1 for ν2, 130.1 cm−1 for ν4, and 86.9 cm−1 for ν6, more than what the experimental assignments suggest. Anharmonic shifts for hyride stretches are often in the ∼150 cm−1 range. Furthermore, the spectra observed are dense with peaks from other species including assignments to Mg2H3, Mg2H, and Mg2H2 among others. Many of these have large intensities, as well. Hence, some of the lines in ref 10 may be misassigned. For instance, a feature at 1114.6 cm−1 in the Ne matrix data10 is assigned to Mg2H3. However, the B3LYP harmonic frequencies for the two isomers of this molecule are 1140.1 and 1162.2 cm−1. Hence, the anharmonicity is likely greater than this. As such, the ν4 band of Mg2H4 (the magnesium hydride dimer) computed by the CCSD(T)-F12/aug-cc-pVTZ QFF to be 1130.9 cm−1 may be a better candidate for this assignment. Additionally, the 1533.5 cm−1 ν2 fundamental frequency could also be reassigned from 1583.7 cm−1 since this region has numerous peaks in the experiment. A Mg2D4 band assigned at 860.8 cm−1 is close to the 841.9 cm−1 ν4 fundamental 7083


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spectrum is needed before any interstellar observations can be undertaken. Magnesium Fluoride. MgF2 Monomer. The MgF2 orbital occupation is (core)(4σg2)(3σu2)(5σg2)(4σu2)(2πu4)(1πg4). The (4σ2g )(3σ2u) orbitals are the in-phase and out-of-phase 2s orbitals on the fluorine; the (5σ2g )(4σ2u) are bonding oribtals between the 3s and 2pz magnesium with the in- and out-ofphase 2pz on the fluorine; and the π orbitals are simply combinations of the out-of-plane 2p orbitals on the fluorine atoms. Hence, the bonding takes place below these π orbitals which can be considered lone-pair-containing, nonbonding orbitals. The CcCR Mg−F Rα vibrationally averaged bond length in the magnesium fluoride dimer is 1.740 987 Å and CCSD(T)F12/aug-cc-pVTZ is 1.743 473 Å in agreement with a previous B3LYP/6-31+G* value of 1.72 Å.11 Naturally, these values are longer than in MgH2, but the application of the same methods as that benchmarked in the hydride should produce a similar accuracy in magnesium fluoride. The rotational constants given in Table 5 are expectedly much less for MgF2 but have the same relative and qualitative behavior. For instance, the B2 rotational constant for the π-bending mode is the largest of the vibrationally averaged rotational constants. The harmonic vibrational frequencies are in line with previous work11 and have relatively small anharmonic shifts as is expected for modes involving only heavy atoms. Even though the ν1 antisymmetric stretch at 879.3 cm−1 has a marked double-harmonic intensity of 160 km/mol, the monomer of this stoichiometry showcases magnesium fluoride’s hallmark of being practically clear through the near- and mid-infrared regions. The CCSD(T)-F12/aug-ccpVTZ vibrational frequencies are notably less for MgF2 compared to the CcCR values falling 24.5 and 15.2 cm−1 below the symmetric and antisymmetric, respectively, Mg−F stretching frequencies. The ν2 bend is more consistent, but these shifts must be considered when making predictions for the dimer. The heavier magnesium isotopic vibrational frequencies are also provided in Table 5 with no surprises. The full set of force constants for MgF2 are listed in Table 6. MgF2 Dimer. The magnesium fluoride dimer has decreases in its vibrational frequencies relative to the monomer in line with that expected for moving toward the bulk, crystalline

frequency computed here for the fully deuterated molecule giving some potential overlap in assigned spectral features. Regardless, the present work strongly suggests that the condensed phase experiment for magnesium hydride may need to be reevaluated. The rotational constants including the vibrationally excited rotational constants are provided in the Supporting Information as well as the cubic and quartic force constants. The quadratic force constants are given in Table 4. Comparison Table 4. MgH2 Dimer CCSD(T)-F12/aug-cc-pVTZ Quadratic Force Constants (in mdyn/Ån radm) F12,12 F11,11 F11,10 F10,10 F99 F98 F88 F77 F76 F66 F55 F54 F44 F33 F32 F22 F31 F21 F11

0.417295 1.050698 0.477870 0.446134 0.824444 0.064414 1.490548 0.119929 0.006348 0.704114 0.092165 0.072570 0.568193 1.503707 −0.015140 0.526774 0.030217 −0.181000 0.848576

between the F33 dimer and F11 monomer values shows that the two are of similar magnitude indicating that the ring structure and its additional mass is what largely leads to the decrease in the vibrational frequencies when moving from the monomer into the dimer. In the exploration of magnesium hydride structures in the ISM, the vibrationally excited rotational constants may be of value in addition to the previously discussed vibrational frequencies. Magnesium hydride dimer is vibrationally bright, but gas phase assignment of its vibrational

Table 5. MgF2 CcCR and CCSD(T)-F12/aug-cc-pVTZ QFF Rotational Constants (in MHz) and VPT2 Frequencies (in cm−1) with MP2/6-31+G* Double Harmonic Intensities (in km/mol in Parentheses) CcCR 24

MgF2

Be B0 B1 B2 B3 De (kHz) He (μHz) ω1(σ+u ) ω2(πg) ω3(σ+g ) ν1(σ+u ) ν2(πg) ν3(σ+g ) zero-point

4394.0 4389.0 4360.9 4404.7 4375.7 1.155 8.118 891.0 (160) 152.9 (146) 571.8 879.3 154.1 569.6 883.3

25

MgF2

4394.0 4388.9 4361.3 4404.4 4375.6 1.155 8.118 880.0 151.0 571.8 868.5 152.2 569.4 875.9

CCSD(T)-F12 26

MgF2

4394.0 4388.9 4361.6 4404.0 4375.5 1.155 8.118 869.8 149.3 571.8 858.6 150.4 569.3 869.1 7084

24

MgF2

4381.7 4376.6 4348.4 4392.2 4363.2 1.179 14.013 878.3 152.5 563.7 854.8 152.3 554.4 867.1

25

MgF2

4381.7 4376.5 4348.7 4391.8 4363.2 1.179 14.013 867.5 150.7 563.7 844.5 150.4 554.3 859.8

26

MgF2

4381.7 4376.4 4349.1 4391.5 4363.1 1.179 14.013 857.4 148.9 563.7 834.9 148.7 554.2 853.1


Article


meaning that the actual, gas-phase frequency may lie closer to 785 cm−1. Regardless, this bright peak transpires in the 12.5− 13.1 μm range which is longer wavelength/lower frequency than bulk magnesium fluoride. Similar behavior has been observed for magnesium oxide where the dimer also exhibits lower-frequency fundamentals before going up in the trimer and likely stabilizing in between in the larger structures.8 In any case, the overall drop in frequency from the monomer to the dimer is expected, and the low-frequency range for such vibrational fundamentals is also expected since only heavy atoms are present. The intensity of this bright peak (359 km/ mol) also nearly doubles in comparison to the monomer, giving further indication of movement toward the bulk, where it is largely opaque in these frequency regimes. While the intensities for the fundamental frequencies in (MgF2)2 are all less than those for (MgH2)2, they are still notable. The b2u motion of the F1 and F2 atoms (from Figure 1) perpendicular to the F3−Mg1−Mg2−F4 line in the ν3 fundamental is not very anharmonic, again as expected for heavy-atom motions, but has an intensity of 239 km/mol. The charge separation between the strongly electropositive magnesium atom and the strongly electronegative fluorine atom drives the bright intensities. The other vibrational frequencies (harmonic and anharmonic) are also given in Table 7 as are inclusions for the other two isotopes of magnesium. There are no surprises for the other isotopologues. The rotational constants as well as cubic and quartic force constants are all in the rid is missing a corresponding ID value.SI. The quadratic force constants for (MgF2)2 are shown in Table 8. From this, the harmonic F33 coordinate indicates that

Table 6. MgF2 CcCR and CCSD(T)-F12/aug-cc-pVTZ Force Constants (in mdyne/Ån radm) CcCR F11 F22 F33 F44 F441 F331 F221 F111

3.660335 3.439059 0.153319 0.153314 −0.0126 −0.0125 −12.9965 −13.2758

F4444 F4433 F3333 F4422 F3322 F2222 F4411 F3311 F2211 F1111

0.39 0.40 0.14 0.15 0.13 44.47 0.12 0.01 44.02 44.65

F4444 F4433 F3333 F4422 F3322 F2222 F4411 F3311 F2211 F1111

0.38 0.34 0.40 −0.02 −0.02 43.03 −0.07 −0.07 42.92 43.27

CCSD(T)-F12 F11 F22 F33 F44 F441 F331 F221 F111

3.557016 3.341709 0.152966 0.152966 −0.0103 −0.0103 −12.5587 −12.8073

form. The highest, observable vibrational frequency, the ν2 antisymmetric, exterior Mg−F stretch red-shifts by nearly 100 cm−1 to 762.6 cm−1 for the CCSD(T)-F12/aug-cc-pVTZ QFF employed here as shown in Table 7. In the monomer, the CcCR value is 25 cm−1 higher than the CCSD(T)-F12

Table 7. MgF2 Dimer CCSD(T)-F12/aug-cc-pVTZ QFF VPT2 Frequencies (in cm−1) with MP2/6-31+G* Double Harmonic Intensities (in km/mol in Parentheses) 24

Mg2F4

ω1(ag) ω2(b3u) ω3(b2u) ω4(ag) ω5(b3u) ω6(b3g) ω7(b1u) ω8(ag) ω9(b3g) ω10(b2g) ω11(b2u) ω12(b1u) ν1(ag) ν2(b3u) ν3(b2u) ν4(ag) ν5(b3u) ν6(b3g) ν7(b1u) ν8(ag) ν9(b3g) ν10(b2g) ν11a(b2u) ν12a(b1u) zero-point

796.4 771.5 496.9 484.4 460.7 441.4 261.5 254.3 144.7 128.6 99.8 53.4 784.8 762.6 491.9 473.0 454.8 440.2 260.1 256.7 141.3 128.0 96.2 51.5 2200.1

(359) (239) (40) (210)

(33) (62)

24

Mg25MgF4 792.4 766.2 494.4 484.3 460.4 439.9 257.3 253.3 143.7 128.4 79.1 35.3 780.4 758.3 489.8 472.9 454.5 438.3 255.8 255.4 147.2 127.8 76.3 34.1 2191.6

24

Mg26MgF4 790.0 760.0 492.1 484.2 460.2 438.4 256.4 252.3 142.7 128.3 79.2 35.5 777.7 752.7 487.8 472.8 454.3 436.4 254.9 254.2 146.4 127.7 76.3 34.3 2183.7

25

Mg2F4

786.7 762.7 491.7 484.2 460.2 438.5 256.3 252.2 142.6 128.3 79.2 35.5 775.7 754.1 487.0 472.8 454.1 437.4 254.9 254.4 145.8 127.7 76.3 34.3 2182.8

25

Mg26MgF4 782.9 757.9 489.4 484.2 460.0 437.2 255.4 251.2 141.7 128.1 79.2 35.8 771.5 750.2 485.0 472.7 453.8 435.6 254.0 253.3 144.9 127.6 76.3 34.3 2174.9

26

Mg2F4

777.7 754.6 486.9 484.1 459.7 435.9 254.5 250.2 140.7 128.0 79.3 36.0 767.3 746.3 482.4 472.6 453.4 434.8 253.1 252.3 143.6 127.4 76.4 34.5 2166.7

a

Like with (MgH2)2, problems in the out-of-plane coordinates preclude a full QFF treatment. These anharmonic values are again scaled by 0.9641. 7085


Article

The Journal of Physical Chemistry A Table 8. MgF2 Dimer CCSD(T)-F12/aug-cc-pVTZ Quadratic Force Constants(in mdyne/Ån radm) F12,12 F11,11 F11,10 F10,10 F99 F98 F88 F77 F76 F66 F55 F54 F44 F33 F32 F22 F31 F21 F11

0.387105 1.492255 0.611284 0.485091 1.638079 0.142768 3.369403 0.189100 −0.056322 1.660071 0.209570 0.112127 1.246641 3.403823 0.007437 0.732643 0.066684 −0.023876 1.822047

■

AUTHOR INFORMATION

Corresponding Author

*(R.C.F.) E-mail: [email protected]. Telephone: 662-9151687. ORCID

Ryan C. Fortenberry: 0000-0003-4716-8225 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS R.C.F. wishes to acknowledge support from NASA Grant NNX17AH15G issued through the Science Mission Directorate. Figure 1 was generated via the CheMVP program developed at the Center for Computational and Quantum Chemistry at the University of Georgia.

■

the external Mg−F bonds are the strongest in this molecule. The internal Mg−F bonds in the ring are weaker from F11 being smaller even after deconvolution from the symmetryinternal to the simple-internal coordinates. The individual bonds should be weaker in the ring due to the atoms involved being bonded to more atoms than the standard valence model would support. Such is the beginning stages of ionic bonding. Additionally, the force constants and, hence, bond strengths are greater in the magnesium fluoride dimer than the magnesium hydride dimer in comparing Tables 4 and 8. While the larger bulk MgH2 and MgF2 bulk structures are supported here to be structurally similar, the fluoride is indicated to be a stronger structure from at least the earliest stages of crystallization.

REFERENCES

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CONCLUSIONS The comparison between the gas phase experiment and CcCR QFF VPT2 results is outstanding for the MgH2 monomer. Further comparison with other Ne matrix modes is also good. However, the dimer does not exhibit such similar correspondence. While some of this is likely due to the computational methods necessarily employed for the larger structure, many of the assignments in the condensed phase experiment for the magnesium hydride structures larger than the monomer may need to be reexamined. The topologically similar magnesium fluoride monomer and dimer have not been explored spectroscopically, and the present data for the monomer should be just as reliable as that for MgH2. The (MgF2)2 data are well-behaved and not largely anharmonic, meaning that there should be less confusion in any spectral assignments for this dimer than the magnesium hydride dimer. In any case, these new data should help to inform the earliest stages of magnesium hydride and fluoride crystal formation both in the laboratory and potentially even in astrophysical regions such as proto-planetary disks.

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Rotational constants, vibrationally-averaged rotational constants, quartic and sextic distortion constants, and the cubic and quartic force constants for both the magnesium uoride and magnesium hydride dimers (PDF)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.8b06611. 7086


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Rovibrational Considerations for the Monomers and Dimers of

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