Quantum Impurity Rotator in a Matrix of Quantum Rotors: Electron

Nov 16, 2018 - Department of Environmental Engineering and Antipollution Control, Technological Educational Institute of Western Macedonia (TEI), Kila...
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Quantum Impurity Rotator in a Matrix of Quantum Rotors: Electron Paramagnetic Resonance Dynamics of CH3 in Solid CD4 Matrix Yurij A. Dmitriev*,† and N. P. Benetis‡ †

Ioffe Institute, 26 Politekhnicheskaya ul, 194021 St. Petersburg, Russia Department of Environmental Engineering and Antipollution Control, Technological Educational Institute of Western Macedonia (TEI), Kila, 50 100 Kozani, Greece

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‡

ABSTRACT: The rotational dynamics and the geometry of a light and flexible impurity molecule like methyl, matrix isolated in van der Waals solid, are supposed to be sensitive to the host molecule dynamics and order alterations of the matrix. In addition, the location of the impurity and its interaction with the matrix molecules is of prime importance. Large energy gaps between rotation levels of quantum rotators allow precise investigation of temperature-assisted quantum tunneling effects. The molecular rotation of methyl radicals isolated in the deuterated solid methane isotopomer, CD4, was investigated both by experimental and theoretical electron paramagnetic resonance (EPR) methods. The reduction of the quantum rotation frequency evident from the EPR spectrum of methyl radical at liquid-He temperatures was explained and connected to the irregular ratio of the central doublet to the outer quartet hf transitions. The involvement of temperature in the alteration of methyl symmetry between the C3 and D3 groups and the molecular host−host and guest−host interaction strengths were also examined by constructing temperature profiles of the rotation correlation times in the three phases of solid methane. The present study proves the deep impact that a van der Waals matrix may have on the geometry and the rotation levels of a substitutionally trapped quantum impurity rotor, effects that are yet very little known. This close correlation between dynamics of an impurity particle and the matrix molecules has great potential in developing sensitive physicochemical probes for van der Waals solids.

1. INTRODUCTION The tensorial g, A, and ΔH electron paramagnetic resonance (EPR) parameters, of the p-electron methyl radical, CH3, are anisotropic in nature, suggesting a complex EPR spectrum. However, the anisotropy in methyl radical is partially averaged by the radical reorientation about the 3-fold, C3, and the 2-fold, C2, axes. In many cases, the residual anisotropy of a matrixisolated methyl is hardly discerned even at the liquid helium temperatures due to tunneling effects. This was the reason why both the theoretical and experimental investigations do not pay sufficient attention to a problem of how the guest−host interaction at the molecular level may be extracted from the shape of the EPR of trapped CH3 radicals. Another source of valuable information about the CH3 interaction with the surrounding molecules is the change in the radical rotation constant. This is seen from the relative intensity of the quartet contribution of the spectrum produced by methyls in the rotational A-symmetry states and a doublet owing to the radicals in the E-symmetry states. (With sufficiently small rotation constant, not only the first but the higher excited rotational states may contribute to the EPR spectrum at elevated sample temperatures.) However, the multiplets are superimposed in such a way that the doublet transitions nearly coincide with the two central lines of the quartet. In the last two decades, high-resolution EPR spectroscopy of methyl © XXXX American Chemical Society

made possible the close inspection of the contribution of the A- and E-state radicals to the EPR spectrum, including the residual anisotropy of methyls in both states.1−7 The matrices thus studied by high-resolution EPR include solid noble gases, Ne, Ar, Kr, molecular hydrogens, H2, D2, and matrices of linear molecules, N2, CO, N2O, CO2, and SiO2 clathrate. In all these cases the matrix molecules were assumed not to perform any rotational motion. This behavior resembles the rotation of the natural H2 and D2 molecules when they form solid H2 and D2 matrices. Indeed, the fast ortho-para H2 and para-ortho D2 conversions, stimulated by the trapped CH3 radical, makes possible a rapid transition (measuring several seconds) of the nearby rotating matrix molecules to their ground rotation level. Therefore, compared to the low sample temperatures, the large energy gap between the ground to the first excited rotation levels of the hydrogen matrix molecules is an obstacle for the thermal transition of the molecules from the nonrotary ground state. A short explanation is given in the appendix. CH3 radicals stabilized in the three known solid methane phases8 is a promising system for the investigation of the expected rotational correlation between the radical and the Received: September 28, 2018 Revised: November 16, 2018 Published: November 16, 2018 A

DOI: 10.1021/acs.jpca.8b09478 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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3. RESULTS 3.1. Methyl Radical Rotation about the Three-Fold Axis. An unexplained effect of the radical C3 rotation about the 3-fold symmetry axis dates back to the late 1960s when Jackel and Gordy reported an 1:1.9:1.9:1 quartet intensity for CH3 in CH4 matrix at 4.2 K.12 This observation differs considerably from the expected 1:1:1:1 low-temperature intensity ratio for the hyperfine transitions.5 The experimental intensity sequence suggested a dramatic increase of the radical inertia and, hence, a decrease of the rotational constant. It is worth noting that such a large matrix change in the CH3 rotational constant is unknown for the methyl trapped in any other matrix. With lowering temperature of the CH4 sample, the intensity ratio became 1:1:1:1 at 2.1 K.12 Applying the classical Maxwell− Boltzmann distribution to the CH3 rotational level population, the authors came to a conclusion that the change in the ratio could not be attributed to the change in the sample temperature alone but should include an increase in the rotational constant with decreasing temperature. Even earlier an increased amplitude ratio of the quartet inner-to-outer components, 1:2.4:2.8:1, was observed by Wall and coauthors for CH3 in γ-irradiated solid CH4 at 4.2 K.13 In our experiments, the intensity ratio of the inner to the outer hyperfine components was obtained using a double integration procedure. Figure 1 presents the temperature

matrix molecules and the anticipated collective effects that may slow down the CH3 rotation. In the solid methane isotopomers CH4 and CD4, the carbon atoms in the center of the tetrahedral molecule occupy a face-centered cubic (fcc) lattice, demonstrating the property of methane to be approximately spherical over all molecules to form close-packed crystal phases.8 In phase I, which is stable below the melting point (at approximately 90 K) and above 20.4 and 27.0 K for CH4 and CD4, respectively, all matrix molecules are orientationally disordered. In phase II, below these temperatures, a quarter of the molecules remain disordered, while the rest of them constitute orientationally ordered sublattices. A low-temperature fully ordered phase III is stable below 22.1 K, for CD4, while for CH4 high pressure, above 200 bar is required in addition to low temperature in order to stabilize the phase. Previously, nonplanar CH3 was suggested to arise in a different system, where solid Ar−F2−CH4 mixture was subjected to ultraviolet laser photolysis.9 These radicals recombined with fluorine atoms shortly after the termination of the photolysis period at 13 K and showed asymmetry of the corresponding EPR spectrum. These features were explained by the presence of a fluorine atom in close proximity to the radical stabilized in Ar matrix. The nonplanarity of CH3 may also be evident from temperature dependence of relative intensities of the A-symmetry and E-symmetry states.10 In the present work, we concentrated on the EPR of CH3 in CD4 matrix because of expected higher resolution of experimental spectra compared to CH3 in CH4 due to smaller deuteron nuclear magnetic moment. The methanes allow, in addition, to study for the first time the effect that the first order phase transitions have on the radical rotational motion in solid gases.

2. EXPERIMENTAL SECTION Both the setup and the experimental technique used are described in detail elsewhere.10 The solid CD4 was obtained by gas condensation on the thin-walled bottom of a quartz finger cooled down with liquid He vapor. The bottom was located at the center of the evacuated microwave cavity of the EPR spectrometer. The substrate temperature during deposition was kept in the range of 16−19 K. A gaseous CH4/He mixture passing through a rf-discharge zone was delivered to the quartz finger bottom through a separate channel. Typically, the CH4 admixture was 5%. Based on the geometry of the deposition system and the known quantities of the gaseous flows, we estimated the whole CH4 impurity content in the matrix to be approximately 0.6%. Deposition time varied in different runs from 40−50 min. The sample temperature was measured using Ge film on a GaAs resistance thermometer11 supplied by the V. Lashkaryov Institute of Semiconductor Physics, and MicroSensor Company, Kiev (V. F. Mitin, MicroSensor available from http://www.microsensor.com.ua). The thermometer was attached to “Triton” temperature gauge (http://terex.kiev. ua). The spectra were simulated and analyzed using EasySpin software. The methyl radical EPR spectrum was simulated by superimposing a quartet and a doublet to mimic the unpaired electron interaction with the molecular F = 1/2 and 3/2 coupled nuclear spin representations.

Figure 1. Temperature dependencies of the inner-to-outer hftransition intensity ratios of the methyl EPR quartet for the radicals in CD4 and Ar matrices. The experimental CH3/CD4 results, black open circles, which fall into the phase III region, fit satisfactorily the Boltzmann statistics for the C3-symmetric pyramidal methyl, black solid curve. The two experimental CH3/CH4 points from Jackel and Gordy,12 blue open triangles, also nicely agree with the fitting curve. The red dashed line is calculated based on the Boltzmann statistics and D3-symmetry planar geometry of the free methyl with B = 6.76 K. The red open squares stand for the experimental CH3/Ar results and are shown here for comparison. The dashed line in green demonstrates failure of fitting the experimental points by taking a model of the planar CH3 obeying the Boltzmann statistics.

dependence of the above intensity ratio. The CH3/CD4 results are presented in Figure 1 together with the solid Ar matrix CH3/Ar results for comparison.10 Three different orientational crystal phases of the CD4 matrix are indicated in the figure together with the two transition temperatures. The figure testifies that the experimental CH3/CD4 points, which fall into the phase III region, are well fitted using Boltzmann statistics for C3-symmetric pyramidal methyl.10 B

DOI: 10.1021/acs.jpca.8b09478 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A In the least-squares fit of the experimental data, the best result was obtained with B = 3.15 K, indicating large shift in the rotational constant of the CD4 trapped methyl radical. The standard deviation (SD) of the calculated intensity ratios from the experimental results plotted versus B in Figure 2 verifies this value for the rotational constant B.

Figure 3. Fitting profiles featuring the temperature dependence of the inner-to-outer intensity ratio of the methyl EPR quartet for variable radical symmetry, visualizing the phase transition temperatures of the CD4 matrix. The blue dashed line was obtained for m = 1.5 with 60% of the radicals belonging to C3 symmetry and 40% belonging to D3 symmetry. The magenta dotted line was obtained for m = 3 with 75% pyramidal structure and 25% planar structure methyls. The green fitting curve was obtained for m = 1 with 50% pyramidal and 50% planar methyls.

Figure 2. Standard deviation, SD, of the calculated inner-to-outer intensity ratio, from the experimental results plotted against the trapped methyl radical rotational constant, B.

as the inner-to-outer hf intensity ratios yielded by CH3 in the cubic and orthorhombic structures, respectively. The weights of these contributions may be stated through the equality

Concluding, Figure 1 demonstrates a drastic distinction in the rotation behavior between the radicals trapped in solid methanes compared to those trapped in Ar matrix. The latter are very close to the free molecule, keeping planar geometry and the rotational constant close to the free radical value. The green dashed-dotted curve fits the CH3/CD4 data based on a shifted rotational constant, B = 3.4 K, and the Boltzmann statistics for the planar radical. It is seen from the figure that the approximation is rather poor. Previously, we found that the CH3 radical in solid N2O was well described by Bose statistics and pyramidal model structure.10 Both matrices, the CD4 at temperatures below 22.1 K and the N2O at any temperature, are orientationally ordered. The ordering is due to strong noncentral forces between the matrix molecules. Considering the results, one may suggest that the strong noncentral interactions between the trapped CH3 radical and matrix molecules are responsible for the change of the radical symmetry from planar to pyramidal. The theoretical Boltzmann statistics curve and the experimental CH3/CD4 results in Figure 1, clearly evidence a phase transition at 22.1 K from a matrix with orientationally ordered to partially ordered lattice. In phase II of the CD4 matrix, one out of four molecules finds itself in a crystal field of high cubic symmetry. It is reasonable to suggest that the CH3 radical located in such a high symmetry surroundings keeps its planar geometry inherent for the free space molecular condition. However, a portion of the CH3 radical species is confined in the orthorhombic matrix surroundings thus changing its planar geometry to pyramidal. The partial orientation order is taken into account in Figure 3 using the following procedure. Let us define two variables, ρ1 and ρ2: ρ1(T ) = I1(E)/I1(A) and ρ2 (T ) = I2(E)/I2(A)

I1(E) + I1(A) = m[I2(E) + I2(A)]

(3.2)

Then the fitting value ρ (T ) =

I1(E) + I2(E) I1(A) + I2(A)

(3.3)

is read as ρ (T ) =

(m + 1)ρ1(T )ρ2 (T ) + mρ1(T ) + ρ2 (T ) m[ρ2 (T ) + 1] + ρ1(T ) + 1

(3.4)

The fitting curves in Figure 3 are calculated using the Boltzmann statistics, and B = 3.15 K. Here, the black solid line is for the pyramidal model of the radical in the fully ordered CD4 phase III. The best result for the two experimental points of phase II, blue dashed line, was obtained with m = 1.5, suggesting that 60% of the radicals are in the substitutional positions of the ordered structure, while 40% of the radicals are confined in sites of cubic symmetry, see Figure 3. This may be compared to the magenta dotted line calculated with m = 3, which is for methyls known to be in phase II with 75% ordered and 25% disordered matrix molecules. One may suppose that the CH3 impurity stimulates preferably the high-symmetry surroundings when the matrix experiences transition into the phase II. Anticipating the possibility of altered pyramidal-to-planar proportion for methyls trapped in phase I CD4 matrix, the three experimental points at the highest temperatures, Figure 3, were fitted separately. The best fit was obtained with m = 1 corresponding to 50% pyramidal and 50% planar methyls, green fitting curve in Figure 3. It is worth noting that all three fitting curves are close at temperatures below 4.2 K. This explains the good correlation of the present CH3/CD4 results, and the data by Jackel and Gordy for CH3 in phase II of the solid CH4 matrix, Figure 1.

(3.1) C

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The Journal of Physical Chemistry A 3.2. EPR Spectral Parameters of Methyl Radical in CD4 Matrix. In obtaining the isotropic g-factor and hf-constant parameters for CH3 stabilized in the CD4 matrix, we utilized the Breit−Rabi formula,14 rendering giso = 2.00258(8) and Aiso = 64.45(12) MHz or 2.3000(43) mT, in magnetic field units. It was found previously5,15 that the hf splittings for CH3 stabilized in various matrices well fit a linear dependence when plotted against a certain linear combination of the energies of the van der Waals attraction, EV, and Pauli repulsion, EP, considering pair interaction between the radical and a matrix particle: −(EV + βEP). The dependence was verified with matrices of spherical particles, Ne, Ar, Kr, and para-H2, and matrices of linear molecules, N2, CO, N2O, and CO2. It turned out that accounting for the anisotropic noncentral interaction between the radical and a linear molecule markedly improves correlation of the experimental results with the linear regression. The present result allows testing this finding when applied to CH3 trapped in the matrix of the tetragonal CD4 lattice. The dimensions of the unit cell of the fcc structure of 5.83 Å in solid CD416 gives 7.793 Bohr radius a0 for the distance from the trapped CH3 radical to the C atom of the nearest matrix molecule. The polarizability volume αCD4 of the CD4 molecule was taken to be equal to that of CH 4 molecule,17 17.3 a03. The depth of the potential well, εCD4, for the CD4−CD4 pair interaction expressed in the form of Lennard-Jones potential18 was also set equal that of the CH4− CH4 interaction,19,20 0.38 kcal/mol = 6.06 × 10−4 ε0 (Hartree atomic unit of energy ε0 = 27.212 eV). Proceeding with the computations along the lines suggested in previous studies,5,15 the isotropic van der Waals and Pauli interactions between the CH3 radical and the CD4 matrix molecule were estimated to − 4.112 × 10−4 ε0 and +0.701 × 10−4 ε0, respectively. As in the case of matrices of linear molecules showing orientational order, likewise in the solid CD4, the anisotropic noncentral interaction between the radical and the matrix molecules should also be accounted for CH3 in CD4. The radical to matrix−particle anisotropic dispersion forces contribute negatively to the van der Waals energy. This contribution is accounted for by the effective dipole anisotropy parameter, k′.15 An approximate estimate of this parameter is derived as half of the ratio of the noncentral energy interaction of a matrix particle with the surroundings to the central attraction energy of the molecule. Combining the latter energy, which is about 150 K in solid methane,21 with the total heat of transition, 21 cal/mol, k′ ≈ 0.035 was obtained. This value is valid over a range of one-half degree on either side of the lower transition temperature, where the total heat of transition was known.22 Figure 4 shows the experimental hf constants for the CH3 radicals in several matrix hosts, plotted against the weighted linear combination of the attraction and repulsion pair interaction energies of the radical with the matrix molecules. The relative weight parameter β = 2.73 of the linear regression in Figure 4 was chosen based on the experimental results of the matrix isolated CH3. It is clear from the figure that the experimental CH3−CD4 results are well fitted by the linear regression, judging from the correlation coefficient 0.98044. The empirical parameter β obtained in the present study is 68% higher than the previously estimated value5,15 using here a corrected value of the εCD4 potential well. The fitting line in Figure 4 predicts A = 2.338 mT for −(EV + βEP) = 0, which almost exactly coincides with the mean value Afree exp =

Figure 4. Isotropic hf constants of methyl radical in low-temperature matrices plotted against an empirical sum of the negative vdW attractive, EV, and the positive Pauli repulsive, EP, interactions between the radical and the nearest matrix particle. The repulsion is weighted by the coefficient 2.73 accounting for its higher relative contribution.

2.337 mT obtained by Davis and coauthors for the free methyl radical hf constant.23 The hf lines show different microwave saturation behavior: the two outer components saturate more rapidly than the two inner components, Figure 5.

Figure 5. Saturation behavior for the hf components of CH3 in CD4. The different components are presented as follows: black circles for MF = 3/2, blue squares for MF = −3/2, red triangles for MF = 1/2, and green asterisks for MF = −1/2. The sample temperature is 5.85 K. For a given hf component, all amplitudes are normalized to the amplitude of the same line at the smallest microwave power, P.

The A-symmetry quartet and the E-symmetry doublet of the two inner lines are not expected to overlap precisely. However, the 0.025 mT shift between the A- and E-components observed earlier for the CH3 radical in solid noble gases1−3,5 was unresolved here because of the ca. 0.09 mT line broadening. The E-lines were found to saturate not as readily as the A-lines, a factum that contributes to a discrepancy in the saturation behavior of the inner and the resolved outer hf components. The difference in the E- and A-spectrum spin− lattice relaxation times originates probably in the different interactions of the radical in the E- and A-states with the D

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results in Figure 1, we obtained the estimation of about 1.1 for the ratio of amplitudes of the E- and A-symmetry lines. This value is utilized in expression 4.2. Figure 7 demonstrates the result of the fitting procedure, black solid line, applied to the component 2 (MF = 1/2).

surrounding matrix molecules. However, this effect has not been addressed theoretically yet. Previously, a three-parameter expression A=

1/2 PP 1

(1 + P /P2)P3

(4.1)

was successfully used24 in analyzing the saturation behavior of the two broad central hf components, which correspond to a superposition of A- and E-symmetry transitions. Here, P is the applied MW power measured experimentally, P1 is a gain constant, P3 is a parameter taking into account the line shape: P3 is 3/2 for a homogeneous first-derivative absorption line, it is unity for an absorption line (zero derivative), and it is 1/2 for a completely inhomogeneous absorption derivative. P2 is the saturation parameter, inversely proportional to the product of the spin−lattice relaxation time, T1, and the spin−spin relaxation time, T2. In our analysis, P1, P2, and P3 are adjustable parameters. The expression 4.1 that was applied to fit the saturation of the A-symmetry component 1 (MF = 3/2) yielded the parameters P1 = 2.24453, P2 = 58.96311, and P3 = 0.49118. The statistical quality parameters of the fitting, χ2/DoF = 0.32016, R2 = 0.99334, indicate that the fitting quality was good. In the reduced chi squared expression here, DoF stands for the degrees of freedom, i.e., the number of observations minus the number of fitted parameters. The obtained value of P3 is very close to 0.5, suggesting that the superhyperfine interaction of the radical electron spin with the nuclear spins of the matrix molecules is the major broadening mechanism. So, we fixed P3 = 0.5 and fitted the experimental points again, Figure 6. The procedure yielded P1 = 2.23449 and P2 = 61.84944.

Figure 7. Saturation behavior of the MF = 1/2 hf component of CH3 in CD4. The experimental points, open triangles, are fitted based on the inhomogeneous nature of the line broadening. The fitting curve (black solid line) is a sum of the A-line saturation (blue dotted) and the E-line saturation (red dashed), as explained in the text.

Fitting details: P1 = 1.34322, P2 = 816.19687, χ2/DoF = 1.60353, and R2 = 0.99029. The two different saturation curves of the E- and A-symmetry components are also presented separately in Figure 7 by the red dashed and blue dotted lines, respectively. One can readily see that even at high microwave powers the E-line shows very slight saturation, while the Acomponent is saturated completely.

4. DISCUSSION The elevated population of the first excited E-symmetry state of CH3 radical in CD4, evident even at the lowest sample temperatures, suggests a noticeable contribution of the Esymmetry doublet into the composite EPR spectrum of the radical. It was found previously25 theoretically and was supported experimentally that the A-symmetry states of the radical yield axially symmetrical g- and hf-coupling tensors. The parameters of the E-symmetry states are more anisotropic being described by an axial g-tensor and an orthorhombic hfcoupling tensor. Rapid tunneling rotation about the radical C3axis averages the parallel to the plane tensor components making it axially symmetrical. However, the perpendicular rotation, i.e., about the C2-axes, is differently hindered by the radical−matrix interaction for CH3 in A- and E-symmetry states. This finding was supported experimentally but had not received a theoretical explanation so far. Figure 8a shows the experimental EPR spectrum of methyl radical in CD4 matrix recorded at 8.7 K. The spectrum was simulated as a superposition of the A-symmetry quartet and the E-symmetry doublet. The microwave frequency was f res = 9400.30 MHz, and the doublet weight coefficient was 0.55. The anisotropic EPR parameters of the matrix isolated rigid CH3 radical are partially averaged by the radical fast libration motion.15 Based on the close van der Waals parameters for N2−N2 and CH4−CH4 interactions, and on the partial solubility of solid N2 and CH4,26 one may expect that the

Figure 6. Saturation behavior of the MF = 3/2 hf component of CH3 in CD4. The experimental points, open circles, are fitted based on the inhomogeneous nature of the line broadening. See the text for details.

The progressive saturation of the inner lines was fitted by the following expression: A=

1.1P1 P 0.5

(1 + P /P2)

+

P1 P (1 + P /61.85)0.5

(4.2)

Here, the first term corresponds to the E-line, while the second one corresponds to the A-line. These lines have nearly equal widths. Hence, the ratio of their amplitudes is expected to be close to the intensity ratio. Based on the experimental E

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The spectrum anisotropy gradually went down at increased sample temperatures due to the faster perpendicular rotation. Finally, the spectrum obtained nearly isotropic appearance at 28.7 K, Figure 9. The bumps at the sides of the each main line

Figure 9. EPR spectrum of CH3 in CD4 recorded at 28.7 K sample temperature. The inset shows an enlarged MF = −3/2 hyperfine component. The arrows are pointing to the “bumps” located symmetrically at both sides of the main line. These “bumps” are due to low intensity forbidden lines. See the text for details. Microwave frequency, f res = 9395.97 MHz.

(marked by arrows in the inset) are due to low intensity forbidden transitions originating from the coupling between the electron spin of the radical and the deuteron spins of the surrounding CD4 molecules. Such forbidden spin-flip satellites were observed as early as 1954 in EPR of atomic hydrogen isolated in strong solid acids by Zeldes and Livingston28 and explained theoretically by Trammell et al.29 The spacing of the satellites to the main line is field-dependent since it is equal to the proton magnetic resonance frequency and has intensity proportional to the inverse of the square of the resonance field.30 The satellites are more pronounced for CH3 in CH4 because of the larger proton nuclear magnetic moment and, therefore, the larger splitting between the two satellite lines next to the same main line.31 Based on the ratio of the proton to deuteron nuclear g-factors, gn(H)/gn(D) = 6.514, and the satellite splitting in CH4 equal to 0.99 mT, the satellites in CD4 are expected to be shifted from each other by 0.15 mT, which is close to the splitting measured in the present study. The EasySpin simulation software was utilized to extract the temperature dependencies of the radical perpendicular rotation correlation time. The results obtained for the CH3 in the Aand E-symmetry states, τcorrA and τcorrE, are shown in Figures 10−12. At the lowest temperatures τcorrA is close in value to the perpendicular correlation times as can be estimated for CH3 in the solid matrices of the spherical Ar and Ne particles at liquid helium temperatures in agreement with Misochko et al.9 who estimated the rotation correlation time of ∼10−9 s for CD3 in Ar at 13 K. Despite the nearly globular shape of the CD4 molecules, they form orthorhombic32 crystals, a nontrivial fact. Indeed, both the decreased rotation constant of the trapped CH3 and its deformation to the C3-symmetric pyramidal structure, Section 3, evidence a strong coupling of the radical to the surrounding host molecules. The radical reorientation is tunneling in nature due to the rather high potential barriers, see the Introduction. This is also true for the CD4 matrix

Figure 8. EPR spectrum of CH3 in CD4 recorded at 8.7 K. (a) Experimental spectrum. (b) Simulated spectrum, sum of the following two: (c) simulated A-line quartet and (d) simulated E-line doublet. See in text for the simulation parameters.

EPR tensor anisotropies ΔA = A|| − A⊥ and Δg = g|| − g⊥ for CH3 in the rigid N2 and CH4 matrices are approximately equal. In the simulation, the static anisotropies were set the same as for CH3 in N2: ΔA = 0.099 mT, Δg = −3.7 × 10−4.25 The static parameters of the two multiplets were taken equal to A⊥ = −2.3487 mT, A|| = −2.2027 mT and g⊥ = 2.002697, g|| = 2.002347, and the principal axes of the hf- and g-tensors were supposed to coincide. The individual line was Gaussian in shape and of 0.083 mT width. In order to account for the radical perpendicular rotation, the EasySpin software was utilized running a garlic function to simulate the fast-motion regime for the A-symmetry radical and a chili function to simulate the slow-motion regime for the E-symmetry radical.27 The spectrum anisotropy was recorded by adjusting the parallel and perpendicular components of the axial hf A- and gtensors. In so doing the isotropic parameters, Aiso = (2·A⊥ + A||)/3 and giso = (2·g⊥ + g||)/3 were kept equal to 2.3000 mT and 2.00258, respectively (see section 3.2). Two additional parameters were adjusted, i.e., the correlation times for the perpendicular rotation of the radical in A- and E-symmetry states, τcorr(A) and τcorr(E). The best fit was obtained with τcorr(A) = 25.1 ns, τcorr(E) = 500 ns, Figure 8, testifying very good match between the experimental and simulated spectra. Best was the agreement when the width of the components, their relative amplitudes, and the asymmetry of the second, MF = 1/2, hf component with respect to the baseline were taken into account. F

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Figure 12. Logarithm of the rotation correlation time τcorrE of the perpendicular rotation of the CH3 E-state radical stabilized in solid CD4 matrix plot against sample temperature. Linear regression verifies near linear temperature dependence.

Figure 10. Correlation time of the perpendicular rotation of the CH3 radical stabilized in solid CD4 matrix in the A-state plotted against the sample temperature.

molecules that experience barrier heights of several hundred Kelvin.33 Being temperature independent at low sample temperatures, the perpendicular rotation correlation time of the A-symmetry radical, Figure 10, starts to decrease at approximately 13 K and reaches a fast rotation plateau at 27 K, the transition temperature to the fully disordered phase I of solid CD4. The temperature interval 13−27 K separates the relatively slow low-temperature quantum rotating inertial methyls from the fast “high-temperature” methyls rotating by the additional contribution of thermal energy. The most rapid drop in the correlation time ranges approximately from 19 to 27 K, thus overlapping with the partially disordered solid CD4 phase II. Due to the correlation of the CH3 and CD4 orientational motions, Figure 10 suggests also tunneling rotation of the matrix molecules even in the orientationally ordered phase III with a temperature-dependent rate. The perpendicular rotation correlation time of the Esymmetry radical, τcorrE, shows different temperature behavior than the τcorrA, Figures 11 and 12. It depends exponentially on the sample temperature as the relation,

T ( 4.011 ) ns, indicates. At low temper-

τcorrE(T ) ≈ 3616 × exp

atures, the radical, is almost static regarding the perpendicular rotation with rotational correlation times up to several hundred nanoseconds. This fact suggests much stronger coupling of the E-symmetry methyls to the nearest neighbor CD4 molecules, which, in turn, are prohibited from rotation tunneling. The tunneling frequencies show a strong exponential dependence on the interaction strength between the matrix molecules,33 giving rise to growing rate of rotation with increasing temperature. Previously, Baer and coauthors observed a thermal expansion for all three phases of solid CD4.16 The concomitant ease of the molecular interaction strength may be among the rotation rate enhancement mechanisms.

5. CONCLUSIONS The present study is one more observation of the conversion of the matrix isolated methyl radical symmetry from the planar D3 structure to a pyramidal C3 structure. For the first time this effect was observed for the substitutional CH3 isolated in solid N2O.10 We suggest that relatively strong and low-symmetry radical−matrix interaction tends to induce transition of the CH3 radical structure from the planar to pyramidal. Another peculiar matrix isolation effect in the present case of the solid CD4 host is the large decrease of the CH3 rotation constant. It turns out that here it deviates from the free radical value far beyond the altitude observed in any other matrix. These facts suggest that it is energetically favorable for the CH3 radical and the molecules of methane to perform correlated rotational motion in the matrix. They are furthermore related with the transformation between the planar and pyramidal structure which is in turn influenced by the matrix orientation ordering. In partially or fully disordered solid CD4 phases both pyramidal and planar methyl radicals are found. A theoretical explanation of such a behavior of CH3 trapped in solid methanes is probably the formation of CH 3 −(CH 4 ) n complexes with intramolecularly rotating methyls. In particular, all the present findings and the sample preparation details indicate the formation mainly of CH3− H−CH3 units. Such a particle would have the properties that are described in the Experimental Section. For example, it will

Figure 11. Correlation time of the perpendicular rotation of the CH3 radical stabilized in the E-state in solid CD4 matrix plotted against the sample temperature. G

DOI: 10.1021/acs.jpca.8b09478 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A appear to have both C3 symmetry and a smaller rotational frequency. As one can understand, such a bulkier particle (i) will have addition restrictions in the C2 rotational degrees of freedom in the solid matrix and (ii) would rotate in a correlated fashion with the CD4 about the C3 axis! In a CH4 matrix, e.g., the relative rotation of the two identical CH3 units about the central H atom would appear as a reduced angular velocity with respect to a laboratory frame. A computational verification of the above facts is in process and will be presented later. The microwave saturation behavior of CH3 and the values of the correlation times of the C2 rotation are ample evidence of the E-state radicals much stronger coupling to the surroundings as compared to the A-state radicals. Even in the orientationally ordered phase III of solid CD4, the trapped A-state CH3 radicals perform rather fast perpendicular rotations with the rate close to that observed in solid Ar and Ne matrices. Due to the correlation of the rotations of the radical and the nearest neighbor molecules, this finding suggests sufficiently rapid tunneling of the host CD4 molecules as well. At low temperatures the E-state radicals are practically immobile with respect to the perpendicular tunneling. One may suggest that the same strongly hindered reorientation is true for the matrix molecules interacting with the radical. The different temperature dependence in the correlation times of the A- and E-state radicals is a fingerprint of the complex orientational behavior of the matrix molecules in solid CD4, which is not limited only to the orientational phase transitions I/II and II/III of the matrix at two specific temperatures. In addition, the changes of a sample temperature influence also markedly the orientational motion mode of the matrix molecules within a given phase. In the orientationally ordered phase III, e.g., the molecular CD4 axes are not only pointing at specific directions but perform also complex motion, which is influenced by the sample temperature. Very recently, in orientationally ordered solid CO2, Krainyukova and Kuchta34 found a complex, temperature-dependent reorientation of the molecular CO2 axes and their libration amplitudes in a wide temperature range.

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anti-symmetric wave functions overall, in contrast to Boson D2 (whole-integer spin) that occupy only symmetrical wavefunctions overall. Consequently, the allowed angular momenta J of the rotating molecules affect the nuclear statistics and through it the low temperature magnetism of the molecular hydrogen isotopes. The symmetrical with respect to mutual exchange of the two identical nuclei ortho-states are the molecules that obtain maximal degeneracy. They are identified with the coupled nuclear spin triplet of the two protons F = 1, for the hydrogen H2 and similarly in the tritium molecule T2. The corresponding symmetrical nuclear spin quintet F = 2 along with the magnetically silent singlet F = 0, for the deuteron molecule D2, are also the most populated molecular states. However, the symmetrical, ortho-modifications of the protons in the H2 and T2 molecules can only posses the odd rotational angular momenta J = 1, 3, 5, etc., while the corresponding D2 molecules can only occupy rotational states with the even angular momenta J = 0, 2, 4, etc. The less populated singlet of the hydrogen H2 and T2 molecules and the molecular deuteron triplet of D2 are allowed only to obtain the even and odd angular momenta, respectively. It means that without thermal excitations, the rotational ground states J = 0 are only available to the hydrogen under-populated nonmagnetic singlet, on the one hand, and the overpopulated magnetic quintet plus the singlet of the deuterons molecules, on the other. The rotational constants, B, are 59.34 cm−1 (85.4 K), for the hydrogen molecule H2, and 29.91 cm−1 (43 K), for the molecular deuterium D2. The corresponding energy gaps, 512.27 K for H2 and 258.21 for D2, between the ground (J = 0) rotational state and the first excited states with the same even parity (J = 0) for all practical cases will be transition-prohibited without thermal excitation.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +7-812-2927130. Fax: +7-812-2971017. Mobile: +7-911-912-4438. ORCID

Yurij A. Dmitriev: 0000-0003-2074-224X N. P. Benetis: 0000-0002-1699-1166

APPENDIX

Nuclear Statistics of ortho−para Solid Molecular Hydrogen Hosts (H2, D2, T2) Established in the Realm of the Matrix-Isolated, Paramagnetic, Methyl Particles

Notes

A H2/ D2 matrix molecule close to a paramagnetic CH3 particle experiences fast, in seconds, ortho−para/para−ortho conversion into the ground rotational state compared to the self-conversion times of hours without participation of neighboring paramagnetic centers; e.g., in solid H2, the orthomolecules of molecular hydrogen next to a trapped substitutional N atom are converted to para-state in just several seconds.35 The conversion rate is proportional to the magnetic moment of the paramagnetic particle. Therefore, the rate caused by a substitutional CH3 would be of the same order as in the N−H2 system. The quantum states of the linear, homo-nuclear molecules, in a forceless 3D space, have to fulfill the restrictions of the symmetry with respect to exchange of the identical nuclei. Since (free) rotation exchanges the nuclei of such molecules, e.g., the molecular isotopomers of hydrogen, H2, D2, and T2, their rotational states become symmetry restricted. The Fermions H2 and T2 (half-integer spin) can occupy only

ACKNOWLEDGMENTS Y.A.D. acknowledges support by the Russian Foundation for Basic Research (RFBR), research project 16-02-00127a.

The authors declare no competing financial interest.

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DOI: 10.1021/acs.jpca.8b09478 J. Phys. Chem. A XXXX, XXX, XXX−XXX