Nuclear Quadrupole Coupling Constants for N2O: Experiment and

Article pubs.acs.org/JPCA

Nuclear Quadrupole Coupling Constants for N2O: Experiment and Theory Alex Brown* and Roderick E. Wasylishen* Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada, T6G 2G2 S Supporting Information *

ABSTRACT: The nuclear quadrupole coupling constants (NQCCs) for the nitrogen and oxygen nuclei in N2O have been determined using a variety of computational methods (MP2, QCISD, DFT with B3LYP, PBE0, and B3PW91 functionals, CCSD, CCSD(T), CASSCF, and MRCI) combined with correlation-consistent basis sets. When compared to the available experimental determinations, the results demonstrate that only CCSD(T) and MRCI methods are capable of accurately predicting the NQCCs of the central and terminal nitrogen atoms. The spin-rotation and magnetic shielding tensors have also been determined and compared to experimental measurements where available. 14N and 17O NMR relaxation data for N2O in the gas phase and a variety of solvents is reported. The increase in the ratio of 14N spin−lattice relaxation times in solvent for the central and terminal nitrogens supports previous reports of the modification of the electric field gradients at these nuclei in van der Waals complexes. Ab initio computations for the linear FH···N2O complex confirm the large change in EFGs imposed by a single perturber.

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INTRODUCTION As well as being one of the first anesthetics (used in dentistry by G. Q. Quincy in the mid-1800s), nitrous oxide has played a fundamental role in the development of chemical physics. It has been the subject of numerous microwave spectroscopic and molecular beam investigations dating back to 1947. In recent years, much attention has been focused on the characterization of N2O van der Waals complexes (e.g., N2O−acetylene,1,2 N2O−HF,3−5 N2O−HCl,6 N2O−CO2,7 N2O−N2,8 N2O− OCS,9 N2O−Ar,10 and N2O−CO11). More recently, nitrous oxide has been utilized as a probe for the onset of superfluidity in He droplets.12,13 The studies of van der Waals complexes demonstrated that the electric field gradient (EFG), as reflected in the nuclear quadrupolar coupling constant (NQCC), of the central nitrogen of N2O is considerably perturbed by complex formation. On the other hand, the NQCC of the terminal nitrogen is only modestly changed. In the present work, we discuss NMR spin−lattice relaxation data for N2O in the gas phase and in various solvents, and connect these measurements with those made for the van der Waals complexes. Several years ago one of the authors (R.E.W.) obtained 14N and 17O NMR spin−lattice relaxation data for N2O dissolved in n-hexane at 21 °C using an applied magnetic field strength of 8.48 T.14 The 14N spin−lattice relaxation time (T1) for the terminal nitrogen, Nt, was 0.275 ± 0.008 s whereas that for the central nitrogen, Nc, was 3.16 ± 0.09 s. For quadrupolar nuclei such as 14N, the rate of NMR spin−lattice relaxation is generally completely dominated by the quadrupolar relaxation mechanism15,16 that leads to the expectation that: [T1(14Nc)/ T1(14Nt)] = [CQ(14Nt)/CQ(14Nc)]2 where CQ(14Nt) and CQ(14Nc) are the 14N nuclear quadrupole coupling constants for the terminal and central nitrogen nuclei, respectively. Reliable CQ(14Nt) and CQ(14Nc) values for nitrous oxide in the © 2012 American Chemical Society

gas phase are available from molecular beam maser studies of Casleton and Kukolich17 who reported CQ(14Nt) = −776.7 ± 1.0 kHz and CQ(14Nc) = −269.4 ± 1.8 kHz yielding a ratio, [CQ(14Nt)/CQ(14Nc)]2, of 8.312. Very similar values were reported three years later by Reinartz et al.18 who found CQ(14Nt) = −773.76 ± 0.27 kHz and CQ(14Nc) = −267.58 ± 0.38 kHz yielding a ratio, [CQ(14Nt)/CQ(14Nc)]2, of 8.362. Clearly, the observed ratio of the 14N T1 values in n-hexane, 11.5 ± 0.7, is significantly greater than expected. In our 1986 paper,14 we suggested that medium effects on the 14N electricfield gradients (EFGs) were probably responsible for the T1 ratio being greater than 8.3. Because the nuclear quadrupole coupling constant CQ for the central 14N is very small, we suspected that it might be more sensitive to medium effects than the terminal nitrogen. The subsequent microwave studies of N2O containing van der Waals complexes1−11 have convincingly demonstrated that even the presence of a single solvent molecule (or atom) can perturb the nitrogen EFGs. Another curious observation that we made in 1986 and in the intervening years is the apparent lack of attempts to compute EFGs for nitrous oxide (e.g., see refs 19−21). Although several researchers have presented theoretical calculations of EFGs at nitrogen for numerous molecules,19−26 values for N2O are almost always absent. The lack of theoretical data for N2O is surprising because the EFG is a first-order property, and hence, one would expect that it could be determined reliably using a number of standard quantum chemistry methods. Although qualitatively, the two resonance structures for N2O could potentially be a source of problem for standard techniques. Received: June 24, 2012 Revised: September 6, 2012 Published: September 6, 2012 9769

dx.doi.org/10.1021/jp306213n | J. Phys. Chem. A 2012, 116, 9769−9776

The Journal of Physical Chemistry A

Article

Table 1. Nitrogen-14 Spin−Lattice Relaxation Times for Nitrous Oxide at 8.46 T (Ratio = [T1(14Nc)/T1(14Nt)]) pressure/atm

solvent

temp/° C

T1/ms (central-14Nc)

T1/ms (terminal-14Nt)

ratio

15 10 10a 6 1.4 19.7b 10 6 6 3 15c 6 6 6 6 6 5.7d 6 6 6 6 6 6 6

none none none none none n-hexane n-hexane n-hexane n-hexane n-hexane n-hexane cyclohexane acetone CH2Cl2 methanol CHCl3 CHCl3 CCl4 CCl4 CCl4 CCl4 n-hexadecane water water

25 26 23 26 24 21 23 23 21 21 21 23 23 23 22 23 21 22 −1 −21 −31 25 22 21

314.7 ± 2.0 270.0 ± 4.7 273.1 ± 2.8 201.5 ± 1.9 46.30 ± 0.15 3160 ± 90 3180 ± 30 3110 ± 100 3137 ± 14 3220 ± 40 2962 ± 50 2560 ± 200 2380 ± 20 2270 ± 30 2120 ± 10 2020 ± 20 1993 ± 68 1815 ± 40 1215 ± 25 923.2 ± 20 757 ± 15 1496 ± 20 1390 ± 10 1360 ± 60

51.56 ± 0.02 43.84 ± 0.44 42.6 ± 0.5 30.17 ± 0.35 7.47 ± 0.20 275 ± 8 273 ± 2 279 ± 3 271 ± 6 277 ± 1 281 ± 10 201 ± 4 176 ± 1 146 ± 2 156 ± 2 144 ± 1 136 ± 2 131 ± 3 92.3 ± 3 64.7 ± 2 55.2 ± 2 105 ± 1 90 ± 1 92.8 ± 1.9

6.10 6.16 6.41 6.68 6.20 11.5 11.6 11.1 11.6 11.6 10.5 12.7 13.5 15.5 13.6 14.0 14.6 13.8 13.2 14.2 13.7 14.2 15.4 14.7

For this same sample, the 17O T1 = 2.42 ± 0.05 ms. bFor this same sample, the 17O T1 = 16.95 ± 0.85 ms.14 Assuming CQ (14Nt) = 0.774 MHz,17 CQ (17O) was estimated to be 12.4 ± 1.2 MHz for nitrous oxide. The value was obtained by assuming both the terminal nitrogen and the oxygen nuclei relax exclusively by the quadrupolar relaxation mechanism. cFrom ref 71. dThis sample was 3.1 atm in 15N14NO and 2.6 atm in 14N15NO. The 15 N T1 values exceeded 30 s and more likely 50 s. a

The purpose of this paper is 2-fold. The first purpose is to provide additional 14N and 17O NMR relaxation data for N2O. Second, we wish to present the results of modern computational quantum chemistry computations of nitrogen and oxygen electric field gradients for N2O. Computational methods are also used to determine the spin-rotation constants to assess the role that this relaxation mechanism may play, especially given the small CQ values for the nitrogens. Computational methods are also used to assess the possible effect of solvent on the EFGs of the central and terminal nitrogens by considering the FH···N2O linear complex.3−5

(MRCI) method.37,38 All post-HF methods, except for the CCSD and CCSD(T) results, have included correlation of the valence electrons only. In the CCSD and CCSD(T) calculations, all electrons have been correlated unless otherwise indicated. For the CASSCF calculations, the active space comprised 16 electrons in 12 orbitals (the three core 1s orbitals were excluded). The CASSCF orbitals and wave functions were used as the starting point for the corresponding MRCI calculations. In addition to these ab initio methods, DFT calculations have been carried out using Becke’s threeparameter hybrid functional in combination with the correlation functional of Lee, Yang, and Parr (B3LYP),39−41 the hybrid Perdew, Burke, and Ernzerhof exchange−correlation function (PBE0),42−44 and Becke’s three-parameter hybrid functional with the correlation function of Perdew and Wang (B3PW91).45−48 The EFGs are converted to NQCCs using the values of the nuclear quadrupole moments from the work of Pyykkö.49 Though the EFGs have been determined using all computational methods discussed above, we have also determined the spin-rotation constants and nuclear magnetic shielding tensors using CCSD(T) theory.50−52 Our primary interest, beyond the EFGs, is in the theoretical determination of the spin-rotation constants, which to our knowledge have not been computed previously for N2O. The spin-rotation constants are more difficult to determine than the EFGs because they require analytical second derivative techniques.53−56 The nuclear magnetic shielding constants are available from the same calculations required to determine the spin-rotation constants and, hence, are reported here for completeness. There have been a number of extensive theoretical studies53,57,58 focusing on the determination of the

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EXPERIMENTAL AND COMPUTATIONAL METHODS The experimental NMR data were acquired exactly as described previously.14 Hence, the experimental methods are not discussed in detail here. The computations for N2O were carried out using a variety of standard quantum chemistry methods including density functional theory (DFT). Rather than performing geometry optimization for each level of theory and basis set utilized, the geometry was fixed at the experimentally determined one with rNN = 1.127292 Å and rNO = 1.185089 Å.27 The EFGs have been determined using Hartree−Fock theory (HF), secondorder Møller−Plesset perturbation theory (MP2),28−30 quadratic configuration interaction with all single and double substitutions (QCISD),31 coupled-cluster theory with single and double excitations (CCSD) as well as perturbative inclusion of triples [CCSD(T)],32−34 complete active space self-consistent field (CASSCF) computations,35,36 and the internally contracted multireference configuration interaction 9770



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Table 2. Nuclear Quadrupole Coupling Constants (NQCC in MHz) of Terminal Nt, Central Nc, and Oxygen in N2O As Determined Using Standard ab Initio Electronic Structure Methods and DFT Methods and from Previously Reported Experimental Measurementsa basis set

aug-cc-pVTZ

aug-cc-pVQZ

previous work 6-311+G(df,pd) aug-cc-pCVTZ(N)/aug-cc-pVTZ(O)

method

terminal Nt

central Nc

experiment experiment experiment HF MP2 QCISD B3LYP PBE0 B3PW91 HF B3LYP PBE0 B3PW91

−0.7767 ± 0.0010 −0.77376 ± 0.00027d −0.88653 ± 0.00012e −1.7972 −0.3249 −0.8598 −0.9321 −0.9077 −0.8761 −1.8552 −1.0188 −0.9898 −0.9575

−0.2694 ± 0.0018 −0.26758 ± 0.00038d −0.25814 ± 0.00018e −2.3417 +0.2922 −0.6623 −0.4608 −0.4987 −0.3979 −2.3619 −0.4508 −0.4988 −0.3909

14.8374 11.6344 12.9476 12.8365 12.6675 12.6739 14.9689 12.9826 12.7943 12.8165

B3PW91 B3PW91

−0.786f −0.843f

−0.244f −0.223f

NR NR

b

oxygen b

12.4 ± 1.2c

NQCCs are determined using computed electric field gradients, and the values of the nuclear quadrupole moments from ref 49, i.e., QN = 20.44 mb and QO = −25.58 mb. bReference 17. cReference 14. dReference 18 for the (0, 0, 0) ground vibrational state. eReference 18 for the (0, 11, 0) first excited bending vibrational state; fReference 70. Note that the results were originally reported used scaled conversion factors going from the EFG to the NQCC. Here we report the results using the nuclear quadrupole moment for N from ref 49. a

nuclear magnetic shielding constants for N2O − we do not attempt to improve upon those results here. All calculations have been carried out using the aug-cc-pVXZ (X = T and Q) family of basis sets.59−61 Because the accurate determination of NQCCs requires the good description of the wave function near the nucleus, we have also utilized the augcc-pCVXZ (X = T and Q) basis sets.62 Calculations have also been performed using the aug-cc-pVDZ and aug-cc-pCVDZ basis sets. However, the agreement with experiment is poor so the results are not presented explicitly in the current work. The single reference calculations (HF, MP2, QCISD, and DFT) calculations were carried out with Gaussian 03.63 All CASSCF and MRCI calculations were carried out with the MOLPRO electronic structure program.64 The CCSD and CCSD(T) calculations have been undertaken with the CFOUR program package.65

role of the spin-rotation relaxation mechanism (see refs 16 and 68). This mechanism will be most important for the central nitrogen because the quadrupolar mechanism is relatively inefficient for Nc. For each nitrogen of N2O, one can write the rate of spin−lattice relaxation, R1 = (T1)−1, as R1(obs) = R1(spin‐rotation) + R1(quadrupolar) = a(C I)2 + b(CQ )2

(1)

where CI and CQ are the nuclear spin-rotation and nuclear quadrupolar coupling constants, and a and b are constants containing the appropriate correlation times, etc. (e.g., see refs 16, 66, and 68). Therefore, for the terminal nitrogen, we have R1(14 N t,obs) = a(− 1.829)2 + b(773.76)2

(2)

and, for the central nitrogen

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R1(14 N c,obs) = a(− 3.06)2 + b(267.58)2

RESULTS AND DISCUSSION The nitrogen-14 spin−lattice relaxation times for N2O at 8.46 T in the gas phase and in a variety of different solvents are presented in Table 1. Results are also given at several temperatures and pressures. The uncertainties in the experimental T1 values given in Table 1 are generally estimated to be 5% or less. The “ ± values” given in Table 1 are a measure of the goodness of fit of the inversion−recovery relaxation data. We will first discuss the gas-phase results and then those in solvent. Gas-Phase Nitrogen-14 Relaxation Data for N2O. The gas-phase NMR relaxation data given in Table 1 indicate that the 14N T1 values increase with increasing pressure (density) as expected.66,67 Important is the observation that the average ratio, T1(14Nc)/T1(14Nt), is 6.3 ± 0.3 independent of pressure within experimental error. As mentioned in the Introduction, if the quadrupolar mechanism was the only mechanism, the ratio would be 8.34 ± 0.03 (based on the average of the two rotational spectroscopic experimental measurements17,18). Our observed ratio is readily explained by considering the possible

(3)

Here we have used the spin-rotation constants provided by Reinartz et al.18 Note that the spin-rotation constant for the central nitrogen is significantly greater than that of the terminal nitrogen, −3.06 ± 0.12 versus −1.829 ± 0.065 kHz; also, note that the values are slightly different than from those of Casleton and Kukolich17 −2.90 ± 0.26 and −2.35 ± 0.20 kHz, respectively, and those of Jameson et al.69 of −2.29 and −1.77 kHz. [Note that the values reported for 15N2O in ref 69 have been converted to those for 14N2O using eq 8 of ref 66.] Nevertheless, all sets of data yield the same qualitative conclusion that the spin-rotation mechanism makes a negligible contribution to relaxation of the terminal 14Nt (vide infra). Using the gas-phase data obtained at a pressure of approximately 10 atm and solving the above two equations for a and b yields R1(14Nt,SR) = 0.32 s−1 and R1(14Nt,Q) = 23.15 s−1 (i.e., for the terminal nitrogen the spin-rotation relaxation mechanism contributes 1.4% to the total rate of relaxation, 23.47 s−1). For the central 14N, R1(14Nc,SR) = 0.89 s−1 and R1(14Nt,Q) = 2.77 s−1; thus the spin-rotation 9771



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mechanism contributes approximately 24% to the total rate of relaxation of the central nitrogen, 3.66 s−1. Similar conclusions about the mechanism of nitrogen-14 relaxation for gaseous nitrous oxide have been previously been made by Jameson, ter Horst, and Jameson.66 Oxygen-17 Nuclear Quadrupolar Coupling Constant from the Gas-Phase Relaxation Data. Using the results above and the observed 17O relaxation time of 2.42 ± 0.05 ms or R1(17O) = 413 s−1 together with well-known expressions for quadupolar relaxation14−16,68 leads to

Table 3. Nuclear Quadrupole Coupling Constants (in MHz) of Terminal Nt, Central Nc, and Oxygen in N2O As Determined Using Multireference CASSCF and MRCI Methodsa basis set aug-cc-pVTZ aug-cc-pVQZ aug-cc-pCVTZ

2 17 ⎛ 8 ⎞⎡ CQ ( O) ⎤ R1( O,obs) 413 ⎢ ⎥ ⎜ ⎟ = = 17.84 = ⎝ 125 ⎠⎢⎣ CQ (14 N t) ⎥⎦ 23.15 R1(14 N t,Q) 17

aug-cc-pCVQZ a

(4)

Taking CQ( Nt) = −773.76 ± 0.27 kHz gives 17.84 = 0.064CQ(17O)2/(0.77376)2 or CQ(17O) = 12.92 MHz. The error in this value is estimated to be approximately 5% (±0.65 MHz) and compares well with the estimate we made using relaxation data obtained for n-hexane solutions in 1986.14 Theoretical Determination of CQ and Spin-Rotation Constants. As mentioned in the Introduction, there is a lack of data for N2O in the work that determines computationally the NQCCs for nitrogen containing species. A notable exception is ref 70, where the NQCCs were determined at the B3PW91/6311+G(df,pd) and B3PW91/aug-cc-pCVTZ(N)/aug-cc-pVTZ(O) levels of theory. The NQCCs of the terminal Nt, central Nc, and oxygen atoms as determined using standard electronic structure theory methods are presented in Table 2. Clearly, the Hartree−Fock results consistently overestimate the NQCC for the terminal nitrogen by a factor of 2 and the middle nitrogen by a factor of 8. Also, the NQCC for the terminal nitrogen is always predicted to be smaller than that for the middle nitrogenin direct contrast to the experimental measurements. On the other hand, the NQCC for the oxygen atom is only overestimated by 18% at the HF level of theory. The MP2 results overestimate the correlation correction, now underestimating the NQCC for the terminal Nt and O, while having the correct magnitude but wrong sign for the central Nc. The QCISD results give the correct magnitudes for the terminal and central nitrogens but overestimate the NQCC for the central Nc by greater than a factor of 2. The DFT results are consistently improved relative to the HF and MP2 results and, based on the NQCC for the central nitrogen, are modestly better than the QCISD results for the aug-cc-pVTZ basis set used here. All functionals considered correctly predict the NQCC for the terminal Nt to be larger than that for the central Nc. However, they predict the NQCCs for the terminal Nt and central Nc to be 13−31% and 45−85% too large, respectively. The NQCC for the oxygen atom is always predicted within the experimental error bars [This is true for all the other methods considered, see below. Hence, the oxygen data are not discussed further.] The DFT values for the nitrogen NQCCs are reasonable but could be improved, and, therefore, we consider more highly correlated ab initio methods. CASSCF and MRCI results are presented in Table 3, and the values determined using CCSD(T) are given in Table 4. The CASSCF and MRCI methods always predict the NQCC for the terminal nitrogen to be larger than that for the middle nitrogen in agreement with experiment. The calculated values for the NQCCs are in reasonable agreement with the experimental values especially considering their rather small values. For example, the MRCI/aug-cc-pCVQZ NQCC for the terminal Nt

method

terminal Nt

central Nc

oxygen

CASSCF MRCI CASSCF MRCI CASSCF MRCI CASSCF MRCI

−0.7923 −0.6838 −0.8404 −0.7464 −0.6658 −0.6754 −0.8293 −0.7357

−0.6449 −0.4221 −0.6453 −0.4387 −0.3882 −0.2618 −0.5680 −0.3689

12.4782 12.5752 12.5833 12.7143 12.3917 12.3652 12.2721 12.3997

In all calculations, the core 1s orbitals are frozen.

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Table 4. Nuclear Quadrupole Coupling Constants (in MHz) of Terminal Nt, Central Nc, and Oxygen in N2O As Determined Using CCSD(T) Methodsa basis set

terminal Nt

central Nc

oxygen

aug-cc-pVTZ aug-cc-pVQZ aug-cc-pCVTZ aug-cc-pCVQZ

−0.6450 −0.7126 −0.6435 −0.7191

−0.3627 −0.3797 −0.2162 −0.3011

12.5544 12.6968 12.3522 12.4477

a

In calculations with aug-cc-pVXZ basis sets, the core orbitals are frozen, whereas for those using aug-cc-pCVXZ basis sets, all orbitals are correlated.

and central Nc are 5% smaller and 37% larger than the experimentally determined gas-phase values. The CCSD(T)/ aug-cc-pCVXZ (X = T and Q) values agree most closely with the experimental data. For example, the CCSD(T)/aug-ccpCVQZ values are 7.4% smaller and 11.8% larger than the measured NQCCs for the terminal and central nitrogens, respectively. From the data presented in Tables 2−4, it is clear that high-level treatments of electron-correlation are necessary to capture correctly the NQCCs for the nitrogen atoms in N2O. All of the computational results presented thus far have been for the experimentally determined geometry. Because the values of the NQCCs are so small, it is interesting to determine the geometric dependence of them, to assess the role that vibrational averaging (over the ground state wave function) may play in determining the experimentally measured NQCCs. Figures 1 and 2 illustrate the MRCI/aug-cc-pCVTZ results for the NQCCs of the terminal and central nitrogens as a function of NN bond distance and NO bond distances [we did not consider bending as that would break symmetry]. The NQCCs are strongly geometry dependent, and hence, a precise theoretical determination of the NQCCs for N2O requires a careful assessment of the effects of vibrational averaging. To quantify the effects of vibrational averaging, we have determined the vibrationally averaged NQCCs at the CCSD/ aug-cc-pCVTZ, CCSD(T)/aug-cc-pCVTZ, and CCSD(T)/ aug-pCVQZ levels of theory using the automated procedures available in CFOUR.65 To evaluate the vibrationally averaged NQCCs, the equilibrium structures had to be determined at each level of theory/basis set. The results are presented in Table 5. Comparing the CCSD and CCSD(T) results at the equilibrium geometries for a given basis set, it is clear that triples play at critical role in the accurate determination of the NQCCs at both the central and terminal nitrogens. In terms of absolute change, the NQCC at oxygen exhibits a similar 9772



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for the central nitrogen changes by approximately 1%. The best values determined here at the vibratonally average CCSD(T)/ aug-cc-pCVQZ level of theory show remakable agreement with the experimentally measured values (Tables 2 and 5), and it is clear that for the terminal nitrogen including the effects of vibrational averaging is important. Nitrogen-14 Relaxation Data for N2O in Various Solvents. For N2O in n-hexane the 14N relaxation times are essentially independent of the gas pressure (Table 1). Also, the data obtained for 15 atm of N2O in n-hexane by Lowenstein and Brenman71 at approximately 1.79 T (5.5 MHz for 14N) are in good agreement with our data obtained at 8.48 T (26.1 MHz for 14N), indicating that chemical shielding anisotropy is not an important relaxation mechanism for either nitrogen of N2O in solution. Bhattacharyya and Dailey72 have obtained Δσ values of 369 ± 15 and 512 ± 10 ppm for the terminal and central nitrogen, respectively. Just how reliable these values are is unclear; however, they are in qualitative agreement with expectations from the spin-rotation constants determined by molecular beam experiments (Table 6). Table 7 reports the

Figure 1. Plot of the dependence of the theoretical nuclear quadrupole coupling constants, CQ, as a function of rNN bond distance for terminal Nt (dash-dotted red line) and central Nc (solid black line). The corresponding experimental results17 are given by the (red) dotted line and (black) dashed lines, respectively. The vertical line indicates the equilibrium bond length rNN = 1.127292 Å.27 Results are determined using MRCI/aug-cc-pCVTZ level of theory.

Table 6. Spin-Rotation Constants (in kHz) of the Terminal Nt and Central Nc in 14N2O and for Oxygen in 14N217O As Determined Using CCSD(T) Methods and the Previous Experimental Measurements for 14N2Oa basis set

terminal Nt

central Nc

aug-cc-pVTZ aug-cc-pVQZ aug-cc-pVTZ aug-cc-pVQZ ref 17 ref 18c ref 18d

−1.748 −1.780 −1.696 −1.728 −2.35 ± 0.90b −1.829 ± 0.065 −1.904 ± 0.015

−2.507 −2.541 −2.433 −2.466 −2.90 ± 1.17b −3.06 ± 0.12 −2.60 ± 0.02

oxygen

2.850 2.909

a

The core orbitals are frozen in all calculations. bOriginally reported with 40% confidence intervals, whereas here they are listed with 95% confidence intervals. cFor the ground (0, 0, 0) vibrational state. dFor the first excited (0, 11, 0) bending vibrational state.

Figure 2. Plot of the dependence of the nuclear quadrupole coupling constants, CQ, as a function of rNO bond distance for terminal Nt (dash-dotted red line) and central Nc (solid black line). The corresponding experimental results17 are given by the (red) dotted line and (black) dashed lines, respectively. The vertical line indicates the equilibrium bond length rNO = 1.185089 Å.27 Results are determined using MRCI/aug-cc-pCVTZ level of theory.

anisotropic nuclear magnetic shielding constants for the nitrogens and oxygen as determined using CCSD(T) methods. We also report the isotropic nuclear magnetic shielding constants from the present work for completeness. However, the isotropic constants have been studied extensively elsewhere53,57,58 and the interested reader should consult these excellent works for further details. Examining Table 7, the quantum chemistry results are in reasonable agreement with the

sensitivity due to the inclusion of triples; however, due to its much larger magnitude, the relative change is small. When the effects of vibrational averaging are included, the NQCC for the terminal nitrogen decreases by approximately 10% whereas that

Table 5. Nuclear Quadrupole Coupling Constants (in MHz) of Terminal Nt, Central Nc, and Oxygen in N2O As Determined Using CCSD and CCSD(T) Methodsa basis set

method

geometry

terminal Nt

central Nc

oxygen

aug-cc-pCVTZ

CCSD CCSD CCSD(T) CCSD(T) CCSD CCSD(T) CCSD(T)

equilibriumb V-averaged equilibriumc V-averaged equilibriumd equilibriume V-averaged

−1.0502 −1.1217 −0.6256 −0.6882 −1.1644 −0.7299 −0.7906

−0.6442 −0.6514 −0.2036 −0.2018 −0.7558 −0.3020 −0.2980

12.8513 12.9206 12.4728 12.4985 12.8500 12.4772 12.5013

aug-cc-pCVQZ

a Results are reported at the computationally optimized geometries and as determined via vibrational averaging. In the calculations, all orbitals are correlated. brNN = 1.11664 Å and rNO = 1.18311 Å. crNN = 1.12968 Å and rNO = 1.18863 Å. drNN = 1.11394 Å and rNO = 1.18016 Å. erNN = 1.12691 Å and rNO = 1.18568 Å.

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Table 7. Isotropic and Anisotropic Nuclear Magnetic Shielding Constants (in ppm) of Terminal Nt, Central Nc, and Oxygen in N2O As Determined Using CCSD(T) Methods in the Present Work, from Previous Theoretical Calculations,b and from Experimental Measurementsa terminal Nt

central Nc

oxygen

method

σ

Δσ

σ

Δσ

σ

Δσ

CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVQZ CCSD(T)/qz2pc,d CCSD(T)/qz2p + zpvcc CCSD(T)/qz2pe CCSDT/qz2pe experimentf experimentg experimentg experimenth experimenti experimentj

115.0 111.2 110.9 100.8 110.5 109.3 99.5 105 ± 10 103 ± 15 NR NR NR

342.8 348.6 NR NR NR NR NR 376 ± 12 369 ± 15 NR NR NR

21.2 17.2 16.1 9.7 15.7 14.7 11.3 27.3 ± 10 22.7 ± 10 NR NR NR

496.0 502.0 NR NR NR NR NR 508 ± 10 512 ± 10 NR NR NR

207.0 203.3 200.3 NR 201.3 200.5 NR NR NR 180.1 181.0 181.8

314.3 320.1 NR NR NR NR NR NR NR NR NR NR

a

In calculations with aug-cc-pVXZ basis sets, the 1s core orbitals are frozen. [Note: NR = Not reported]. bThe nuclear magnetic shielding constants for N2O have been studied extensively using theoretical techniques, and hence, only a small subset of the reported results is provided here. Please see refs 57 and 58 for more complete data sets including the effects of vibrational ZPE. cNitrogen data from ref 57 and determined at CCSD(T)/ccpVQZ optimized geometry. dOxygen data from ref 58 and determined at CCSD(T)/qz2p optimized geometry. eReference 53 as determined at the experimental geometry of ref 74. Note that the terminal and central nitrogens are mislabeled in Table 2 of ref 53. fReference 75. gReference 72. Anisotropic nuclear magnetic shielding constants were derived from the experimental data of ref 72 in ref 75. hReference 76. iReference 77. j Reference 78.

and −229.0 kHz for the terminal and central nitrogen, respectively. These can be compared to the gas-phase values of −643.5 and −216.2 kHz for the isolated N2O molecule (computed at the same level of theory, Table 4). Although the NQCC for the central nitrogen remains relatively unchanged (an increase in magnitude of 6%), the value for the terminal nitrogen is decreased in magnitude by 40%. Experimentally,4 the NQCCs have been measured in the linear FH···N2O complex to be −288.4 ± 0.10 kHz for the central N and −512.50 ± 0.69 kHz for the terminal N: these represent an increase in magnitude of 8% and a decrease in magnitude of 34%, respectively, compared to the experimental values for gasphase N2O.18 These changes in NQCCs will lead to a decrease in the ratio of the spin−lattice relaxation times (opposite to what is observed in solution, Table 1). However, the difference is related to the linear geometry of the FH···N2O complex, such that the terminal nitrogen, which is bound the hydrogen, is more strongly perturbed than the central nitrogen. On the other hand, for the HCl−N2O complex, where the chlorine is bound to the central nitrogen in a T-shaped geometry, the NQCC for the central nitrogen has been measured to be more strongly perturbed than that for the terminal nitrogen:6 the NQCC for Nt increases in magnitude while that for Nc decreases in magnitude. Though the changes to the NQCCs relative to the gas phase depend intimately on the complex geometry and the nature of the species bound to N2O, the computation and measurements for the single perturber molecule demonstrates the large effect that can be realized.

experimental measurements. It is important to recognize that even if magnetic shielding anisotropy were an important relaxation mechanism, it would contribute more to the relaxation of the central nitrogen than the terminal nitrogen. Likewise, if the spin-rotation mechanism plays a role, it contributes more to the central nitrogen than the terminal nitrogen. The dipole−dipole (14N,14N) mechanism would make the same contribution to both the rate of relaxation for the terminal and central nitrogen nuclei. Thus considering all possible relaxation mechanisms it is difficult to rationalize how the ratio, T1(14Nc)/T1(14Nt), can exceed 8.3! The most logical argument we can propose is that the CQ(14N) values in solution are perturbed from their gas-phase values. The central nitrogen has a very small field gradient (for dinitrogen the value of CQ is −5.39 ± 0.05 MHz).73 How much of a perturbation is required to rationalize the observed relaxation data? Suppose CQ(14Nt) increased in magnitude by 5% (i.e., by 38.7 kHz to 812.4 kHz) while CQ(14Nc) decreases by the same amount in kHz, to 228.9 kHz; this would lead to a ratio, T1(14Nc)/T1(14Nt), of 12.6. Changes of this magnitude (and greater) have been observed in the studies of van der Waals dimers containing N2O.1−11 To confirm the hypothesis that the CQ(14N) values in solution are perturbed from their gas-phase values, as has been shown experimentally for a number of van der Waals complexes,1−11 we have determined computationally their values for the linear hydrogen fluoride−nitrous oxide complex. We have chosen the linear complex to preserve the symmetry of the system. The linear complex has been observed experimentally by a number of groups.3−5 Note that in the linear isomer, the hydrogen in HF is bonded to the terminal nitrogen in N2O, i.e., FH···N2O. Rather than optimizing the geometry, we choose to use the experimentally determined geometry with rNN = 1.127292 Å, rNO = 1.185089 Å, rNH = 2.059 Å, and rHF = 0.9256 Å.3 The NQCCs of the central and terminal nitrogen atoms have been computed using the CCSD(T)/aug-cc-pCVTZ level of theory with all electrons correlated. In the FH···N2O complex, the NQCCs are −385.9

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CONCLUSIONS In the present work, the nuclear quadrupole coupling constants for nitrogen and oxygen have been determined computationally for N2O. The results demonstrate that the NQCC for oxygen can be reliably computed using a wide variety of electronic structure theory methods including DFT. On the other hand, the NQCCs of the terminal and central nitrogen atoms are very small and, in general, overestimated with many methods (Table 9774



Article

Fund) for support for computational infrastructure. Experimental measurements have been performed by A. Martin de P. Nicholas, Marco L. H. Gruwel, Jan O. Friedrich, and R.E.W. We thank Aatto Laaksonen and Guy Bernard for early computational results.

2). However, reliable agreement can be obtained through the use of high-level methods such as CCSD(T) and MRCI with large basis sets (Tables 3 and 4). The problem with many methods can be rationalized, for example, by considering the CASSCF wave function, where several configurations involving double excitations contribute significantly. It has also been shown (Figures 1 and 2 and Table 5) that to obtain precise agreement with experimentally measured NQCCs, vibrational zero-point energy effects need to be taken into account. Using the CCSD(T)/aug-cc-pVXZ (X = T or Q) method, the spinrotation constants for N2O have been determined computationally for the first time, and the results in general support the microwave measurements of Reinartz et al.18 (Table 6). More importantly, they confirm that the spin-rotation mechanism makes a negligible contribution to relaxation of the terminal 14 Nt while making a relatively significant contribution to that of the central 14Nc. The measured values of the relative relaxation times in various solvents (Table 1) suggest that the magnitude of the NQCC for the central nitrogen must decrease (or the magnitude of the terminal nitrogen must increase). To confirm the effect of a solvent on the NQCCs (as has been observed previously in van der Waals complexes),1−11 the NQCCs for the nitrogens have been determined computationally in the linear FH···N2O complex. Although a decrease in the ratio is computed in agreement with the experimental measurements on the van der Waals complex,4 the most important point is that the presence of a “solvent” (in our case a single HF molecule) can strongly influence the nitrogen NQCCs. The detailed explanation for the measurements made for the solvents considered in Table 1 remains to be explored and is beyond the scope of the present work. However, it is clear that any explanation must be based on high-level (CCSD(T) or MRCI) ab initio electronic structure computations of the NQCCs, will need the account for the effects of vibrational averaging, and will require explicit consideration of temperature effects (see for example the measurements of the NQCCs and spin-rotation constants made by Reinartz et al. for the two lowest vibrational states,18 Tables 2 and 6). The sensitivity of the NQCCs to the electronic structure theory method and details of dealing with vibrational effects will make the parametrization of models for molecular dynamics simulations, which could be used to understand the spin−lattice relaxation times in solvents reported here, exceedingly computationally demanding.

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ASSOCIATED CONTENT

* Supporting Information S

Full references for refs 63−65. This material is available free of charge via the Internet at http://pubs.acs.org/.

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REFERENCES

(1) Didriche, K.; Lauzina, C.; Mackoa, P.; Hermana, M.; Lafferty, W. Chem. Phys. Lett. 2009, 469, 35−37. (2) Leung, H. O. J. Chem. Phys. 1997, 107, 2232−2241. (3) Zeng, Y. P.; Sharpe, S. W.; Reifschneider, D.; Wittig, C.; Beaudet, R. A. J. Chem. Phys. 1990, 93, 183−196. (4) Leung, H. O.; Ibidapo, O. M.; Abruña, P. I.; Bianchi, M. M. J. Mol. Spectrosc. 2003, 222, 3−14. (5) Kukolich, S. G.; Bumgarner, R. E.; Pauley, D. J. Chem. Phys. Lett. 1987, 141, 12−15. (6) Leung, H. O.; Cashion, W. T.; Duncan, K. K.; Hagan, C. L. J. Chem. Phys. 2004, 121, 237−247. (7) Leung, H. O. J. Chem. Phys. 1998, 107, 3955−3961. (8) Leung, H. O. J. Chem. Phys. 1999, 110, 4394−4401. (9) Leung, H. O.; Osowski, A. M.; Oyeyemi, O. A. J. Chem. Phys. 2001, 114, 4828−4836. (10) Leung, H. O.; Gangwani, D.; Grabow, J. U. J. Mol. Spectrosc. 1997, 185, 106−112. (11) Ngarĩ, M. S.; Xu, Y.; Jäger, W. J. Mol. Spectrosc. 1999, 197, 244− 253. (12) Nauta, K.; Miller, R. J. Chem. Phys. 2001, 115, 10254−10260. (13) McKellar, A. R. W. J. Chem. Phys. 2007, 127, 044315. (14) Wasylishen, R. E.; de P. Nicholas, A. M. Magn. Reson. Chem. 1986, 24, 1031−1033. (15) Abragam, A. The principles of magnetic resonance; Oxford University Press: Oxford, U.K., 1961. (16) Kowalewski, J.; Mäler, L. Nuclear spin relaxation in liquids: Theory, Experiments, and Applications; Taylor and Francis: Boston, 2006. (17) Casleton, K. H.; Kukolich, S. G. J. Chem. Phys. 1975, 62, 2696− 2699. (18) Reinartz, J. M. L. J.; Meerts, W. L.; Dymanus, A. Chem. Phys. 1978, 31, 19−29. (19) Cummins, P. L.; Bacskay, G. B.; Hush, N. S.; Ahlrichs, R. J. Chem. Phys. 1987, 86, 6908−6917. (20) Rizzo, A.; Ruud, K.; Helgaker, T.; Jaszuński, M. J. Chem. Phys. 1998, 109, 2264−2274. (21) Sicilia, E.; de Luca, G.; Chiodo, S.; Russo, N.; Calaminici, P.; Koster, A. M.; Jug, K. Mol. Phys. 2001, 99, 1039−1051. (22) Polák, R.; Fišer, J. Chem. Phys. 2008, 351, 83−90. (23) Polák, R.; Fišer, J. Chem. Phys. 2010, 375, 85−91. (24) Brzyska, A.; Jaszuński, M. Int. J. Quantum Chem. 2012, 112, 2281−2286. (25) Puzzarini, C. Theor. Chem. Acc. 2008, 121, 1−10. (26) Puzzarini, C.; Cazzoli, G. J. Mol. Spectrosc. 2006, 240, 260−264. (27) Teffo, J. L.; Chédin, A. J. Mol. Spectrosc. 1989, 135, 389−409. (28) Møller, C.; Plesset, M. Phys. Rev. 1930, 46, 618−622. (29) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503−506. (30) Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett. 1990, 166, 281−289. (31) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968−5975. (32) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1988, 157, 479−483. (33) Bartlett, R. J.; Watts, J. D.; Kucharski, S. A.; Noga, J. Chem. Phys. Lett. 1990, 165, 513−522. (34) Stanton, J. F. Chem. Phys. Lett. 1997, 281, 130−134. (35) Knowles, P. J.; Werner, H. J. Chem. Phys. Lett. 1985, 115, 259− 267. (36) Werner, H. J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053− 5063.

AUTHOR INFORMATION

Corresponding Author

*E-mail: A.B., [email protected]; R.E.W., roderick. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC). A.B. thanks the Canadian Foundation for Innovation (New Opportunities 9775



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(76) Wasylishen, R. E.; Bryce, D. L. J. Chem. Phys. 2002, 117, 10061− 10066. (77) Makulski, W.; Jackowski, K. J. Mol. Struct. 2003, 651, 265−269. (78) Jameson, C. J. Chemical shift scales on an absolute basis. In Encyclopedia of Magnetic Resonance; Harris, R. K., Wasylishen, R. E., Eds.; John Wiley and Sons Ltd.: Chichester, U.K., 2011; DOI: 10.1002/9780470034590.emrstm0072.pub2.

(37) Werner, H. J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803− 5814. (38) Knowles, P. J.; Werner, H. J. Chem. Phys. Lett. 1988, 145, 514− 522. (39) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (40) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (41) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200− 1211. (42) Perdew, J. P.; Burke, K.; Ernzerhoff, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (43) Perdew, J. P.; Burke, K.; Ernzerhoff, M. Phys. Rev. Lett. 1996, 78, 1396. (44) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158−6169. (45) Perdew, J. P.; Chevray, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhau, C. Phys. Rev. B 1992, 46, 6671− 6687. (46) Perdew, J. P.; Chevray, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhau, C. Phys. Rev. B 1993, 48, 4978. (47) Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1996, 54, 16533− 16539. (48) Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1998, 54, 14999. (49) Pyykkö, P. Mol. Phys. 2008, 106, 1965−1974. (50) Flygare, W. H. Chem. Rev. 1974, 74, 653−687. (51) Gauss, J.; Sundholm, D. Mol. Phys. 1997, 91, 449−458. (52) Gauss, J.; Ruud, K.; Helgaker, T. J. Chem. Phys. 1996, 105, 2804−2812. (53) Gauss, J. J. Chem. Phys. 2002, 116, 4773−4776. (54) Kállay, M.; Gauss, J. J. Chem. Phys. 2004, 120, 6841−6848. (55) Gauss, J.; Stanton, J. F. J. Chem. Phys. 1996, 104, 2574−2583. (56) Gauss, J.; Stanton, J. Chem. Phys. Lett. 1997, 276, 70−77. (57) Prochnow, E.; Auer, A. A. J. Chem. Phys. 2010, 132, 064109. (58) Auer, A. A. J. Chem. Phys. 2010, 131, 024116. (59) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796−6806. (60) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358− 1371. (61) Dunning, T. H., Jr. J. Chem. Phys. 1990, 90, 1007−1023. (62) Woon, D. E.; Dunning, T. H. J. Chem. Phys. 1995, 103, 4572− 4585. (63) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (64) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schütz, M; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B et al. MOLPRO, version 2008.1, a package of ab initio programs, 2008, see http://www.molpro.net. (65) Stanton, J. F.; Gauss, J.; Harding, M. E.; Szalay, P. G. CFOUR, Coupled-Cluster techniques for Computational Chemistry, a quantumchemical program package, 2010, For the current version, see http:// www.cfour.de. (66) Jameson, C. J.; ter Horst, M. A.; Jameson, A. K. J. Chem. Phys. 1998, 109, 10227−10237. (67) Speight, P. A.; Armstrong, R. L. Can. J. Phys. 1969, 47, 1475− 1483. (68) Spiess, H. W. In NMR - Basic Principles and Progress; Diehl, P., Fluck, E., Kosfeld, R., Eds.; Springer-Verlag: Berlin, 1978; Vol. 15, pp 55−214. (69) Jameson, C. J.; Jameson, A. K.; Hwang, J. K.; Smith, N. C. J. Chem. Phys. 1988, 89, 5642−5649. (70) Bailey, W. C. Chem. Phys. 2000, 252, 57−66. (71) Lowenstein, A.; Brenman, M. J. Magn. Reson. 1979, 34, 193− 198. (72) Bhattacharyya, P. K.; Dailey, B. P. J. Chem. Phys. 1973, 59, 5820−5823. (73) Scott, T. A. Phys. Rep. 1976, 27, 89−157. (74) Amiot, C. J. Mol. Spectrosc. 1976, 59, 380−395. (75) Jameson, C. J.; Jameson, A. K.; Oppusunggu, D.; Wille, S.; Burrell, P. M.; Mason, J. J. Chem. Phys. 1981, 74, 81−89. 9776


Nuclear Quadrupole Coupling Constants for N2O: Experiment and

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