Improved bond length determination technique for C3 and other linear molecules with a large amplitude bending vibration

2020 ◽  
Vol 1219 ◽  
pp. 128329
Author(s):  
Alexander A. Breier ◽  
Thomas F. Giesen ◽  
Stephen C. Ross ◽  
Koichi M.T. Yamada
1996 ◽  
Vol 352-354 ◽  
pp. 32-35 ◽  
Author(s):  
R.V. Vedrinskii ◽  
A.I. Taranukhina ◽  
L.A. Bugaev ◽  
V.L. Kraizman ◽  
A.V. Morozov ◽  
...  

1987 ◽  
Vol 65 (7) ◽  
pp. 739-752 ◽  
Author(s):  
H. Lew ◽  
R. Groleau

An analysis of 15 bands of the [Formula: see text] system of D2O+ is given. All assigned lines are tabulated. The rotational structures of the [Formula: see text], 1, and 3 levels of the ground state are fitted to the Watson asymmetric rotor Hamiltonian with added spin-rotation terms. For the upper state, the rotational structures of various substates are expressed: for [Formula: see text], in terms of a simple formula for linear molecules; and for [Formula: see text], 2, and 3, in terms of a modified Hill – Van Vleck formula given by Jungen, Hallin, and Merer. From the rotational constants of the ground state, term values are calculated and a small portion of a Type-B infrared band is derived. Some predicted microwave lines are also given. The bond length and bond angle of the molecule in the ground state (ν = 0) are r0 = 0.9987 ± 0.0002 Å and θ0 = 110.17 ± 0.02 deg.


2001 ◽  
Vol 8 (2) ◽  
pp. 695-697 ◽  
Author(s):  
C. Hennig ◽  
T. Reich ◽  
H. Funke ◽  
A. Rossberg ◽  
M. Rutsch ◽  
...  

2017 ◽  
Vol 73 (8) ◽  
pp. 1202-1207
Author(s):  
Agata Gapinska ◽  
Alan J. Lough ◽  
Ulrich Fekl

Two coordination compounds containing tetra-n-butylammonium cations and bis-tfd-chelated molybdenum(IV) [tfd2− = S2C2(CF3)2 2−] and oxalate (ox2−, C2O4 2−) in complex anions are reported, namely bis(tetra-n-butylammonium) bis(1,1,1,4,4,4-hexafluorobut-2-ene-2,3-dithiolato)oxalatomolybdate(IV)–chloroform–oxalic acid (1/1/1), (C16H36N)2[Mo(C4F6S2)2(C2O4)]·CHCl3·C2H2O4 or (N n Bu4)2[Mo(tfd)2(ox)]·CHCl3·C2H2O4, and bis(tetra-n-butylammonium) μ-oxalato-bis[bis(1,1,1,4,4,4-hexafluorobut-2-ene-2,3-dithiolato)molybdate(IV)], (C16H36N)2[Mo2(C4F6S2)4(C2O4)] or (N n Bu4)2[(tfd)2Mo(μ-ox)Mo(tfd)2]. They contain a terminal oxalate ligand in the first compound and a bridging oxalate ligand in the second compound. Anion 1 2− is [Mo(tfd)2(ox)]2− and anion 2 2−, formally generated by adding a Mo(tfd)2 fragment onto 1 2−, is [(tfd)2Mo(μ-ox)Mo(tfd)2]2−. The crystalline material containing 1 2− is (N n Bu4)2-1·CHCl3·oxH2, while the material containing 2 2− is (N n Bu4)2-2. Anion 2 2− lies across an inversion centre. The complex anions afford a rare opportunity to compare terminal oxalate with bridging oxalate, coordinated to the same metal fragment, here (tfd)2MoIV. C—O bond-length alternation is observed for the terminal oxalate ligand in 1 2−: the difference between the C—O bond length involving the metal-coordinating O atom and the C—O bond length involving the uncoordinating O atom is 0.044 (12) Å. This bond-length alternation is significant but is smaller than the bond-length alternation observed for oxalic acid in the co-crystallized oxalic acid in (N n Bu4)2-1·CHCl3·oxH2, where a difference (for C=O versus C—OH) of 0.117 (14) Å was observed. In the bridging oxalate ligand in 2 2−, the C—O bond lengths are equalized, within the error margin of one bond-length determination (0.006 Å). It is concluded that oxalic acid contains a localized π-system in its carboxylic acid groups, that the bridging oxalate ligand in 2 2− contains a delocalized π-system and that the terminal oxalate ligand in 1 2− contains an only partially localized π-system. In (N n Bu4)2-1·CHCl3·oxH2, the F atoms of two of the –CF3 groups in 1 2− are disordered over two sets of sites, as are the N and eight of the C atoms of one of the N n Bu4 cations. In (N n Bu4)2-2, the whole of the unique N n Bu4 + cation is disordered over two sets of sites. Also, in (N n Bu4)2-2, a region of disordered electron density was treated with the SQUEEZE routine in PLATON [Spek (2015). Acta Cryst. C71, 9–18].


1976 ◽  
Vol 54 (1) ◽  
pp. 80-91 ◽  
Author(s):  
J. L. Hardwick ◽  
J. C. D. Brand

The anharmonic potential function of the ground electronic state of nitrogen dioxide has been determined within the framework of three different vibrational Hamiltonians. The first of these, which involves a perturbation expansion of the vibrational wave functions in terms of normal coordinate harmonic oscillator wave functions, is the most widely used and generally applicable of the three. It suffers, however, from demonstrably large systematic errors. The other two are vibration–rotation Hamiltonians which allow explicitly for a large amplitude vibration in the bending vibration of a triatomic molecule; they set up the Hamiltonian operator as an explicit function of the bond angle and solve the Schrödinger equation numerically. The more sophisticated of these, the so-called nonrigid bender Hamiltonian, reproduces the spin-free virtual term values to the (0, ν2, 0) manifold of 14NO2 to a standard deviation of 0.026 cm−1 for states with N ≤ 10 and ν2 ≤ 3. It is, moreover, observed to be a more useful tool for extrapolation than is the ordinary parametrized Hamiltonian.The potential function for the bending coordinate is defined by αe = 133.888 ± 0.002°, fαα = 1.61022 ± 0.00005 mdyn Å/rad2, fααα = −2.1172 ± 0.0003 mdyn Å/rad3, and fαααα = 6.0228 ± 0.0020 mdyn Å/rad4. The equilibrium bond length, re, is found to be 1.19464 ± 0.00015 Å.


The absorption spectra of <super>14</super>NH 2 , <super>15</super>NH 2 and <super>14</super>ND 2 have been photographed in the region 3900 to 8300 A with a 21 ft. concave grating spectrograph. The radicals are produced by the flash photolysis of <super>14</super>NH 3 , <super>15</super>NH 3 and <super>14</super>ND 3 respectively. A detailed study of the <super>14</super>NH 2 - <super>15</super>NH 2 isotope shifts suggests that the molecule has a linear configuration in the excited state and that the spectrum consists of a long progression of the bending vibration in this state. These conclusions have been confirmed by detailed rotational and vibrational analyses of the 14NH2 and 14ND2 spectra. The spectra consist of type C bands for which the transition moment is perpendicular to the plane of the molecule. For NH2, sixteen bands of the progression (0, v'%, 0) <- (0, 0, 0) have been identified with v'% — 3, 4, ..., 18. In addition four bands of a subsidiary progression (1, v'2, 0) <- (0, 0, 0) have been found; these bands derive most of their intensity from a Fermi-type resonance between (0, v'2) 0) and (1, v2 —4, 0) levels in the excited state. The interaction constant W nl is 72 + 3 cm <super>-1</super>. For ND 2 , fourteen bands of the principal progression (v2 — 5 to 18) and one band of the subsidiary progression have been identified. The upper state vibration frequencies w?' and (i)' are 3325 cm <super>-1</super> and 622 cm <super>-1</super> for NH 2 and 2520 cm <super>-1</super> and 422 cm <super>-1</super> for ND 2 respectively. The bending frequencies are unusually low ; moreover, the anharmonicities of the bending vibration are unusually large and negative (x22—11.4 cm <super>-1</super> for NH 2 and 8.1 cm <super>-1</super> for ND 2 ). The origin of the system lies in the region o f 10000 cm <super>-1</super>. Ground-state rotational term values have been derived from observed com bination differences; values for the rotational constants Aooo, B'ooo and Cooo and for the centrifugal distortion constants D"A, D"b and D"0 have been determined. The bond lengths and bond angles for NH 2 and ND 2 agree and are 1.024 + 0.005 A and 103° 20' + 30' respectively. Small spin splittings have been observed. In the excited state an unusual type of vibronic structure has been found. Successive levels of the bending vibration consist alternately of 27, d , T, ... and ... vibronic sub-levels with large vibronic splittings. The origins of the vibronic sub-bands may be represented by the formula yf = Vq—GK2, where G is ~ 27 cm -1 for NH 2 and ~ 19 cm <super>-1</super> for ND 2 . The rotational levels show both spin and A-type doubling. No simple formula has been found to fit the energies o f the II, A, 0 and -T rotational levels; the 27 levels fit the formula F(N) = 1) — D N2(N + 1)2, though with a negative value for D . By extrapolating the B values for the 27 levels to = 0 we obtain B'00o = 8.7 8 cm <super>-1</super> for NH 2 and 4.4 1 cm<super>-1</super> for ND 2 . These values are consistent with a linear configuration with a bond length of 0.97 5 A. The significance of this short bond length is discussed. An explanation of the complex vibronic structure is given. The two combining states are both derived from an electronic II state which is split by electronic-vibrational coupling for the reasons advanced by Renner. A detailed correlation diagram is given. A quantitative treatment of this effect by Pople & Longuet-Higgins gives good agreement with the experimental data.


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