Femtosecond degenerate four-wave mixing (fs-DFWM) rotational coherence spectroscopy (RCS) has been used to determine the rotational and centrifugal distortion constants of the 00 (0)0 ground and 01 (1)0 vibrationally excited states of gas-phase CS(2). RCS transients were recorded over the 0-3300 ps optical delay range, allowing the observation of 87 recurrences. The fits yield rotational constants B(00 (0)0)=3.271 549 2(18) GHz for (12)C(32)S(2) and B(00 (0)0)=3.175 06(21) GHz for the (12)C(32)S(34)S isotopomer. The rotational constants of the degenerate 01 (1)0 bending level of (12)C(32)S(2) are B(01 (1)0)=3.276 72(40) and 3.279 03(40) GHz for the e and f substrates, respectively. These fs-DFWM rotational constants are ten times more accurate than those obtained by CO(2) laser/microwave heterodyne measurements and are comparable to those obtained by high-resolution Fourier transform infrared spectroscopy. Ab initio calculations were performed at two levels, second-order Moller-Plesset theory and coupled-cluster singles, doubles, and iterative triples [CCSD(T)]. The equilibrium and vibrationally averaged C=S distances were calculated using large Dunning basis sets. An extrapolation procedure combining the ab initio rotational constants with the experiment yields an equilibrium C=S bond length of 155.448 pm to an accuracy of +/-20 fm. The theoretical C=S bond length obtained by a complete basis set extrapolation at the CCSD(T) level is r(e)(C=S)=155.579 pm, or 0.13 pm longer than that in the experiment.
We combine femtosecond time-resolved rotational coherence spectroscopy with high-level ab initio theory to obtain accurate structural information for the nonpolar antiaromatic molecule 1,3,5,7-cyclooctatetraene (C8H8, COT) and its perdeuterated isotopomer COT-d8 (C8D8). We measure the rotational B0 and centrifugal distortion constants D(J), D(JK) of the v = 0 states of COT and COT-d8 to high accuracy, e.g. B0 (COT) = 2710.329(56) MHz, as well as B(v) for the v = 1 states nu6, nu11, nu17, nu22, and nu41/nu42 of COT. The experimental rotational constants are compared to those obtained from calculations at the coupled-cluster with single, double, and perturbative triples [CCSD(T)] level. The latter also take into account vibrational averaging effects of the ground and vibrationally excited states. Combining the experimental and calculated rotational constants with the calculated equilibrium bond lengths and angles allows us to determine accurate equilibrium structure parameters, e.g., r(e) (C-C) = 147.0 +/- 0.05 pm, r(e) (C=C) = 133.7 +/- 0.1 pm, and r(e) (C-H) = 107.9 +/- 0.1 pm. The equilibrium C-C and C=C bond lengths of COT are compared to those of 1,3-butadiene. The expected effect of decreased pi-electron delocalization due to the twisting of adjacent C=C double bonds in COT relative to butadiene is observed for the C-C bonds but not for the C=C bonds.
Femtosecond degenerate four-wave mixing (fs-DFWM) is applied for the measurement of rotational constants of cyclopropane (C3H6). The rotational coherence method yields a very accurate B0 = 20,093.322(12) MHz and centrifugal distortion constants D(J) and D(JK). To exploit the full resolution of the fs-DFWM method, the accuracy of the optical delay measurement was increased by nearly two orders of magnitude, including elimination of effects from the refractive index of air. The fs-DFWM molecular constants are comparable in accuracy to those from high-resolution infrared spectroscopy and are only surpassed by those of dipole distortion microwave spectroscopy. In parallel, the equilibrium structure, vibrationally averaged structure parameters and rotational constants were calculated using high-level ab initio methods and large basis sets. Combining these with the results of previous calculations and the measured rotational constants yields r(e)(C-C) = 1.5034(3) A, r(e)(C-H) = 1.0775(5) A, and alpha(e)(H-C-H) = 115.09(10) degrees.
The femtosecond degenerate four-wave mixing (fs-DFWM) technique is applied for the measurement of accurate rotational constants of cyclobutane (C4H8). The vibrational levels of C4H8 exhibit tunneling splitting due to the ring-puckering interconversion between the symmetry-equivalent D2d minima via a planar D4h barrier. For the v = 0 ground state, the fs-DFWM method yields a rotational constant B + 0 = 10663.452(18) MHz. The ring-puckering tunneling leads to slightly different rotational constants for the 0+ and 0- levels, B + 0 - B -0 = 33 +/- 2 kHz. This difference increases by a factor of approximately 90 in the v = 1+/1- ring-puckering states to B +1 - B -1 = -3059 +/- 4 kHz. Combining the experimental rotational constants with the structure parameters and rotational constants calculated by high-level ab initio calculations allows us to determine accurate equilibrium and vibrationally averaged structure parameters for cyclobutane, for example, re(C-C) = 1.5474 A, re(C-Haxial) = 1.0830 A, re(C-Hequatorial) = 1.0810 A, and ring puckering angle theta e = 29.8 degrees .
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