_{2}

^{1}

^{1}

^{1}

^{2}

^{1}

^{1}

^{2}

New _{2}, coupled by the Renner-Teller (RT) effect and meant for the spectroscopic study, are presented. The surfaces are constructed using a dual-level strategy. The internally contracted multireference
configuration interaction calculations with the Davidson correction, using the

The CH_{2} biradical has been the subject of many theoretical and experimental studies, due to its distinct electronic characteristics and chemical and physical properties. It is the direct chemical precursor of the widely observed CH radical [_{2} plays a significant role in the chemistry of hydrocarbon combustion and the astrophysics of interstellar medium [

Since Herzberg and Johns [_{2} in the near ultraviolet region half a century ago, several groups [_{2}^{−1} were recorded at Doppler-limited resolution utilizing a transient frequency-modulation (FM) laser absorption spectrometer by Chang and coworkers [

The study of the RT effect on the vibronic levels for nonlinear three-atom molecules has been an active area for several decades [_{2}, which is seen in the red and yellow parts of the spectrum, is one of the best examples in which the RT coupling should be observed [_{2}, which become a degenerate

Theoretically, some researchers [_{2} with state-of-the-art _{2}, where a mixed numerical and analytical method was employed in the PES construction. This surface shows no barrier for the C_{2V} insertion, while a barrier of 4319 cm^{−1} (12.35 kcal/mol) is present for the collinear approach. Unfortunately, visible discrepancies were found between the theoretical calculations on this surface and the experimental results [_{2}; it should be mentioned that their two lowest-lying singlet PESs are not degenerate at linearity. Joseph and Varandas [_{2} with the DMBE scaled-external-correlations method [

Liu and co-workers [_{2} reactive system systematically and determined the minimum energy crossing points (MECPs) accurately. The nonadiabatic interaction near MECPs may play an important role in spectroscopy and dynamics [_{2}, which is only 8797 cm^{−1} above the CH_{2}_{2} asymptote in energy and thus are not expected to intervene most of the vibronic spectra of the two lowest-lying singlet electronic states. However, it is clear that the RT coupling must be taken into account in the vibronic energy level calculations of the two lowest-lying states.

A few PESs for the RT coupled _{2} with the RT terms required.

So far most of the _{2} has been based on the traditional correlated _{2} with the inclusion of the nonadiabatic RT terms.

The organization of the present article is as follows. Section _{2} (called MZB) and vibronic energy level calculations are discussed in Section

For computational convenience, the molecule is placed in the _{s} symmetry, the

The electronic configurations of CH_{2} can be represented as shown in Table _{2V} or C_{s} symmetry.

| |

| |

The

Two levels of _{2} asymptote in the present

In the higher-level calculations, the methods and algorithm are the same as the lower-level, but the active space and basis set are different. The active space consists of all electrons distributed among eight orbitals, which include 1s, all valence, and 3s orbital of carbon. The carbon

For the

All

In order to cover the region of spectroscopic interest with two deep potential wells,

We concentrate on the geometries with the CH bond length smaller than 3.0 bohrs in the process of the present PES construction. Dozens of geometries are also selected for the description of the higher energy regions. In the important regions, points were computed with small increments of 0.1–0.5 bohrs for bond length and 2.0–5.0° for bond angle, while in other regions coarser grids of 1.0-2.0 bohrs and 10.0–20.0° were used. Geometries with energies higher than 100 kcal/mol above the global minimum of

To construct the PESs for the _{2}, we choose three-body expansion functional forms for the analytical representation of the PESs with respect to the internal coordinates _{2}, resp.). Then, a set of higher-level points with the CV effect, calculated at the

By applying the Levenberg-Marquardt technique for the nonlinear optimization, it was found that there are numerical problems for

For the analytical representation of

The parameters

The core correlation surface

To fit the matrix elements of

Many test calculations were performed with different polynomial orders ^{−1} for the ^{−1}, respectively. In the fit of ^{−1} for the ^{−1}, respectively. The numerical values of all parameters to generate the surfaces and coupling terms reported in the present study are presented in Tables S2, S3, and S4.

Figure

(a) Contour plot for the _{2} as a function of _{2} as a function of _{2} asymptote.

Contour plots for the _{2} asymptote.

Two adiabatic potentials for the _{2}, which are going to be degenerate at linearity, are represented as follows:

From the experimental side, a wide number of studies have led to the determination of accurate equilibrium geometries for the _{2}. Geometries and relative energies of minima obtained from our work along with the available experimental and other theoretical values are given in Table _{2} available, ^{−1}. The inclusion of core and core-valence correlation decreases the bond lengths by 0.0051 and 0.0016 bohrs and increases the bond angle by 0.28 and 1.48° for the

Geometries and relative energies of the minima of the two lowest-lying singlet states of CH_{2}.

Geometries |
Relative energies^{−1})* | |||

^{a} | 2.0965 | 102.10 | −100.54 | |

^{b} | 2.0914 | 102.38 | −100.70 | |

Our PESs^{c} | 2.0920 | 102.45 | −100.70 | |

Liu et al.^{d} | 2.098 | 102.0 | −100.3 | |

Flores and Gdanitz^{e} | 2.0917 | 102.31 | ||

Bussery-Honvault et al.^{f} | 2.09 | 102.5 | −99.7 | |

DMBE^{g} | 2.09 | 102.4 | −99.75 | |

Exp.^{h} | 2.099 | 102.38 | ||

Exp.^{i} | ||||

^{a} | 2.0316 | 143.12 | −77.71 | |

^{b} | 2.0300 | 144.60 | −77.96 | |

Our PESs^{c} | 2.0300 | 144.36 | −77.97 | |

Liu et al.^{d} | 2.032 | 143.2 | −76.8 | |

Flores and Gdanitz^{e} | 2.0165 | 143.39 | ||

Bussery-Honvault et al.^{f} | 2.02 | 141 | −79.9 | |

Exp.^{h} | 1.990 | |||

Exp.^{j} | 2.052 | 139.30 |

*Energies are relative to the C(_{2} asymptote.

^{
a}Our

^{
b}Our

^{
c}From our PESs.

^{
d}

^{
e}

^{
f}PES values from [

^{
g}PES values from [

^{
h}Experimental values from [

^{
i}Experimental values from [

^{
j}Experimental values from [

Contour plot (cm^{−1}) for _{2} as a function of

The

The bending potential energy curves for the four singlet states (_{2} calculated at the _{2} (

While the energy changes with the CH bond stretched, the degeneracy of the _{2} is not lifted so long as the molecule is linear. The barrier to linearity plays a very important role in quantum mechanical calculations of vibronic energy levels when the RT effect is considered [_{2} has been a long standing source of controversy. The range of reported barrier heights for linearity in the _{2} is quite large, varying from 8000 to 10000 cm^{−1} , which is summarized in Table ^{−1}, estimated from the spacing of the ^{−1} by fitting a bending potential function to the (^{−1} [^{−1}. In 2009, the DMBE PES predicted 9644 cm^{−1} in agreement with the experimental determination of 9800 cm^{−1} [

The barrier to linearity of the

Barrier to linearity | Note | |

^{−1}) | ^{−1}) | |

9073.5 | 885.2 | Our calculation at |

8895.1 | 907.3 | Our calculation at |

8735.8 | 706.2 | Our calculation at |

8715.1 | 760.2 | Our PESs |

8800 | The empirically adjusted value based on the visible spectra^{a} | |

8797 | ^{b} | |

8666 | 725 | The fit of empirically spectra and ^{c} |

The derived value from experiment^{d} | ||

8000 | The derived value from experiment^{e} | |

9217.7 | 953.2 | ^{f} |

9644 | ^{g} | |

9451.1 | 1193.0 | Others^{h} |

Others^{i} | ||

9600 | Others^{j} | |

9870 | Others^{k} | |

9144 | 879 | Others^{l} |

9356 | 1049 | Others^{m} |

^{
a}From Ref. [^{b}From [^{c}From [^{d}From [^{e}From [^{f}From [^{g}From [^{h}From [^{i}From [^{j}From [^{k}From [^{l}From [^{m}From [

Green Jr. et al. [^{−1} and empirically adjusted it to about 8800 cm^{−1} according to the visible spectra around 15000 cm^{−1}. And this value is in very good agreement with the derived value of 8600 ± 400 cm^{−1} from the experiment by Hartland et al. [^{−1} was obtained from the PESs constructed by Gu et al. [^{−1} based upon the ^{−1}, but when the core correlation is taken into account, we obtain the ^{−1}. The core correlations reduce this value by 160 cm^{−1}. It may be due to the fact that the ^{2}^{−1} for the barriers to linearity in the _{2}, respectively.

The fit of the RT nonadiabatic coupling terms has an RMS error of 0.0060, 0.0225, and 0.0148 for _{2} as functions of bond length

The stretching potential curves of the five singlet states (_{2} as functions of the bond length _{2} (

In Figure _{2} as function of CH stretching and

Contour plots for the Renner-Teller terms of CH_{2} for the two lowest-lying singlet electronic states as functions of

The Renner-Teller terms (_{2} for the two lowest-lying singlet electronic states as functions of the bending angle ∠HCH, with the CH-distance optimized for the

We have calculated the vibronic energy levels of the

The calculated ^{−1}, relative to the zero point energy of the

Green Jr. et al.^{a} | Gu et al.^{b} | Ours | Expt. | ||||
---|---|---|---|---|---|---|---|

0 | 1 | 0 | 1356 | 1351.2 | 1350.9 | 1352.6^{d} | |

0 | 2 | 0 | 2675 | 2664.1 | 2666.9 | 2667.7^{d} | |

1 | 0 | 0 | 2808 | 2807.5 | 2808.9 | 2806.0^{e} | |

0 | 0 | 1 | 2863 | 2864.5 | 2862.5 | 2865.0^{e} | |

0 | 3 | 0 | 3962 | 3945.6 | 3950.6 | 3950.5^{d} | |

1 | 1 | 0 | 4159 | 4156.5 | 4150.4 | 4152.8^{f} | |

0 | 4 | 0 | 5216 | 5191.5 | 5199.2 | 5196.6^{d} | |

1 | 2 | 0 | 5452 | 5437.6 | 5444.1 | 5444.9^{f} | |

2 | 0 | 0 | 5538 | 5529.3 | 5529.3 | 5531.4^{f} | |

0 | 5 | 0 | 6430 | 6397.9 | 6406.8 | 6403.0^{d,f} | |

1 | 3 | 0 | 6706.4 | 6712.0 | 6714.1^{f} | ||

0 | 0 | 0 | 8383 | 8354 | 8349 | 8350^{h} | |

0 | 1 | 0 | 9566 | 9537 | 9534 | 9537^{h} | |

0 | 2 | 0 | 10848 | 10831 | 10828 | 10827^{h,i} | |

0 | 3 | 0 | 12231 | 12226 | 12220 | 12220^{g,i,j} | |

0 | 4 | 0 | 13681 | 13684 | 13673 | 13678^{g} | |

1 | 2 | 0 | 13850 | 13840 | 13835 | 13834^{g} | |

1 | 3 | 0 | 15116 | 15121 | 15106 | 15114^{g} | |

0 | 5 | 0 | 15317 | 15326 | 15313 | 15319^{g} | |

2 | 2 | 0 | 16749 | 16749 | 16738 | 16742^{k} | |

0 | 6 | 0 | 16929 | 16948 | 16934 | 16941^{c,g} | |

1 | 5 | 0 | 18186 | 18201 | 18182 | 18192^{k} | |

0 | 7 | 0 | 18590 | 18617 | 18603 | 18610^{c,g} |

^{
a}From [^{b}From [^{c}From [^{d}From [^{e}From [^{f}From [^{g}From [^{h}From [^{i}From [^{j}From [^{k}From [

Our calculated results are in excellent agreement with the experimental values, reflecting the accuracy of the constructed ^{−1} is closer to the experimental value 10827 cm^{−1} from Sears et al. [^{−1} from Herzberg and Johns [

In this work, we report fully _{2} suitable for the spectroscopic study, based on the _{2} electronic states. The analytical representations of the two lowest-lying singlet PESs, with the inclusion of the matrix elements of electronic angular momentum _{2} reactive scattering studies, is in progress, and various PES intersections as revealed in our previous work [

This work is supported by National Natural Science Foundation of China (nos. 20733005 and 21173232), Chinese Academy of Sciences, and Beijing National Laboratory for Molecular Sciences. The authors would like to thank Professor H. Partridge for useful discussions of the modified basis set

_{2}. I. Potential energy surfaces of the dissociation into CH and H

_{2}

_{2}revisited

_{2}(

_{2 }and CD

_{2}

_{2}v

_{2}= 2

_{2}by flash photolysis stimulated emission pumping

_{2}

_{2}

_{2}near 9500

_{2}

_{2}

_{2}by frequency modulated diode laser absorption

_{2}near 1.36 and 0.92

_{2}near 780 nm

_{2}

_{2}

_{2}(

^{2}

^{2}

^{2}

_{2}in the near ultraviolet

_{2}and quantum dynamics of a sideways insertion mechanism for the

^{3}P) with isobutene

_{2}(2

^{3}

^{′′,3}3

^{3}

_{2}S(

_{3}, S

_{3}, SO

_{2}, and S

_{2}O

_{4}abstraction reaction using an

_{2}

_{2}reactive system

_{12}-)MR-CI. VIII. Valence excited states of methylene (CH

_{2})

_{2}The Renner-Teller effect

^{1}CH

_{2}: The analysis of the

_{2}

_{2}(