also show discrepancies larger than the reported uncertainties (see bottom of Table 10). For the vertical transition energy, our TBE/aug-cc-pVTZ is the same as the result of a CIPSI calculation performed with the same basis set, and logically exceeds the experimental 0-0 energy. For the ES dipole we are aware of two experiments,¹⁸⁴,¹⁸⁵ but the former investigated $\mu_a$ (one of the two dipole components) only. The most recent experiment yields a total $\mu^{\text{ES}}$ of 1.69±0.01 D,¹⁸⁵ which indicates a very slight increase as compared to the GS dipole. Our $\mu_{\text{vert}}^{\text{ES}}$ (1.69±0.01 D) and $\mu_{\text{adia}}^{\text{ES}}$ (1.80±0.01 D) values apparently slightly undershoots and overestimates the measured change of dipole moment. Again, the final call on the relative accuracy of theory and experiment is hard to make.

<table><caption>Table 11: Ground-state dipole moment $\mu^{\text{GS}}$, vertical transition energies $\Delta E_{\text{vert}}$, oscillator strengths $f$, and excited state dipole moments, $\mu_{\text{vert}}^{\text{ES}}$ and $\mu_{\text{adia}}^{\text{ES}}$, determined of fluorocarbene. We report the norm of the dipoles. See caption of Table 1 for details.</caption><thead><tr><th rowspan="2">Basis</th><th rowspan="2">Method</th><th colspan="2">$1A'$</th><th colspan="2">$1A''$</th></tr><tr><th>$\mu^{\text{GS}}$</th><th>$\Delta E_{\text{vert}}$</th><th>$f$</th><th>$\mu_{\text{vert}}^{\text{ES}}$</th></tr></thead><tbody><tr><td rowspan="4">6-31+G(d)</td><td>CCSD</td><td>1.572</td><td>2.581</td><td>0.009</td><td>1.316</td></tr><tr><td>CCSDT</td><td>1.552</td><td>2.573</td><td>0.009</td><td>1.287</td></tr><tr><td>CCSDTQ</td><td>1.549</td><td>2.577</td><td>0.009</td><td>1.282</td></tr><tr><td>CCSDTQP</td><td>1.549</td><td>2.578</td><td>0.009</td><td>1.282</td></tr><tr><td rowspan="4">aug-cc-pVDZ</td><td>CCSD</td><td>1.451</td><td>2.541</td><td>0.007</td><td>0.991</td></tr><tr><td>CCSDT</td><td>1.430</td><td>2.529</td><td>0.006</td><td>0.970</td></tr><tr><td>CCSDTQ</td><td>1.428</td><td>2.534</td><td>0.006</td><td>0.965</td></tr><tr><td>CCSD</td><td>1.465</td><td>2.507</td><td>0.006</td><td>0.991</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>CCSD</td><td>1.441</td><td>2.493</td><td>0.006</td><td>0.969</td></tr><tr><td>CCSDT</td><td>1.468</td><td>2.500</td><td>0.006</td><td>0.994</td></tr><tr><td rowspan="2">d-aug-cc-pVDZ</td><td>CCSD</td><td>1.445</td><td>2.536</td><td>0.006</td><td>0.978</td></tr><tr><td>CCSDT</td><td>1.425</td><td>2.524</td><td>0.006</td><td>0.958</td></tr><tr><td rowspan="2">d-aug-cc-pVTZ</td><td>CCSD</td><td>1.461</td><td>2.505</td><td>0.006</td><td>0.987</td></tr><tr><td>CCSDT</td><td>1.437</td><td>2.491</td><td>0.006</td><td>0.965</td></tr><tr><td>d-aug-cc-pVQZ</td><td>CCSD</td><td>1.468</td><td>2.500</td><td>0.006</td><td>0.994</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>TBE<sup>a</sup></td><td>1.438</td><td>2.498</td><td>0.006</td><td>0.964</td></tr><tr><td>TBE<sup>b</sup></td><td>1.44±0.01</td><td>2.48±0.01</td><td>0.006±0.001</td><td>0.97±0.01</td></tr><tr><td rowspan="2">CBS</td><td>Th.</td><td>1.426<sup>c</sup></td><td>2.49<sup>d</sup></td><td>0.006<sup>e</sup></td><td></td></tr><tr><td>Exp.</td><td>1.403<sup>f</sup></td><td>2.14<sup>g</sup></td><td></td><td></td></tr></tbody></table>

a,b See corresponding footnotes in Table 7; c CISD value from Ref. 187;

d exFCI/aug-cc-pVTZ transition energies corrected for basis set effects up to aug-cc-pV5Z from Ref. 8; e LR-CC3/aug-cc-pVTZ f from Ref. 8;

f From Stark effects measurements (Ref. 186); g Experiment 0-0 energy from Ref. 188.

Table 11 provides the dipole moments, oscillator strength, and transition energies for the smallest halocarbene, HCF, a system isoelectronic to the previous one. Although we note a small oscillation of the GS dipole and transition energies going from CCSD to CCSDT and CCSDTQ, it is obvious that the convergence with respect to the CC order is fast. Likewise, basis set effects are moderate in the Dunning series, whereas the use of Pople's basis set yields grossly overestimated oscillator strengths, and ES dipole moments. In short reaching accurate values is not problematic. Our TBE/CBS for $\mu^{\text{GS}}$, 1.44±0.01 D, is very close to an earlier CISD estimate, (1.43 D)¹⁸⁷ and both are slightly larger than the most recent measurement we are aware of (1.40 D).¹⁸⁹ As for ni-

troxyl, our TBE for the vertical transition energy is equivalent to the result of a recent CIPSI calculation, and both are logically larger than the experimental 0-0 energy. The small oscillator strength determined here is also the same as our CC3/aug-cc-pVTZ value. We could not find previous estimates of the ES dipole in the literature, and our calculations yield a decrease of ca. 50% as compared to the ground state value, which contrasts with the very similar values obtained for the two states of HNO.

### 3.9 Silylidene

Let us finish our tour by considering silylidene, $H_2C=Si$, a small original molecule presenting two well-defined low-lying Rydberg ES.¹⁹¹⁻¹⁹³ Our results are collected in Table 12. The values of $\mu^{\text{GS}}$ are small in magnitude for all methods and one notes that CCSD significantly overestimates the dipole whereas one needs at least a triple-$\zeta$ basis set to obtain reasonable data. Our TBE of 0.16 D for the GS dipole is close to the only previous theoretical value we found.¹⁹⁰ There is, to the best of our knowledge, no experimental measurement available. The values of $\Delta E_{\text{vert}}$ of the two lowest transitions are insensitive to the addition of quadruples in the CC series and they converge quite well with respect to the basis set size. The current TBEs are equal to the ones we obtained earlier applying a different strategy to reach the FCI limit,⁷ and they remain slightly larger than the experimental 0-0 energies.¹⁹¹,¹⁹² For the two ESs, we disclose here the two first estimates of the dipole moments. For the lowest excitation, the dipole clearly flips direction as compared to the GS, which contrasts with thioformaldehyde, and also becomes much larger than the GS dipole with a trustworthy TBE of -1.92±0.01 D. For the second ES, all methods predict relatively small $\mu_{\text{vert}}^{\text{ES}}$ values, with the CCSD and CCSDT signs sometimes in disagreement for a given basis set. Although the addition of a second set of diffuse orbitals has a quite small effect, the convergence with the size of the basis is quite slow, and we can only state that the final dipole should be almost null, though its sign remains unknown. Finally, one notes that 6-31+G(d) provides too large oscillator strengths for the second ES, but that the stability is otherwise remarkable. One can likely be confident in the proposed TBE value (0.034).

### 4. CONCLUSIONS

In this contribution, we have considered 30 singlet excited states in thirteen small molecules and strived to obtain oscillator strengths and dipole moments as accurate as possible. To this end, we have performed a series of CC calculations going from (LR) CCSD to CCSDTQP using a large panel of basis sets containing one or two sets of diffuse functions. In all cases, we have obtained FCI/aug-cc-pVTZ quality properties, as well as estimates of the corresponding FCI/CBS values, the latter coming with quite large uncertainties in some cases. While FCI results do obviously yield rather definitive answers, we treated only small molecules here with computationally expensive methods, so that the transferability of this strategy to larger compounds is indeed limited. Regarding the CC expansion, we found that the correction brought by the P term is always negligible, whereas the impact of Q is often rather small, although some exceptions
also show discrepancies larger than the reported uncertainties (see bottom of Table 10). For the vertical transition energy, our TBE/aug-cc-pVTZ is the same as the result of a CIPSI calculation performed with the same basis set, and logically exceeds the experimental 0-0 energy. For the ES dipole we are aware of two experiments,¹⁸⁴,¹⁸⁵ but the former investigated $\mu_a$ (one of the two dipole components) only. The most recent experiment yields a total $\mu^{\text{ES}}$ of 1.69±0.01 D,¹⁸⁵ which indicates a very slight increase as compared to the GS dipole. Our $\mu_{\text{vert}}^{\text{ES}}$ (1.69±0.01 D) and $\mu_{\text{adia}}^{\text{ES}}$ (1.80±0.01 D) values apparently slightly undershoots and overestimates the measured change of dipole moment. Again, the final call on the relative accuracy of theory and experiment is hard to make.

<table><caption>Table 11: Ground-state dipole moment $\mu^{\text{GS}}$, vertical transition energies $\Delta E_{\text{vert}}$, oscillator strengths $f$, and excited state dipole moments, $\mu_{\text{vert}}^{\text{ES}}$ and $\mu_{\text{adia}}^{\text{ES}}$, determined of fluorocarbene. We report the norm of the dipoles. See caption of Table 1 for details.</caption><thead><tr><th rowspan="2">Basis</th><th rowspan="2">Method</th><th colspan="2">$^1A'$</th><th colspan="2">$^1A''$</th></tr><tr><th>$\mu^{\text{GS}}$</th><th>$\Delta E_{\text{vert}}$</th><th>$f$</th><th>$\mu_{\text{vert}}^{\text{ES}}$</th></tr></thead><tbody><tr><td rowspan="4">6-31+G(d)</td><td>CCSD</td><td>1.572</td><td>2.581</td><td>0.009</td><td>1.316</td></tr><tr><td>CCSDT</td><td>1.552</td><td>2.573</td><td>0.009</td><td>1.287</td></tr><tr><td>CCSDTQ</td><td>1.549</td><td>2.577</td><td>0.009</td><td>1.282</td></tr><tr><td>CCSDTQP</td><td>1.549</td><td>2.578</td><td>0.009</td><td>1.282</td></tr><tr><td rowspan="4">aug-cc-pVDZ</td><td>CCSD</td><td>1.451</td><td>2.541</td><td>0.007</td><td>0.991</td></tr><tr><td>CCSDT</td><td>1.430</td><td>2.529</td><td>0.006</td><td>0.970</td></tr><tr><td>CCSDTQ</td><td>1.428</td><td>2.534</td><td>0.006</td><td>0.965</td></tr><tr><td>CCSD</td><td>1.465</td><td>2.507</td><td>0.006</td><td>0.991</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>CCSD</td><td>1.441</td><td>2.493</td><td>0.006</td><td>0.969</td></tr><tr><td>CCSDT</td><td>1.468</td><td>2.500</td><td>0.006</td><td>0.994</td></tr><tr><td rowspan="2">d-aug-cc-pVDZ</td><td>CCSD</td><td>1.445</td><td>2.536</td><td>0.006</td><td>0.978</td></tr><tr><td>CCSDT</td><td>1.425</td><td>2.524</td><td>0.006</td><td>0.958</td></tr><tr><td rowspan="2">d-aug-cc-pVTZ</td><td>CCSD</td><td>1.461</td><td>2.505</td><td>0.006</td><td>0.987</td></tr><tr><td>CCSDT</td><td>1.437</td><td>2.491</td><td>0.006</td><td>0.965</td></tr><tr><td>d-aug-cc-pVQZ</td><td>CCSD</td><td>1.468</td><td>2.500</td><td>0.006</td><td>0.994</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>TBE<sup>a</sup></td><td>1.438</td><td>2.498</td><td>0.006</td><td>0.964</td></tr><tr><td>TBE<sup>b</sup></td><td>1.44±0.01</td><td>2.48±0.01</td><td>0.006±0.001</td><td>0.97±0.01</td></tr><tr><td rowspan="2">CBS</td><td>Th.</td><td>1.426<sup>c</sup></td><td>2.49<sup>d</sup></td><td>0.006<sup>e</sup></td><td></td></tr><tr><td>Exp.</td><td>1.403<sup>f</sup></td><td>2.14<sup>g</sup></td><td></td><td></td></tr></tbody></table>

a,b See corresponding footnotes in Table 7; c CISD value from Ref. 187;

d exFCI/aug-cc-pVTZ transition energies corrected for basis set effects up to aug-cc-pV5Z from Ref. 8; e LR-CC3/aug-cc-pVTZ f from Ref. 8;

f From Stark effects measurements (Ref. 186); g Experiment 0-0 energy from Ref. 188.

Table 11 provides the dipole moments, oscillator strength, and transition energies for the smallest halocarbene, HCF, a system isoelectronic to the previous one. Although we note a small oscillation of the GS dipole and transition energies going from CCSD to CCSDT and CCSDTQ, it is obvious that the convergence with respect to the CC order is fast. Likewise, basis set effects are moderate in the Dunning series, whereas the use of Pople's basis set yields grossly overestimated oscillator strengths, and ES dipole moments. In short reaching accurate values is not problematic. Our TBE/CBS for $\mu^{\text{GS}}$, 1.44±0.01 D, is very close to an earlier CISD estimate, (1.43 D)¹⁸⁷ and both are slightly larger than the most recent measurement we are aware of (1.40 D).¹⁸⁹ As for ni-

troxyl, our TBE for the vertical transition energy is equivalent to the result of a recent CIPSI calculation, and both are logically larger than the experimental 0-0 energy. The small oscillator strength determined here is also the same as our CC3/aug-cc-pVTZ value. We could not find previous estimates of the ES dipole in the literature, and our calculations yield a decrease of ca. 50% as compared to the ground state value, which contrasts with the very similar values obtained for the two states of HNO.

### 3.9 Silylidene

Let us finish our tour by considering silylidene, $H_2C=Si$, a small original molecule presenting two well-defined low-lying Rydberg ES.¹⁹¹⁻¹⁹³ Our results are collected in Table 12. The values of $\mu^{\text{GS}}$ are small in magnitude for all methods and one notes that CCSD significantly overestimates the dipole whereas one needs at least a triple-$\zeta$ basis set to obtain reasonable data. Our TBE of 0.16 D for the GS dipole is close to the only previous theoretical value we found.¹⁹⁰ There is, to the best of our knowledge, no experimental measurement available. The values of $\Delta E_{\text{vert}}$ of the two lowest transitions are insensitive to the addition of quadruples in the CC series and they converge quite well with respect to the basis set size. The current TBEs are equal to the ones we obtained earlier applying a different strategy to reach the FCI limit,⁷ and they remain slightly larger than the experimental 0-0 energies.¹⁹¹,¹⁹² For the two ESs, we disclose here the two first estimates of the dipole moments. For the lowest excitation, the dipole clearly flips direction as compared to the GS, which contrasts with thioformaldehyde, and also becomes much larger than the GS dipole with a trustworthy TBE of -1.92±0.01 D. For the second ES, all methods predict relatively small $\mu_{\text{vert}}^{\text{ES}}$ values, with the CCSD and CCSDT signs sometimes in disagreement for a given basis set. Although the addition of a second set of diffuse orbitals has a quite small effect, the convergence with the size of the basis is quite slow, and we can only state that the final dipole should be almost null, though its sign remains unknown. Finally, one notes that 6-31+G(d) provides too large oscillator strengths for the second ES, but that the stability is otherwise remarkable. One can likely be confident in the proposed TBE value (0.034).

### 4. CONCLUSIONS

In this contribution, we have considered 30 singlet excited states in thirteen small molecules and strived to obtain oscillator strengths and dipole moments as accurate as possible. To this end, we have performed a series of CC calculations going from (LR) CCSD to CCSDTQP using a large panel of basis sets containing one or two sets of diffuse functions. In all cases, we have obtained FCI/aug-cc-pVTZ quality properties, as well as estimates of the corresponding FCI/CBS values, the latter coming with quite large uncertainties in some cases. While FCI results do obviously yield rather definitive answers, we treated only small molecules here with computationally expensive methods, so that the transferability of this strategy to larger compounds is indeed limited. Regarding the CC expansion, we found that the correction brought by the P term is always negligible, whereas the impact of Q is often rather small, although some exceptions
<table><caption>Table 12: Ground-state dipole moment $\mu^{GS}$, vertical transition energies $\Delta E_{\text{vert}}$, oscillator strengths $f$, and excited state dipole moments $\mu_{\text{vert}}^{\text{ES}}$ determined of silylidene (GS geometry). See caption of Table 1 for details.</caption><thead><tr><th rowspan="2">Basis</th><th rowspan="2">Method</th><th colspan="2"><sup>1</sup>A<sub>1</sub></th><th colspan="2">Ryd</th><th colspan="2"><sup>1</sup>B<sub>2</sub>(Ryd)</th></tr><tr><th>μ<sup>GS</sup></th><th>ΔE<sub>vert</sub></th><th>μ<sup>ES</sup><sub>vert</sub></th><th>ΔE<sub>vert</sub></th><th>f</th><th>μ<sup>ES</sup><sub>vert</sub></th></tr></thead><tbody><tr><td rowspan="4">6-31+G(d)</td><td>CCSD</td><td>0.091</td><td>2.254</td><td>-1.845</td><td>3.966</td><td>0.045</td><td>-0.080</td></tr><tr><td>CCSDT</td><td>0.028</td><td>2.107</td><td>-1.891</td><td>3.874</td><td>0.042</td><td>-0.237</td></tr><tr><td>CCSDTQ</td><td>0.019</td><td>2.101</td><td>-1.909</td><td>3.876</td><td>0.042</td><td>-0.256</td></tr><tr><td>CCSDTQP</td><td>0.018</td><td>2.101</td><td>-1.911</td><td>3.877</td><td>0.042</td><td>-0.259</td></tr><tr><td rowspan="4">aug-cc-pVDZ</td><td>CCSD</td><td>0.181</td><td>2.289</td><td>-1.836</td><td>3.875</td><td>0.036</td><td>0.162</td></tr><tr><td>CCSDT</td><td>0.115</td><td>2.146</td><td>-1.889</td><td>3.795</td><td>0.034</td><td>0.005</td></tr><tr><td>CCSDTQ</td><td>0.105</td><td>2.140</td><td>-1.905</td><td>3.798</td><td>0.034</td><td>-0.012</td></tr><tr><td>CCSDT</td><td>0.235</td><td>2.286</td><td>-1.851</td><td>3.877</td><td>0.036</td><td>0.161</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>CCSD</td><td>0.153</td><td>2.128</td><td>-1.905</td><td>3.779</td><td>0.033</td><td>-0.018</td></tr><tr><td>CCSDT</td><td>0.249</td><td>2.301</td><td>-1.848</td><td>3.891</td><td>0.037</td><td>0.186</td></tr><tr><td rowspan="4">d-aug-cc-pVDZ</td><td>CCSD</td><td>0.187</td><td>2.290</td><td>-1.831</td><td>3.876</td><td>0.036</td><td>0.164</td></tr><tr><td>CCSDT</td><td>0.121</td><td>2.146</td><td>-1.885</td><td>3.796</td><td>0.034</td><td>0.007</td></tr><tr><td>CCSDT</td><td>0.236</td><td>2.287</td><td>-1.848</td><td>3.877</td><td>0.036</td><td>0.166</td></tr><tr><td>CCSDT</td><td>0.155</td><td>2.130</td><td>-1.902</td><td>3.779</td><td>0.033</td><td>-0.014</td></tr><tr><td>d-aug-cc-pVQZ</td><td>CCSD</td><td>0.249</td><td>2.301</td><td>-1.847</td><td>3.890</td><td>0.037</td><td>0.186</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>TBE<sup>a</sup></td><td>0.142</td><td>2.122</td><td>-1.924</td><td>3.783</td><td>0.034</td><td>-0.039</td></tr><tr><td>TBE<sup>b</sup></td><td>0.16±0.01</td><td>2.15±0.00</td><td>-1.92±0.01</td><td>3.81±0.01</td><td>0.034±0.01</td><td>0.00±0.04</td></tr><tr><td rowspan="2">CBS</td><td>Lit.</td><td>0.144<sup>c</sup></td><td>2.12<sup>d</sup></td><td></td><td>3.80<sup>d</sup></td><td>0.033<sup>e</sup></td><td></td></tr><tr><td>Th.</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>Exp.</td><td></td><td>1.88<sup>f</sup></td><td></td><td>3.63<sup>g</sup></td><td></td><td></td></tr></tbody></table>

a,b See corresponding footnotes in Table 7; c CCSD(T)/cc-pVCQZ from Ref. 190; d exFCI/aug-cc-pVTZ transition energies corrected for basis set effects up to aug-cc-pV5Z from Ref. 8; e LR-CC3/aug-cc-pVTZ f from Ref. 8; g 0-0 energy from Ref. 191; h 0-0 energy from Ref. 192.

to the latter statement have been observed for the considered set. For instance, a reduction of the oscillator strength and ES dipole by -15% and -0.40 D, respectively, is observed for the valence $\pi \rightarrow \pi^*$ transition of thioformaldehyde. More problematic is the convergence of the computed properties while increasing the size of the atomic basis set: this convergence can go from very smooth to erratic. For some states, huge differences between the results obtained with simply- and doubly-augmented basis sets are indeed found. The oscillator strengths determined for the three close-lying $\Pi_u$ excited states of dinitrogen being a typical example of this problem caused by state mixing. All in all, when choices have to be made, it seems a better option to use CCSDT with a very large basis set rather than CCSDTQ with a smaller one when one wishes to perform comparisons with experiment, which as explained in the Introduction is always a challenging task. We have also found several examples herein in which one property, e.g., the oscillator strength, is rather independent from the selected basis set, whereas another, e.g., the ES dipole, is not. One must therefore carefully check the basis set convergence and dependence for all considered states and properties.

Despite these challenges, it is certainly noteworthy that for the vast majority of the properties studied here, we could not only establish the most accurate theoretical estimates available to date, but also obtain values that are compatible with the experimental knowledge when these are accessible, which is not always the case even for the small molecules considered here. Theory sometimes deliver smaller error bars than the corresponding experimental data. This is certainly the case for the smallest compounds treated here, for which very large basis sets could be employed. It should be stressed that the measurements of both $f$ and $\mu^{\text{ES}}$ are difficult, so

that depending on the experimental techniques, apparently incompatible results are quite commonly reported and that the role of theory is likely critical. At this stage, it might be important to recall that we did not use any experimental input, as even our geometries are theoretically determined. The present effort is thus truly *ab initio*. However, it only provides an idealized picture as we did not aim at modeling vibronic effects.

As we expected at the beginning of the study, getting the right answer for the right reason in the context of ES properties is certainly more challenging than for the corresponding energies. It is therefore our hope that the reference values reported here will be useful benchmarks and will stimulate further studies in both the theoretical and experimental communities.

## ACKNOWLEDGEMENTS

AC and DJ are indebted to the LumoMat program for support in the framework of the Fluo-34 grant. PFL thanks the Centre National de la Recherche Scientifique for funding. This research used resources of (i) the GENCI-TGCC (Grant No. 2019-A0060801738); (ii) CALMIP under allocation 2020-18005 (Toulouse); (iii) CCIPL (Centre de Calcul Intensif des Pays de Loire); (iv) a local Troy cluster and (v) HPC resources from ArronaxPlus (grant ANR-11-EQPX-0004 funded by the French National Agency for Research).

## SUPPORTING INFORMATION AVAILABLE

Extra data and Cartesian coordinates. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/doi.
<table><caption>Table 12: Ground-state dipole moment $\mu^{\text{GS}}$, vertical transition energies $\Delta E_{\text{vert}}$, oscillator strengths $f$, and excited state dipole moments $\mu_{\text{vert}}^{\text{ES}}$ determined of silylidene (GS geometry). See caption of Table 1 for details.</caption><thead><tr><th rowspan="2">Basis</th><th rowspan="2">Method</th><th colspan="2"><sup>1</sup>A<sub>1</sub></th><th colspan="2">Ryd</th><th colspan="2"><sup>1</sup>B<sub>2</sub>(Ryd)</th></tr><tr><th>μ<sup>GS</sup></th><th>ΔE<sub>vert</sub></th><th>μ<sup>ES</sup><sub>vert</sub></th><th>ΔE<sub>vert</sub></th><th>f</th><th>μ<sup>ES</sup><sub>vert</sub></th></tr></thead><tbody><tr><td rowspan="4">6-31+G(d)</td><td>CCSD</td><td>0.091</td><td>2.254</td><td>-1.845</td><td>3.966</td><td>0.045</td><td>-0.080</td></tr><tr><td>CCSDT</td><td>0.028</td><td>2.107</td><td>-1.891</td><td>3.874</td><td>0.042</td><td>-0.237</td></tr><tr><td>CCSDTQ</td><td>0.019</td><td>2.101</td><td>-1.909</td><td>3.876</td><td>0.042</td><td>-0.256</td></tr><tr><td>CCSDTQP</td><td>0.018</td><td>2.101</td><td>-1.911</td><td>3.877</td><td>0.042</td><td>-0.259</td></tr><tr><td rowspan="4">aug-cc-pVDZ</td><td>CCSD</td><td>0.181</td><td>2.289</td><td>-1.836</td><td>3.875</td><td>0.036</td><td>0.162</td></tr><tr><td>CCSDT</td><td>0.115</td><td>2.146</td><td>-1.889</td><td>3.795</td><td>0.034</td><td>0.005</td></tr><tr><td>CCSDTQ</td><td>0.105</td><td>2.140</td><td>-1.905</td><td>3.798</td><td>0.034</td><td>-0.012</td></tr><tr><td>CCSDT</td><td>0.235</td><td>2.286</td><td>-1.851</td><td>3.877</td><td>0.036</td><td>0.161</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>CCSD</td><td>0.153</td><td>2.128</td><td>-1.905</td><td>3.779</td><td>0.033</td><td>-0.018</td></tr><tr><td>CCSDT</td><td>0.249</td><td>2.301</td><td>-1.848</td><td>3.891</td><td>0.037</td><td>0.186</td></tr><tr><td rowspan="4">d-aug-cc-pVDZ</td><td>CCSD</td><td>0.187</td><td>2.290</td><td>-1.831</td><td>3.876</td><td>0.036</td><td>0.164</td></tr><tr><td>CCSDT</td><td>0.121</td><td>2.146</td><td>-1.885</td><td>3.796</td><td>0.034</td><td>0.007</td></tr><tr><td>CCSDT</td><td>0.236</td><td>2.287</td><td>-1.848</td><td>3.877</td><td>0.036</td><td>0.166</td></tr><tr><td>CCSDT</td><td>0.155</td><td>2.130</td><td>-1.902</td><td>3.779</td><td>0.033</td><td>-0.014</td></tr><tr><td>d-aug-cc-pVQZ</td><td>CCSD</td><td>0.249</td><td>2.301</td><td>-1.847</td><td>3.890</td><td>0.037</td><td>0.186</td></tr><tr><td rowspan="2">aug-cc-pVTZ</td><td>TBE<sup>a</sup></td><td>0.142</td><td>2.122</td><td>-1.924</td><td>3.783</td><td>0.034</td><td>-0.039</td></tr><tr><td>TBE<sup>b</sup></td><td>0.16±0.01</td><td>2.15±0.00</td><td>-1.92±0.01</td><td>3.81±0.01</td><td>0.034±0.01</td><td>0.00±0.04</td></tr><tr><td rowspan="2">CBS</td><td>Lit.</td><td>0.144<sup>c</sup></td><td>2.12<sup>d</sup></td><td></td><td>3.80<sup>d</sup></td><td>0.033<sup>e</sup></td><td></td></tr><tr><td>Th.</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>Exp.</td><td></td><td>1.88<sup>f</sup></td><td></td><td>3.63<sup>g</sup></td><td></td><td></td></tr></tbody></table>

a,b See corresponding footnotes in Table 7; c CCSD(T)/cc-pVCQZ from Ref. 190; d exFCI/aug-cc-pVTZ transition energies corrected for basis set effects up to aug-cc-pV5Z from Ref. 8; e LR-CC3/aug-cc-pVTZ f from Ref. 8; g 0-0 energy from Ref. 191; h 0-0 energy from Ref. 192.

to the latter statement have been observed for the considered set. For instance, a reduction of the oscillator strength and ES dipole by -15% and -0.40 D, respectively, is observed for the valence $\pi \rightarrow \pi^*$ transition of thioformaldehyde. More problematic is the convergence of the computed properties while increasing the size of the atomic basis set: this convergence can go from very smooth to erratic. For some states, huge differences between the results obtained with simply- and doubly-augmented basis sets are indeed found. The oscillator strengths determined for the three close-lying $\Pi_u$ excited states of dinitrogen being a typical example of this problem caused by state mixing. All in all, when choices have to be made, it seems a better option to use CCSDT with a very large basis set rather than CCSDTQ with a smaller one when one wishes to perform comparisons with experiment, which as explained in the Introduction is always a challenging task. We have also found several examples herein in which one property, e.g., the oscillator strength, is rather independent from the selected basis set, whereas another, e.g., the ES dipole, is not. One must therefore carefully check the basis set convergence and dependence for all considered states and properties.

Despite these challenges, it is certainly noteworthy that for the vast majority of the properties studied here, we could not only establish the most accurate theoretical estimates available to date, but also obtain values that are compatible with the experimental knowledge when these are accessible, which is not always the case even for the small molecules considered here. Theory sometimes deliver smaller error bars than the corresponding experimental data. This is certainly the case for the smallest compounds treated here, for which very large basis sets could be employed. It should be stressed that the measurements of both $f$ and $\mu^{\text{ES}}$ are difficult, so

that depending on the experimental techniques, apparently incompatible results are quite commonly reported and that the role of theory is likely critical. At this stage, it might be important to recall that we did not use any experimental input, as even our geometries are theoretically determined. The present effort is thus truly *ab initio*. However, it only provides an idealized picture as we did not aim at modeling vibronic effects.

As we expected at the beginning of the study, getting the right answer for the right reason in the context of ES properties is certainly more challenging than for the corresponding energies. It is therefore our hope that the reference values reported here will be useful benchmarks and will stimulate further studies in both the theoretical and experimental communities.

## ACKNOWLEDGEMENTS

AC and DJ are indebted to the LumoMat program for support in the framework of the Fluo-34 grant. PFL thanks the *Centre National de la Recherche Scientifique* for funding. This research used resources of (i) the GENCI-TGCC (Grant No. 2019-A0060801738); (ii) CALMIP under allocation 2020-18005 (Toulouse); (iii) CCIPL (*Centre de Calcul Intensif des Pays de Loire*); (iv) a local Troy cluster and (v) HPC resources from ArronaxPlus (grant ANR-11-EQPX-0004 funded by the French National Agency for Research).

## SUPPORTING INFORMATION AVAILABLE

Extra data and Cartesian coordinates. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/doi.
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(145) Head-Gordon, M.; Maurice, D.; Oumi, M. A Perturbative Correction to Restricted Open-Shell Configuration-Interaction with Single Substitutions for Excited-States of Radicals. *Chem. Phys. Lett.* **1995**, *246*, 114–121.

(146) Gwaltney, S. R.; Bartlett, R. J. An Application of the Equation-Of-Motion Coupled Cluster Method to the Excited States of Formaldehyde, Acetaldehyde, and Acetone. *Chem. Phys. Lett.* **1995**, *241*, 26–32.

(147) Wiberg, K. B.; Stratmann, R. E.; Frisch, M. J. A Time-Dependent Density Functional Theory Study of the Electronically Excited States of Formaldehyde, Acetaldehyde and Acetone. *Chem. Phys. Lett.* **1998**, *297*, 60–64.

(148) Wilberg, K. B.; de Oliveria, A. E.; Trucks, G. A Comparison of the Electronic Transition Energies for Ethene, Isobutene, Formaldehyde, and Acetone Calculated Using RPA, TDDFT, and EOM-CCSD. Effect of Basis Sets. *J. Phys. Chem. A* **2002**, *106*, 4192–4199.

(149) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. Excitation Energies in Density Functional Theory: an Evaluation and a Diagnostic Test. *J. Chem. Phys.* **2008**, *128*, 044118.

(150) Shen, J.; Li, S. Block Correlated Coupled Cluster Method with the Complete Active-Space Self-Consistent-Field Reference Function: Applications for Low-Lying Electronic Excited States. *J. Chem. Phys.* **2009**, *131*, 174101.

(151) Caricato, M.; Trucks, G. W.; Frisch, M. J.; Wiberg, K. B. Electronic Transition Energies: A Study of the Performance of a Large Range of Single Reference Density Functional and Wave Function Methods on Valence and Rydberg States Compared to Experiment. *J. Chem. Theory Comput.* **2010**, *6*, 370–383.

(152) Li, X.; Paldus, J. Multi-Reference State-Universal Coupled-Cluster Approaches to Electronically Excited States. *J. Chem. Phys.* **2011**, *134*, 214118.

(153) Leang, S. S.; Zahariev, F.; Gordon, M. S. Benchmarking the Performance of Time-Dependent Density Functional Methods. *J. Chem. Phys.* **2012**, *136*, 104101.

(154) Hoyer, C. E.; Ghosh, S.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration Pair-Density Functional Theory Is as Accurate as CASPT2 for Electronic Excitation. *J. Phys. Chem. Lett.* **2016**, *7*, 586–591.

(155) Kánnár, D.; Tajti, A.; Szalay, P. G. Accuracy of Coupled Cluster Excitation Energies in Diffuse Basis Sets. *J. Chem. Theory Comput.* **2017**, *13*, 202–209.

(156) Müller, T.; Lischka, H. Simultaneous Calculation of Rydberg and Valence Excited States of Formaldehyde. *Theor. Chem. Acc.* **2001**, *106*, 369–378.

(157) Hachey, M.; Bruna, P. J.; Grein, F. Configuration Interaction Studies on the $S_2$ Surface of $H_2CO$:
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(144) Head-Gordon, M.; Rico, R. J.; Oumi, M.; Lee, T. J. A Doubles Correction to Electronic Excited States From Configuration Interaction in the Space of Single Substitutions. *Chem. Phys. Lett.* **1994**, *219*, 21–29.

(145) Head-Gordon, M.; Maurice, D.; Oumi, M. A Perturbative Correction to Restricted Open-Shell Configuration-Interaction with Single Substitutions for Excited-States of Radicals. *Chem. Phys. Lett.* **1995**, *246*, 114–121.

(146) Gwaltney, S. R.; Bartlett, R. J. An Application of the Equation-Of-Motion Coupled Cluster Method to the Excited States of Formaldehyde, Acetaldehyde, and Acetone. *Chem. Phys. Lett.* **1995**, *241*, 26–32.

(147) Wiberg, K. B.; Stratmann, R. E.; Frisch, M. J. A Time-Dependent Density Functional Theory Study of the Electronically Excited States of Formaldehyde, Acetaldehyde and Acetone. *Chem. Phys. Lett.* **1998**, *297*, 60–64.

(148) Wilberg, K. B.; de Oliveria, A. E.; Trucks, G. A Comparison of the Electronic Transition Energies for Ethene, Isobutene, Formaldehyde, and Acetone Calculated Using RPA, TDDFT, and EOM-CCSD. Effect of Basis Sets. *J. Phys. Chem. A* **2002**, *106*, 4192–4199.

(149) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. Excitation Energies in Density Functional Theory: an Evaluation and a Diagnostic Test. *J. Chem. Phys.* **2008**, *128*, 044118.

(150) Shen, J.; Li, S. Block Correlated Coupled Cluster Method with the Complete Active-Space Self-Consistent-Field Reference Function: Applications for Low-Lying Electronic Excited States. *J. Chem. Phys.* **2009**, *131*, 174101.

(151) Caricato, M.; Trucks, G. W.; Frisch, M. J.; Wiberg, K. B. Electronic Transition Energies: A Study of the Performance of a Large Range of Single Reference Density Functional and Wave Function Methods on Valence and Rydberg States Compared to Experiment. *J. Chem. Theory Comput.* **2010**, *6*, 370–383.

(152) Li, X.; Paldus, J. Multi-Reference State-Universal Coupled-Cluster Approaches to Electronically Excited States. *J. Chem. Phys.* **2011**, *134*, 214118.

(153) Leang, S. S.; Zahariev, F.; Gordon, M. S. Benchmarking the Performance of Time-Dependent Density Functional Methods. *J. Chem. Phys.* **2012**, *136*, 104101.

(154) Hoyer, C. E.; Ghosh, S.; Truhlar, D. G.; Gagliardi, L. Multiconfiguration Pair-Density Functional Theory Is as Accurate as CASPT2 for Electronic Excitation. *J. Phys. Chem. Lett.* **2016**, *7*, 586–591.

(155) Kánnár, D.; Tajti, A.; Szalay, P. G. Accuracy of Coupled Cluster Excitation Energies in Diffuse Basis Sets. *J. Chem. Theory Comput.* **2017**, *13*, 202–209.

(156) Müller, T.; Lischka, H. Simultaneous Calculation of Rydberg and Valence Excited States of Formaldehyde. *Theor. Chem. Acc.* **2001**, *106*, 369–378.

(157) Hachey, M.; Bruna, P. J.; Grein, F. Configuration Interaction Studies on the $S_2$ Surface of $H_2CO$:
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(158) Gómez-Carrasco, S.; Müller, T.; Köppel, H. Ab Initio Study of the VUV-Induced Multistate Photodynamics of Formaldehyde. *J. Phys. Chem. A* **2010**, *114*, 11436–11449.

(159) Fabricant, B.; Krieger, D.; Muenter, J. S. Molecu- lar Beam Electric Resonance Study of Formaldehyde, Thioformaldehyde, and Ketene. *J. Chem. Phys.* **1977**, *67*, 1576–1586.

(160) Haner, D. A.; Dows, D. A. Electric-Field-Induced Spectra: Excited-State Dipole Moment from Line-Shape Analysis. *J. Chem. Phys.* **1968**, *49*, 601–605.

(161) Weiss, M. J.; Kuyatt, C. E.; Mielczarek, S. Inelas- tic Electron Scattering from Formaldehyde. *J. Chem. Phys.* **1971**, *54*, 4147–4150.

(162) Causley, G. C.; Russell, B. R. Electric Dipole Moment and Polarizability of the 1749 Å, $1^1B_2$ Excited State of Formaldehyde. *J. Chem. Phys.* **1978**, *68*, 3797–3800.

(163) Causley, G. C.; Russell, B. R. Electric Dichroism Spectroscopy in the Vacuum Ultraviolet. 2. Formalde- hyde, Acetaldehyde, adn Acetone. *J. Am. Chem. Soc.* **1979**, *101*, 5573–5578.

(164) Vaccaro, P. H.; Zabludoff, A.; Carrera-Patiño, M. E.; Kinsey, J. L.; Field, R. W. High Precision Dipole Mo- ments in Ā $1^1A_2$ Formaldehyde Determined via Stark Quantum Beat Spectroscopy. *J. Chem. Phys.* **1989**, *90*, 4150–4167.

(165) Cooper, G.; Anderson, J. E.; Brion, C. Absolute Pho- toabsorption and Photoionization of Formaldehyde in the VUV and Soft X-ray Regions (3–200 eV). *Chem. Phys.* **1996**, *209*, 61–77.

(166) Benková, Z.; Černušák, I.; Zahradník, P. Elec- tric Properties of Formaldehyde, Thioformaldehyde, Urea, Formamide, and Thioformamide – Post-HF and DFT Study. *Int. J. Quantum Chem.* **2007**, *107*, 2133– 2152.

(167) Clouthier, D. J.; Ramsay, D. A. The Spectroscopy of Formaldehyde and Thioformaldehyde. *Annu. Rev. Phys. Chem.* **1983**, *34*, 31–58.

(168) Suzuki, T.; Saito, S.; Hirota, E. Dipole Moments of H₂CS in the Ā$^1A_2(ν = 0)$ and $ā^3A_2(ν_3 = 1)$ States by MODR Spectroscopy. *J. Mol. Spectrosc.* **1985**, *111*, 54–61.

(169) Goetz, W.; Moule, D. C.; Ramsay, D. A. The Electric Dipole Moment of the $\tilde{C}^1B_2(3s \leftarrow n)$ State of Thio- formaldehyde. *Can. J. Phys.* **1981**, *59*, 1635–1639.

(170) Johnson, D. R.; Powell, F. X.; Kirchhoff, W. H. Microwave Spectrum, Ground State Structure, and Fipole Moment of Thioformaldehyde. *J. Mol. Spectrosc.* **1971**, *39*, 136–145.

(171) Fung, K. H.; Ramsay, D. A. Doppler-free Stark Spec- tra of the $4^1_0$ Band of the Ā$^1A_2 - \tilde{X}^1A_1$ System of Thioformaldehyde. *Mol. Phys.* **1996**, *88*, 997–1004.

(172) Freeman, D. E.; Klemperer, W. Dipole Moments of Excited Electronic States of Molecules: The $^1A_2$ State of Formaldehyde. *J. Chem. Phys.* **1964**, *40*, 604–605.

(173) Freeman, D. E.; Klemperer, W. Electric Dipole Mo- ment of the $^1A_2$ Electronic State of Formaldehyde. *J. Chem. Phys.* **1966**, *45*, 52–57.

(174) Bridge, N. J.; Haner, D. A.; Dows, D. A. Electric- Field-Induced Spectra: Theory and Experimental Study of Formaldehyde. *J. Chem. Phys.* **1968**, *48*, 4196–4210.

(175) Mentall, J. E.; Gentieu, E. P.; Krauss, M.; Neu- mann, D. Photoionization and Absorption Spectrum of Formaldehyde in the Vacuum Ultraviolet. *J. Chem. Phys.* **1971**, *55*, 5471–5479.

(176) Suto, M.; Wang, X.; Lee, L. C. Fluorescence from VUV excitation of formaldehyde. *J. Chem. Phys.* **1986**, *85*, 4228–4233.

(177) Matsuzawa, N. N.; Ishitani, A.; Dixon, D. A.; Uda, T. Time-Dependent Density Functional Theory Calcula- tions of Photoabsorption Spectra in the Vacuum Ul- traviolet Region. *J. Phys. Chem. A* **2001**, *105*, 4953– 4962.

(178) Jensen, P.; Bunker, P. The Geometry and the Out-Of- Plane Bending Potential Function of Thioformalde- hyde in the Ā$^1A_2$ and ā$^3A_2$ Electronic States. *J. Mol. Spectrosc.* **1982**, *95*, 92–100.

(179) Dunlop, J. R.; Karolczak, J.; Clouthier, D. J.; Ross, S. C. Pyrolysis Jet Spectroscopy: The $S_1 - S_0$ Band System of Thioformaldehyde and the Excited- State Bending Potential. *J. Phys. Chem.* **1991**, *95*, 3045–3062.

(180) Dixon, R.; Webster, C. The Determination of the Elec- tric Dipole Moment of H₂CS in the Ā$^1A_2$ Excited State Using Dye-Laser Electric Field Spectroscopy. *J. Mol. Spectrosc.* **1978**, *70*, 314–322.

(181) Dixon, R.; Gunson, M. The Dipole Moment of Thio- formaldehyde in its Singlet and Triplet $\pi^* - n$ Excited States. *J. Mol. Spectrosc.* **1983**, *101*, 369–378.

(182) Judge, R.; Drury-Lessard, C.; Moule, D. The Far Ul- traviolet Spectrum of Thioformaldehyde. *Chem. Phys. Lett.* **1978**, *53*, 82–83.

(183) Saito, S.; Takagi, K. Microwave Spectrum of Nitroxyl. *J. Mol. Spectrosc.* **1973**, *47*, 99–106.

(184) Dixon, R.; Noble, M. The Dipole Moment of HNO in its Ā$^1A''$ Excited State Determined using Optical- Optical Double Resonance Stark Spectroscopy. *Chem. Phys.* **1980**, *50*, 331–339.

(185) Takagi, K.; Suzuki, T.; Saito, S.; Hirota, E. Microwave Optical Double Resonance of HNO: Dipole Moment of HNO in Ā$^1A''$ (100). *J. Chem. Phys.* **1985**, *83*, 535– 538.

(186) Johns, J. W. C.; McKellar, A. R. W. Laser Stark Spec- troscopy of the Fundamental Bands of HNO ($v_2$ and $v_3$) and DNO ($v_1$ and $v_2$). *J. Chem. Phys.* **1977**, *66*, 1217–1224.

(187) Scuseria, G. E.; Duran, M.; Maclagan, R. G. A. R.; Schaefer, H. F. Halocarbenes CHF, CHCl, and CHBr: Geometries, Singlet-Triplet Separations, and Vibra- tional Frequencies. *J. Am. Chem. Soc.* **1986**, *108*, 3248–3253.
$2^1A'(\sigma, \pi^*/\pi, \pi^*)$ as Perturber of $1^1B_2(n, 3s)$. *J. Chem. Soc., Faraday Trans.* **1994**, *90*, 683–688.

(158) Gómez-Carrasco, S.; Müller, T.; Köppel, H. Ab Initio Study of the VUV-Induced Multistate Photodynamics of Formaldehyde. *J. Phys. Chem. A* **2010**, *114*, 11436–11449.

(159) Fabricant, B.; Krieger, D.; Muenter, J. S. Molecu- lar Beam Electric Resonance Study of Formaldehyde, Thioformaldehyde, and Ketene. *J. Chem. Phys.* **1977**, *67*, 1576–1586.

(160) Haner, D. A.; Dows, D. A. Electric-Field-Induced Spectra: Excited-State Dipole Moment from Line-Shape Analysis. *J. Chem. Phys.* **1968**, *49*, 601–605.

(161) Weiss, M. J.; Kuyatt, C. E.; Mielczarek, S. Inelas- tic Electron Scattering from Formaldehyde. *J. Chem. Phys.* **1971**, *54*, 4147–4150.

(162) Causley, G. C.; Russell, B. R. Electric Dipole Moment and Polarizability of the 1749 Å, $1^1B_2$ Excited State of Formaldehyde. *J. Chem. Phys.* **1978**, *68*, 3797–3800.

(163) Causley, G. C.; Russell, B. R. Electric Dichroism Spectroscopy in the Vacuum Ultraviolet. 2. Formalde- hyde, Acetaldehyde, adn Acetone. *J. Am. Chem. Soc.* **1979**, *101*, 5573–5578.

(164) Vaccaro, P. H.; Zabludoff, A.; Carrera-Patiño, M. E.; Kinsey, J. L.; Field, R. W. High Precision Dipole Mo- ments in Ā $1^1A_2$ Formaldehyde Determined via Stark Quantum Beat Spectroscopy. *J. Chem. Phys.* **1989**, *90*, 4150–4167.

(165) Cooper, G.; Anderson, J. E.; Brion, C. Absolute Pho- toabsorption and Photoionization of Formaldehyde in the VUV and Soft X-ray Regions (3–200 eV). *Chem. Phys.* **1996**, *209*, 61–77.

(166) Benková, Z.; Černušák, I.; Zahradník, P. Elec- tric Properties of Formaldehyde, Thioformaldehyde, Urea, Formamide, and Thioformamide – Post-HF and DFT Study. *Int. J. Quantum Chem.* **2007**, *107*, 2133– 2152.

(167) Clouthier, D. J.; Ramsay, D. A. The Spectroscopy of Formaldehyde and Thioformaldehyde. *Annu. Rev. Phys. Chem.* **1983**, *34*, 31–58.

(168) Suzuki, T.; Saito, S.; Hirota, E. Dipole Moments of H₂CS in the Ā$^1A_2(ν = 0)$ and $ā^3A_2(ν_3 = 1)$ States by MODR Spectroscopy. *J. Mol. Spectrosc.* **1985**, *111*, 54–61.

(169) Goetz, W.; Moule, D. C.; Ramsay, D. A. The Electric Dipole Moment of the $\tilde{C}^1B_2(3s \leftarrow n)$ State of Thio- formaldehyde. *Can. J. Phys.* **1981**, *59*, 1635–1639.

(170) Johnson, D. R.; Powell, F. X.; Kirchhoff, W. H. Microwave Spectrum, Ground State Structure, and Fipole Moment of Thioformaldehyde. *J. Mol. Spectrosc.* **1971**, *39*, 136–145.

(171) Fung, K. H.; Ramsay, D. A. Doppler-free Stark Spec- tra of the $4^1_0$ Band of the Ā$^1A_2 - \tilde{X}^1A_1$ System of Thioformaldehyde. *Mol. Phys.* **1996**, *88*, 997–1004.

(172) Freeman, D. E.; Klemperer, W. Dipole Moments of Excited Electronic States of Molecules: The $^1A_2$ State of Formaldehyde. *J. Chem. Phys.* **1964**, *40*, 604–605.

(173) Freeman, D. E.; Klemperer, W. Electric Dipole Mo- ment of the $^1A_2$ Electronic State of Formaldehyde. *J. Chem. Phys.* **1966**, *45*, 52–57.

(174) Bridge, N. J.; Haner, D. A.; Dows, D. A. Electric- Field-Induced Spectra: Theory and Experimental Study of Formaldehyde. *J. Chem. Phys.* **1968**, *48*, 4196–4210.

(175) Mentall, J. E.; Gentieu, E. P.; Krauss, M.; Neu- mann, D. Photoionization and Absorption Spectrum of Formaldehyde in the Vacuum Ultraviolet. *J. Chem. Phys.* **1971**, *55*, 5471–5479.

(176) Suto, M.; Wang, X.; Lee, L. C. Fluorescence from VUV excitation of formaldehyde. *J. Chem. Phys.* **1986**, *85*, 4228–4233.

(177) Matsuzawa, N. N.; Ishitani, A.; Dixon, D. A.; Uda, T. Time-Dependent Density Functional Theory Calcula- tions of Photoabsorption Spectra in the Vacuum Ul- traviolet Region. *J. Phys. Chem. A* **2001**, *105*, 4953– 4962.

(178) Jensen, P.; Bunker, P. The Geometry and the Out-Of- Plane Bending Potential Function of Thioformalde- hyde in the Ā$^1A_2$ and ā$^3A_2$ Electronic States. *J. Mol. Spectrosc.* **1982**, *95*, 92–100.

(179) Dunlop, J. R.; Karolczak, J.; Clouthier, D. J.; Ross, S. C. Pyrolysis Jet Spectroscopy: The $S_1 - S_0$ Band System of Thioformaldehyde and the Excited- State Bending Potential. *J. Phys. Chem.* **1991**, *95*, 3045–3062.

(180) Dixon, R.; Webster, C. The Determination of the Elec- tric Dipole Moment of H₂CS in the Ā$^1A_2$ Excited State Using Dye-Laser Electric Field Spectroscopy. *J. Mol. Spectrosc.* **1978**, *70*, 314–322.

(181) Dixon, R.; Gunson, M. The Dipole Moment of Thio- formaldehyde in its Singlet and Triplet $\pi^* - n$ Excited States. *J. Mol. Spectrosc.* **1983**, *101*, 369–378.

(182) Judge, R.; Drury-Lessard, C.; Moule, D. The Far Ul- traviolet Spectrum of Thioformaldehyde. *Chem. Phys. Lett.* **1978**, *53*, 82–83.

(183) Saito, S.; Takagi, K. Microwave Spectrum of Nitroxyl. *J. Mol. Spectrosc.* **1973**, *47*, 99–106.

(184) Dixon, R.; Noble, M. The Dipole Moment of HNO in its Ā$^1A''$ Excited State Determined using Optical- Optical Double Resonance Stark Spectroscopy. *Chem. Phys.* **1980**, *50*, 331–339.

(185) Takagi, K.; Suzuki, T.; Saito, S.; Hirota, E. Microwave Optical Double Resonance of HNO: Dipole Moment of HNO in Ā$^1A''$ (100). *J. Chem. Phys.* **1985**, *83*, 535– 538.

(186) Johns, J. W. C.; McKellar, A. R. W. Laser Stark Spec- troscopy of the Fundamental Bands of HNO ($v_2$ and $v_3$) and DNO ($v_1$ and $v_2$). *J. Chem. Phys.* **1977**, *66*, 1217–1224.

(187) Scuseria, G. E.; Duran, M.; Maclagan, R. G. A. R.; Schaefer, H. F. Halocarbenes CHF, CHCl, and CHBr: Geometries, Singlet-Triplet Separations, and Vibra- tional Frequencies. *J. Am. Chem. Soc.* **1986**, *108*, 3248–3253.
(188) Kakimoto, M.; Saito, S.; Hirota, E. Doppler-Limited Dye Laser Excitation Spectroscopy of HCF. *J. Mol. Spectrosc.* **1981**, *88*, 300–310.

(189) Wagner, M.; Gamperling, M.; Braun, D.; Prohaska, M.; Hüttner, W. Rotational Transitions and Electric Dipole Moment of Fluorocarbene, HCF. *J. Mol. Struct.* **2000**, *517-518*, 327–334.

(190) Lu, T.; Hao, Q.; Wilke, J. J.; Yamaguchi, Y.; Fang, D.-C.; Schaefer, H. F. Silylidene (SiCH₂) and its Isomers: Anharmonic Rovibrational Analyses for Silylidene, Silaacetylene, and Silavinylidene. *J. Mol. Struct.* **2012**, *1009*, 103–110.

(191) Smith, T. C.; Evans, C. J.; Clouthier, D. J. Discovery of the Optically Forbidden S<sub>1</sub> – S<sub>0</sub> Transition of Silylidene (H<sub>2</sub>C=Si). *J. Chem. Phys.* **2003**, *118*, 1642–1648.

(192) Harper, W. W.; Waddell, K. W.; Clouthier, D. J. Jet Spectroscopy, Structure, Anomalous Fluorescence, and Molecular Quantum Beats of Silylidene (H<sub>2</sub>C=Si), the Simplest Unsaturated Silylene. *J. Chem. Phys.* **1997**, *107*, 8829–8839.

(193) Hilliard, R. K.; Grev, R. S. The Excited Electronic States of H<sub>2</sub>CSi. *J. Chem. Phys.* **1997**, *107*, 8823–8828.
(188) Kakimoto, M.; Saito, S.; Hirota, E. Doppler-Limited Dye Laser Excitation Spectroscopy of HCF. *J. Mol. Spectrosc.* **1981**, *88*, 300–310.

(189) Wagner, M.; Gamperling, M.; Braun, D.; Prohaska, M.; Hüttner, W. Rotational Transitions and Electric Dipole Moment of Fluorocarbene, HCF. *J. Mol. Struct.* **2000**, *517-518*, 327–334.

(190) Lu, T.; Hao, Q.; Wilke, J. J.; Yamaguchi, Y.; Fang, D.-C.; Schaefer, H. F. Silylidene (SiCH₂) and its Isomers: Anharmonic Rovibrational Analyses for Silylidene, Silaacetylene, and Silavinylidene. *J. Mol. Struct.* **2012**, *1009*, 103–110.

(191) Smith, T. C.; Evans, C. J.; Clouthier, D. J. Discovery of the Optically Forbidden S₁ – S₀ Transition of Silylidene (H₂C=Si). *J. Chem. Phys.* **2003**, *118*, 1642–1648.

(192) Harper, W. W.; Waddell, K. W.; Clouthier, D. J. Jet Spectroscopy, Structure, Anomalous Fluorescence, and Molecular Quantum Beats of Silylidene (H₂C=Si), the Simplest Unsaturated Silylene. *J. Chem. Phys.* **1997**, *107*, 8829–8839.

(193) Hilliard, R. K.; Grev, R. S. The Excited Electronic States of H₂CSi. *J. Chem. Phys.* **1997**, *107*, 8823–8828.
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Graphical TOC Entry

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