1. Ab initio Electronic and Rovibrational Structure of Fulminic Acid
steps towards ab initio rovibrational spectra of quasilinear molecules
Mirjana Mladenović and Marius Lewerenz
Université Paris Est, Marne la Vallée, France

2. Fulminic acid, HCNO
Historic importance , the first experimental evidence for isomerism (silver fulminate and
silver cyanate), Liebig, Wöhler, Berzelius (1830)
Experiment
Isolation of the pure substance by Beck et al.
1967 M. Winnewisser and Bodenseh
quasi-linear, B. Winnewisser and M. Winnewisser
r(CH) distance derived on the basis of a linear molecule model is unreasonably short of Å (1.94 a0)
quasi-bent, semi-rigid bender study of Bunker, Landsberg, B. Winnewisser
since 1969: high-resolution infrared and microwave spectra by
B. Winnewisser, M. Winnewisser ν5 = cm-1, ν4 = cm-1, ν3 = 1254 cm-1,
K. Albert, S. Albert et al ν1 = 3336 cm-1, ν2 = 2196 cm-1
Theory
1992, 1993, 1996 : MP2, MP4, MCSCF favour bent equilibrium structure
SCF, MP3, CISD, CCSD, CCSD(T)/TZ2P favour linear equilibrium structure
CCSD(T)/cc-pVQZ by Koput et al. gave Elin of 7 cm-1
1993 Handy et al. developed MP2/DZP 6D PES
Questions/Motivation
rotational and vibrational energy levels not reproduced by theoretical means

3. quasi-linear, B. Winnewisser and M. Winnewisser,
28th Ohio Symposium (Paper 02)
Giessen, Germany

4. quasilinearity quantified by
γ0= 1-4 E(ν51) / E(2ν50)
γ0 =-1 for ideal linear molecules
γ0 =+1 for ideal bent molecules
γ0( HNCO) =
γ0( HCCN) =
γ0( HCNO) =
Characteristics of quasilinear modes:
large amplitude motion
large anharmonicity
large centrifugal distortion
particularly complicated
rovibrational spectra

5. our theoretical study CCSD(T) level of theory - basis sets: cc-pVXZ (X=2-6) and cc-pCVXZ (X=2-5) due to Dunning and Woon MOLPRO
Total energies Emin and Elin at optimized planar and linear configurations, bond lengths (in a0), and bond angles (in degrees) for HCNO obtained at the CCSD(T) level of theory for cc-pVXZ (X=2-6) and cc-pCVXZ (X=2-5) basis sets. The height of the barrier to linearity is calculated as Ebar=Elin-Emin. All electron results for cc-pVXZ and cc-pCVXZ are denoted by cc-pVXZ(all) and cc-pCVXZ(all), respectively.

6. RHF barrier to linearity and correlation energy contribution to the CCSD(T) barrier to linearity obtained for HCNO at the optimized cc-pV6Z, cc-pV5Z(all), and cc-pCV5Z(all) geometries (first three rows) and the optimized frozen core cc-pV5Z geometry denoted here by geo5 (last five rows). The latter series of calculations, cc-pVXZ(geo5), is carried out at the geometry geo5 with the cc-pVXZ basis set for X=2-6. All quantities are given in cm-1.

7. CHNO Isocyanic acid, HNCO Cyanic acid, HOCN Fulminic acid, HCNO
Isofulminic acid, HONC
CHNO

8. Absolute CCSD(T) energy of optimized HCNO, HNCO, HOCN, and HONC as a function of the cardinal number X of the cc-pVXZ, cc-pVXZ(all), and cc-pCVXZ(all) basis set families.
CCSD(T)/cc-pVQZ ca. 150, 500, CPUs for linear, planar, general CHNO arrangements
CCSD(T)/cc-pVQZ(all) ca. 300, 1000, CPUs * factor 2
CCSD(T)/cc-pCVQZ(all) ca.1350, 3500, CPUs * factor 8
PES

9. Variation of the equilibrium HXY and XYZ angles with the cardinal number X of the cc-pVXZ, cc-pVXZ(all), and cc-pCVXZ(all) basis sets for planar HCNO, HNCO, HOCN, and HONC.
Minimum energy path along the HCN angle of HCNO, calculated at the CCSD(T) level of theory for the cc-pVXZ and cc-pCVXZ basis sets using X=2-4. Both valence electron and all electron correlation results are shown. For easier comparison, all profiles are drawn to a common scale.

10. Minimum energy paths along the bending angle for the HCNO, HCCN, and HCCH molecules. The angle HXY denotes the HCN angle θ1 of HCNO and the HCC angle of HCCN and HCCH, respectively. An additional profile is shown for the CNO angle θ2 in HCNO.
HCCN ν4
small-amplitude mode ν5
quasilinear mode

11. Minimum energy paths of HCNO, HNCO, HOCN, and HONC from CCSD(T) calculations with the cc-pVQZ basis and all electrons correlation. Each of the curves shown is measured relative to the energy of the respective optimum linear configuration.
Variation of the optimum bond lengths ropt(HX), ropt(XY), and ropt(YZ) of HXYZ along the minimum energy path in the direction of the HXY angle from CCSD(T)/ cc-pVQZ(all) calculations. H X Y Z

12. angular momentum operator
vibrational angular momentum H r1 α r2 X Y
Kinetic energy operator for tetratomic molecules in orthogonal description of the internal geometry r3 β Z
vibrational contribution
rotational contribution
vibrational doubling/resonance effects
rotational doubling/resonance effects
fR=1/μR R2 , f(R,di) =1/μR R2 +1/μi di2 , whereas ∂θ = ∂/∂θ and ∂2θ = ∂2/∂θ2
angular momentum operator

13. Minimum energy paths along the torsion angle.
Minimum energy paths along the bending angle XYZ for the HCNO, HNCO, HOCN, and HONC molecules from CCSD(T) calculations with the cc-pVQZ basis set and all electron correlation. The curves are measured relative to the respective optimum configuration.
Geometrical parameters of the hockey-stick structures at the CCSD(T)/cc-pVQZ(all) level. Δ is measured relative to the respective optimum minimum.
angular momentum conservation
l4+l5 = K ≤ J
Minimum energy paths along the torsion angle.

14. C N N C O O HNCO 0 HOCN 8600 cm-1 HCNO 24500 cm-1 HONC 29500 cm-1
HCNO /HONC cm-1
hockey-stick path
Bond-distance-bond-angle coordinates:
HNCO (1.90 a0,2.29 a0,2.20 a0, 124o, 172o )
HOCN (1.82 a0,2.46 a0,2.19 a0, 110o, 177o )
HCNO (2.00 a0,2.19 a0,2.27 a0, 180o, 180o )
HONC (1.82 a0,2.51 a0,2.22 a0, 105o, 173o )
cis path
angle HCN-180
angle HNC
HCNO CNOH
HNCO NCOH H H H H C N N C O O

15. kind regards from
Marius Lewerenz

17. Linear-molecule model
Bent-molecule model
Linear-molecule model
angular momentum conservation
l4+l5 = K ≤ J
quantum state label (n4ν4, n5ν5, n6ν6,K )p
quantum state label (n4ν4|l 4|, n5ν5|l5| )K,p

18. Ab initio Electronic and Rovibrational Structure of Fulminic Acid
steps towards ab initio rovibrational spectra of quasilinear molecules
Mirjana Mladenović and Marius Lewerenz
Université Paris Est, Marne la Vallée, France