Precision analysis of 12C/13C ratios in Orion IRc2 acetylene isotopologs via χ2 fitting

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Table C.1

Infrared vibrational frequencies (ν₁, ν₂, ν₃, ν₄, ν₅) and rotational constants (B̃) for acetylene isotopologs (¹²C₂H₂, ¹³C-substituted, and deuterium-substituted variants) calculated using various quantum chemical methods: Hartree–Fock (HF), B3LYP, PBE0, and MP2.

Isotopolog ID	Method FSF = 1.000000	ν₁ [cm⁻¹]	ν₂ [cm⁻¹ ]	ν₃ [cm⁻¹]	ν₄ [cm⁻¹]	ν₅ [cm⁻¹]	B̃ [cm⁻¹]
0	HF	3719.692	2246.893	3607.484	793.610	882.237	1.2113
	B3LYP	3542.390	2087.886	3442.297	534.175	774.627	1.1766
	PBE0	3563.447	2102.532	3460.432	575.732	780.424	1.1770
	MP2	3568.687	2001.497	3480.443	374.534	747.863	1.1585
1	HF	3705.880	2211.601	3601.439	787.455	880.998	1.1824
	B3LYP	3529.920	2054.704	3436.511	530.081	773.484	1.1485
	PBE0	3550.771	2069.187	3454.626	571.308	779.278	1.1489
	MP2	3557.340	1969.037	3474.553	371.702	746.750	1.1307
2	HF	3670.580	2082.710	2843.301	657.380	837.488	1.0184
	B3LYP	3498.078	1946.382	2695.795	466.499	697.315	0.9901
	PBE0	3517.957	1958.769	2712.453	499.230	707.655	0.9903
	MP2	3528.849	1883.762	2696.072	332.028	662.589	0.9762
3	HF	3691.056	2175.212	3596.685	781.435	879.596	1.1529
	B3LYP	3516.414	2020.534	3431.992	526.002	772.308	1.1197
	PBE0	3537.079	2034.844	3450.073	566.906	778.088	1.1201
	MP2	3544.806	1935.681	3470.024	368.870	745.624	1.1022
4	HF	3650.710	2053.231	2836.946	655.611	831.742	0.9935
	B3LYP	3479.841	1917.850	2690.606	463.780	694.732	0.9659
	PBE0	3499.486	1930.164	2707.181	496.565	704.675	0.9661
	MP2	3511.667	1854.562	2692.251	329.755	660.872	0.9522
5	HF	3668.247	2067.710	2803.612	648.627	837.200	1.0018
	B3LYP	3496.169	1930.915	2659.920	460.335	697.020	0.9740
	PBE0	3515.974	1943.344	2676.210	492.517	707.511	0.9742
	MP2	3527.424	1866.274	2663.404	327.934	661.778	0.9601
6	HF	2997.782	1972.156	2648.723	662.808	647.765	0.8692
	B3LYP	2833.916	1846.155	2527.438	445.952	568.754	0.8457
	PBE0	2853.342	1857.424	2540.753	480.778	573.011	0.8458
	MP2	2817.727	1793.148	2555.446	312.166	549.103	0.8346
7	HF	3648.706	2036.737	2797.652	646.773	831.499	0.9764
	B3LYP	3478.197	1901.036	2655.100	457.617	694.411	0.9491
	PBE0	3497.776	1913.382	2671.303	489.848	704.507	0.9493
	MP2	3510.435	1835.879	2659.907	325.662	660.044	0.9355
8	HF	2965.050	1955.340	2640.730	656.746	644.736	0.8542
	B3LYP	2804.642	1829.336	2519.795	441.000	567.229	0.8310
	PBE0	2823.697	1840.609	2533.075	475.411	571.500	0.8311
	MP2	2791.728	1774.858	2547.684	308.749	547.595	0.8201
9	HF	2931.432	1937.423	2633.996	648.181	644.163	0.8387
	B3LYP	2774.495	1811.482	2513.385	436.132	565.592	0.8159
	PBE0	2793.182	1822.756	2526.626	470.176	569.825	0.8160
	MP2	2764.762	1755.579	2541.237	305.350	546.050	0.8050

Notes. The “Structure” column visually distinguishes the isotopologs, with substituted ¹³C and deuterium (D) atoms marked by red circles. Vibrational frequencies shown in black indicate infrared-active modes, while gray denotes infrared-inactive modes. A frequency scaling factor (FSF) of 1.000000 was used for all calculations; however, users can adjust the FSF as needed to align the theoretically computed vibrational frequencies more closely with experimental values. These results, detailed further in Sect. C, are essential for accurate spectral modeling and provide key data for isotopologs not covered in standard databases such as HITRAN.

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