Anharmonic force fields and spectroscopic constants of H 2 AsO: An ab initio study

Abstract

The anharmonic force fields and spectroscopic constants of the electronic ground state ( ${\tilde{X}}^{1} A^{'}$ ) for H₂AsO are calculated employing DFT (B3LYP, B3PW91, and B3P86) and MP2 methods with the aug-cc-pVQZ and aug-cc-pV5Z basis sets. The calculated equilibrium geometries, ground state rotational constants, harmonic frequencies, and anharmonic constants of H₂AsO are in comparison with the experimental or previous theoretical data. The best agreement is found at the B3PW91/aug-cc-pV5Z theoretical level. The theoretically predicted fundamental vibrational frequencies, vibration–rotation interaction constants, equilibrium quartic and sextic centrifugal distortion constants, Coriolis coupling constants, cubic and quartic force constants of H₂AsO are obtained at the B3PW91/aug-cc-pV5Z level and expected to provide help for the observation of the high-resolution rotational spectrum of H₂AsO in the future.

Keywords

Spectroscopic constant anharmonic force field

1 Introduction

Arsenic-containing molecules have come into notice in the chemical vapor deposition (CVD) or metal-organic chemical vapor deposition (MOCVD) processes of the semiconductor industry. The H₂AsO molecule is a reactive intermediate generated in CVD or MOCVD processes and can be used to modify the electronic characteristics of semiconducting materials [1]. Together with the similar arsenic-containing small molecule such as AsH₂ [2], C₂As [3, 4], HAsO [5] and AsC [6], H₂AsO [7] has caught much attention in the past decade. In addition, the oxidized arsenic free radicals may damage health as well as be harmful to the environment [8]. Nevertheless, there are rare reports about the anharmonic force fields and spectroscopic constants of H₂AsO up to now.

In 2009, Tarroni and Clouthier theoretically predicted the energies, geometries, and vibrational frequencies of the ground and first two excited states of the H₂AsO free radicals [9]. The results showed that the ground state of H₂AsO was a nonplanar (pyramidal) structure. At the same year, He et al. first detected the existence of the H₂AsO molecule in argon matrices and reported the identification of the H₂AsO free radical in the gas phase by laser induced fluorescence (LIF) and wavelength resolved emission spectroscopy [7]. The analysis of the experimental data supported the preliminary theoretical results [9]. In 2012, Stojanvić obtained the arsenic isotropic and anisotropic hyperfine parameters of three small radicals AsH₂, AsO₂, and H₂AsO using various density functional theory, MP2, and CCSD methods [10].

The above studies concentrated on the emission spectra of H₂AsO. There is a little theoretical and experimental research on the rotational spectrum for ${\tilde{X}}^{1} A^{'}$ of H₂AsO. With the development of the program of analytic second derivatives of molecular energy, the spectroscopic constants and anharmonic force field of small or middle molecules can be calculated by ab initio method (such as MP2, DFT, CCSD(T), et al.) [11 –19]. Thus, the goal of this work is to calculate the anharmonic force field and spectroscopic constants of the ${\tilde{X}}^{1} A^{'}$ of H₂AsO employing the B3P86, B3PW91, B3LYP and MP2 methods with aug-cc-pVQZ and aug-cc-pV5Z basis sets.

The paper is organized as follows: in Section 2, we briefly review the computational details. In Section 3, results and discussion are presented. Finally, Section 4 closes with the conclusions.

2 Computational details

Quantum-chemical calculations are carried out at second-order Møller-Plesset (MP2) [20], and density functional theory (DFT) methods. In the process of the calculations, three DFT methods are B3LYP, B3P86, and B3PW91 [21 –24] in Gaussian 09 program [25], respectively. The aug-cc-pVQZ and aug-cc-pV5Z basis sets [26, 27] are carried out. For aug-cc-pVQZ basis set, the contracted set is [5 s,4p,3d,2f] /(7 s,4p,3d,2f) for the H atom, [8 s,7p,5d,3f,2g]/(22 s,17p,13d,3f,2 g) for the As atom, and [6 s,5p,4d,3f,2g]/(13 s,7p,4d,3f,2 g) for the O atom, respectively. For the aug-cc-pV5Z basis set, the corresponding contracted set is [6 s,5p,4d,3f,2g]/(9 s,5p,4d,3f,2 g), [9 s,8p,6d,4f,3 g,2h]/(27 s,18p,14d,4f,3 g,2 h), and [7 s,6p,5d,4f,3 g,2h]/(15 s,9p,5d,4f,3 g,2 h).

2.1 Vibration-rotation interaction constants

For asymmetric top molecules, the effective rotation constant along the b axis can be expressed as, $X_{v} = X_{e} - \sum_{i} α_{i}^{X} (v_{i} + \frac{1}{2}) + \dots$ (2.1)

Where X is the rotational constant including A, B and C. $α_{r}^{X}$ is vibration-rotation interaction constants, the expression is, $- α_{r}^{X} = (2 X_{e}^{2} / ω_{r}) [\sum_{ξ} 3 {(a_{r}^{(b ξ)})}^{2} / 4 I_{ξ} + \sum_{s \neq r} {(ζ_{r, s}^{(b)})}^{2} (3 ω_{r}^{2} + ω_{s}^{2}) / (ω_{r}^{2} - ω_{s}^{2})$ (2.2) $+ π (c / h)^{1 / 2} \sum_{s} φ_{rrs} a_{s}^{(bb)} (ω_{r} / ω_{s}^{3 / 2})]$

2.2 Coriolis coupling constants

In Equation (2.2), $ζ_{r, s}^{(b)}$ is coriolis coupling constants, which indicates the coupling between Q_r coordinates and Q_s coordinates rotating around b axis and can be expressed as, $ζ_{r, s}^{(b)} = \sum_{i} (L_{ir}^{(β)} L_{is}^{(γ)} - L_{ir}^{(γ)} L_{is}^{(β)})$ (2.3)

For asymmetric top molecules, when the approximate degeneracy of two vibration dynamics (ω_r = ω_s) occurs, in Equation (2.2), this part will be replaced with $(ζ_{r, s}^{(b)})^{2} (3 {ω_{r}}^{2} + ω_{s}^{2}) / (ω_{r}^{2} - ω_{s}^{2}) \to - \frac{1}{2} (ζ_{r, s}^{(b)})^{2} (ω_{r} - ω_{s})^{2} / ω_{s} (ω_{r} + ω_{s})$ (2.4)

This substitution ignores the first order term, resulting in the inaccuracy of the eigenenergy calculation, and the diagonalization of the vibration Hamiltonian matrix will solve such problems.

2.3 Centrifugal distortion constants

Centrifugal distortion tensor are reported by Wilson and Howard [28] and expressed as, $\sum_{α β γ δ} \frac{1}{4} τ_{α β γ δ} J_{α} J_{β} J_{γ} J_{δ}$ (2.5) where $τ_{α β γ δ} = - (ℏ^{4} / 2 hc I_{α} I_{β} I_{γ} I_{δ}) \sum_{k} a_{k}^{(α β)} a_{k}^{(γ δ)} / λ_{k}$ (2.6)

The quartic centrifugal distortion constant can be expressed as, $D_{J} = - \frac{1}{32} [3 τ_{bbbb} + 3 τ_{cccc} + 2 (τ_{bbcc} + 2 τ_{bcbc})]$ (2.7) $D_{K} = D_{J} - \frac{1}{4} [τ_{aaaa} - (τ_{aabb} + 2 τ_{abab}) - (τ_{ccaa} + 2 τ_{caca})]$ $D_{JK} = - D_{J} - D_{K} - \frac{1}{4} τ_{aaaa}$ $R_{5} = - \frac{1}{32} [τ_{bbbb} - τ_{cccc} - 2 (τ_{aabb} + 2 τ_{abab}) + 2 (τ_{ccaa} + 2 τ_{caca})]$ $R_{6} = \frac{1}{64} [τ_{bbbb} + τ_{cccc} - 2 (τ_{bbcc} + 2 τ_{bcbc})]$ $δ_{J} = - \frac{1}{16} (τ_{bbbb} - τ_{cccc})$

The sextic centrifugal distortion constants can be expressed as, $H_{J} = Φ_{600} + 2 Φ_{204}$ (2.8) $H_{JK} = Φ_{420} - 12 Φ_{204} + 2 Φ_{024} + 16 σ Φ_{006} - 16 (R_{5} - 2 σ R_{6}) S_{111} + 8 (2 {A^{'}}_{0} - {B^{'}}_{0} - {C^{'}}_{0}) S_{111}^{2}$ $H_{KJ} = Φ_{240} + \frac{10}{3} Φ_{420} - 30 Φ_{204} - \frac{10}{3} H_{JK}$ $H_{K} = Φ_{060} - \frac{7}{3} Φ_{420} + 28 Φ_{204} + \frac{7}{3} H_{JK}$ $h_{J} = Φ_{402} + Φ_{006}$ $h_{JK} = Φ_{222} - 10 Φ_{006} + 4 σ Φ_{204} + 2 (D_{JK} - 2 σ δ_{J} - 4 R_{6}) S_{111} - 4 ({B^{'}}_{0} - {C^{'}}_{0}) S_{111}^{2}$ $h_{K} = Φ_{042} + \frac{4}{3} σ Φ_{024} + (9 + \frac{32}{3} σ^{2}) Φ_{006} + 4 [D_{K} - \frac{2}{3} σ R_{5} + 2 (1 + \frac{8}{3} σ^{2}) R_{6}] S_{111}$ $+ (6 + \frac{10}{3} σ^{2}) ({B^{'}}_{0} - {C^{'}}_{0}) S_{111}^{2}$

The defined constant In Equation (2.8) is a linear combination of seven deterministic constants of ten six centrifugal distortion constants.

2.4 Anharmonic constants

For asymmetric top molecules, the anharmonic correction constants can be divided into diagonal and non-diagonal parts, which can be expressed as, $χ_{rr} = \frac{1}{16} φ_{rrrr} - \frac{1}{16} \sum_{s} φ_{rrs}^{2} (8 ω_{r}^{2} - 3 ω_{s}^{2}) / ω_{s} (4 ω_{r}^{2} - ω_{s}^{2})$ (2.9)

Non-diagonal parts can be expressed as, $χ_{rs} = \frac{1}{4} φ_{rrss} - \frac{1}{4} \sum_{l} φ_{rrl} φ_{lss} / ω_{l} - \frac{1}{2} \sum_{l} φ_{rsl}^{2} ω_{l} (ω_{l}^{2} - ω_{r}^{2} - ω_{s}^{2}) / Δ_{rsl}$ (2.10) $+ [A_{e} (ζ_{rs}^{(a)})^{2} + B_{e} (ζ_{rs}^{(b)})^{2} + C_{e} (ζ_{rs}^{(c)})^{2}] (ω_{r} / ω_{s} + ω_{s} / ω_{r})$

Where $Δ_{rsl} = (ω_{r} + ω_{s} + ω_{l}) (ω_{r} + ω_{s} - ω_{l}) (ω_{r} - ω_{s} + ω_{l}) (ω_{r} - ω_{s} - ω_{l})$ (2.11)

2.5 Fundamental frequency

The ith fundamental frequency of H₂AsO can be obtained by the ith harmonic frequency (ω_i) and anharmonic constant (χ_ij) shown in Table 5 as follow, $ν_{i} = ω_{i} + 2 χ_{ii} + \frac{1}{2} \sum_{i \neq j} χ_{ij}$ (2.12)

The calculation detail of the spectroscopic constants and anharmonic force field of H₂AsO is the same as that of Refs. 13–16, therefore, we will not repeat too much in this article.

3 Results and discussion

The anharmonic force fields and spectroscopic constants of H₂AsO are showed in Tables 1–11. The MP2, B3LYP, B3P86, and B3PW91 methods with the aug-cc-pVQZ and aug-cc-pV5Z basis sets are employed in order to fully appreciate the change of the calculated results. In the following discussion, the two basis sets used in the Tables 1–11 are abbreviated as QZ and 5Z, respectively. In order to test the validity of the employed levels of theory, we compare the calculated results with the existed experimental or theoretical data.

Table 1
Molecular geometries, dipole moments and total energies of H₂AsO

R_As - O(Å) R_As - H(Å) Φ_HAsO(°) Φ_HAsH(°) Θopp(°) μ(Debye) Energy(a.u.)

B3LYP/QZ 1.681 1.529 106.834 99.765 63.292 2.97 –2312.37

B3LYP/5Z 1.681 1.529 106.809 99.783 63.328 2.96 –2312.36

B3P86/QZ 1.665 1.524 107.824 100.278 61.473 3.00 –2313.29

B3P86/5Z 1.665 1.524 107.792 100.296 61.521 3.00 –2313.29

B3PW91/QZ 1.669 1.526 107.698 100.163 61.722 2.97 –2312.31

B3PW91/5Z 1.669 1.526 107.665 100.182 61.772 2.97 –2312.3

MP2/QZ 1.599 1.493 119.263 103.94 39.492 4.50 –2310.78

MP2/5Z 1.599 1.493 119.169 104.178 37.512 4.48 –2310.88

B3LYP/6-31G^a 1.702 1.530 106.0 98.6 65.1 2.85

B3LYP/6-31++G^a 1.683 1.528 106.7 99.8 63.5 2.98

B3LYP/aug-cc-pVTZ^a 1.685 1.529 106.6 99.7 63.7 2.96

QCISD/6-31G^a 1.709 1.517 105.5 98.5 65.8 2.68

QCISD/6-31++G^a 1.683 1.52 107.3 100.2 62.5 2.97

QCISD/aug-cc-pVTZ^a 1.679 1.508 106.9 100.2 63.1 2.93

CCSD(T)/6-31G^a 1.698 1.52 106.8 99.0 63.5 –

CCSD(T)/6-31++G^a 1.669 1.522 109.4 101.0 58.5 –

CCSD(T)/aug-cc-pVTZ^a 1.669 1.522 109.4 101.0 58.5 –

CCSD/6-31G^a 1.71 1.511 104.6 98.3 67.3 2.64

CCSD/6-31++G^a 1.67 1.511 107.5 100.4 61.9 3.03

CCSD/aug-cc-pVTZ^a 1.667 1.498 106.7 100.1 63.5 2.98

UCCSD/aug-cc-pVTZ^c 1.6722 1.5074 107.356 100.469 62.209

Exp.^b 1.672 1.513 106.6 101.8 63.1

	R_As - O(Å)	R_As - H(Å)	Φ_HAsO(°)	Φ_HAsH(°)	Θopp(°)	μ(Debye)	Energy(a.u.)
B3LYP/QZ	1.681	1.529	106.834	99.765	63.292	2.97	–2312.37
B3LYP/5Z	1.681	1.529	106.809	99.783	63.328	2.96	–2312.36
B3P86/QZ	1.665	1.524	107.824	100.278	61.473	3.00	–2313.29
B3P86/5Z	1.665	1.524	107.792	100.296	61.521	3.00	–2313.29
B3PW91/QZ	1.669	1.526	107.698	100.163	61.722	2.97	–2312.31
B3PW91/5Z	1.669	1.526	107.665	100.182	61.772	2.97	–2312.3
MP2/QZ	1.599	1.493	119.263	103.94	39.492	4.50	–2310.78
MP2/5Z	1.599	1.493	119.169	104.178	37.512	4.48	–2310.88
B3LYP/6-31G**^a	1.702	1.530	106.0	98.6	65.1	2.85
B3LYP/6-31++G^a	1.683	1.528	106.7	99.8	63.5	2.98
B3LYP/aug-cc-pVTZ^a	1.685	1.529	106.6	99.7	63.7	2.96
QCISD/6-31G**^a	1.709	1.517	105.5	98.5	65.8	2.68
QCISD/6-31++G^a	1.683	1.52	107.3	100.2	62.5	2.97
QCISD/aug-cc-pVTZ^a	1.679	1.508	106.9	100.2	63.1	2.93
CCSD(T)/6-31G**^a	1.698	1.52	106.8	99.0	63.5	–
CCSD(T)/6-31++G^a	1.669	1.522	109.4	101.0	58.5	–
CCSD(T)/aug-cc-pVTZ^a	1.669	1.522	109.4	101.0	58.5	–
CCSD/6-31G**^a	1.71	1.511	104.6	98.3	67.3	2.64
CCSD/6-31++G^a	1.67	1.511	107.5	100.4	61.9	3.03
CCSD/aug-cc-pVTZ^a	1.667	1.498	106.7	100.1	63.5	2.98
UCCSD/aug-cc-pVTZ^c	1.6722	1.5074	107.356	100.469	62.209
Exp.^b	1.672	1.513	106.6	101.8	63.1

^aUsing various methods from Ref. 2; ^bFrom Ref. 7; ^cUsing UCCSD/aug-cc-pVTZ from Ref. 10.

Table 2

The geometry structures of H₂XO (X = As, P, N)

Parameter		H₂AsO					H₂PO			H₂NO
r_XO(Å)	1.667^a	1.672^b	1.669^d	1.4875^e	1.487^f	1.497^g		1.0003ⁱ	1.028^j
r_HX(Å)	1.498^a	1.513^b	1.526^d	1.4287^e	1.407^f	1.421^g	1.278^h	1.259ⁱ	1.297^j
φ_HXO(°)	106.7^a	106.6^b	107.665^d	115.52^e	114.6^f	114.0^g
φ_HX_H(°)	100.1^a	101.8^b	100.182^d	102.56^e	102.4^f	101.9^g	121^h	121ⁱ	115.0^j

^aUsing CCSD/aug-cc-pVTZ methods From Ref.2; ^bFrom Ref.7; ^dUsing B3PW91/aug-cc-pV5Z level in the present work; ^eFrom Ref. 29; ^fUsing CCSD/aug-cc-pV(T + d)Z from Ref. 30; ^gUsing B3LYP/cc-pVTZ + 1 Collected from Ref. 31; ^hUsing CCSD(T)/aug-cc-pVTZ methods From Ref. 2; ⁱUsing HF/cc-pVDZ from Ref. 32; ^jMCSCF optimized geometries from Ref.33.

Table 3

Calculated ground-state and equilibrium rotational constants of H₂AsO (cm^-1)

	A₀	B₀	C₀	A_e	B_e	C_e
B3LYP/QZ	3.98	0.423	0.41	3.946	0.421	0.408
B3LYP/5Z	3.978	0.423	0.41	3.945	0.421	0.408
B3P86/QZ	4.048	0.431	0.416	4.008	0.428	0.414
B3P86/5Z	4.046	0.431	0.416	4.007	0.428	0.414
B3PW91/QZ	4.029	0.429	0.415	3.991	0.426	0.412
B3PW91/5Z	4.027	0.429	0.415	3.989	0.427	0.412
MP2/QZ	5.000	0.464	0.437	4.990	0.465	0.438
MP2/5Z	4.990	0.464	0.437	4.981	0.465	0.438
Exp.^a	4.04989	0.428843	0.413912

^aFrom Ref. 7.

Table 4

Calculated harmonic and fundamental vibrational frequencies of H₂AsO (cm^-1)

	ω ₁	ω ₂	ω ₃	ω ₄	ω ₅	ω ₆	ν ₁	ν ₂	ν ₃	ν ₄	ν ₅	ν ₆
B3LYP/QZ	2103.115	975.521	844.269	545.954	2140.786	717.155	2056.348	954.374	829.958	564.901	2083.929	723.351
B3LYP/5Z	2103.812	975.300	844.144	546.735	2141.657	717.859	2060.611	952.709	829.477	564.774	2088.081	723.310
B3P86/QZ	2128.959	73.517	871.593	555.813	2167.445	718.092	2087.011	953.173	856.119	576.364	2115.891	723.687
B3P86/5Z	2129.366	973.308	871.440	556.617	2168.068	719.075	2091.009	952.187	855.851	574.822	2119.694	722.850
B3PW91/QZ	2122.628	972.242	865.148	546.810	2160.279	717.139	2071.280	951.090	849.143	567.201	2099.429	721.448
B3PW91/5Z	2123.252	972.128	865.017	547.559	2161.122	718.092	2075.912	950.082	849.052	567.043	2103.880	721.174
MP2/QZ	2281.572	1595.604	1011.551	792.113	2316.712	679.423	2158.509	1398.231	991.068	743.260	2217.595	669.201
MP2/5Z	2274.068	1591.417	1019.003	789.359	2308.918	679.661	2160.459	1388.182	991.991	738.585	2218.106	668.215
B3LYP/6-31G**^a	2100	994	806	519	2137	717
B3LYP/6-31++G^a	2105	978	843	538	2144	716
B3LYP/aug-cc-pVTZ^a	2105	975	841	541	2144	717
QCISD/6-31G**^a	2203	1032	807	497	2224	741
QCISD/6-31++G^a	2203	994	859	520	2229	735
QCISD/aug-cc-pVTZ^a	2235	1003	863	524	2272	738
CCSD(T)/6-31G**^a	2178	1021	812	454	2204	733
CCSD(T)/6-31++G^a	2174	973	875	507	2206	712
CCSD(T)/aug-cc-pVTZ^a	2204	981	878	515	2244	705
CCSD/6-31G**^a	2214	1039	808	451	2234	754
CCSD/6-31++G^a	2239	1003	880	499	2267	743
CCSD/aug-cc-pVTZ^a	2260	1014	883	485	2302	750
Exp.^b	2033.7	969.3	855.85	523.67

^aUsing various methods from Ref. 2; ^bFrom Ref. 7.

Table 5

Calculated anharmonic constants χ_ij of H₂AsO (cm^-1)

Parameter	B3LYP		B3P86		B3PW91		MP2		Exp.7
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
x ₁₁	–13.762	–12.778	–11.375	–10.294	–13.770	–12.643	–27.272	–24.761
x ₁₂	–13.587	–13.800	–12.468	–12.666	–12.945	–13.206	–12.726	–13.042	–15.85
x ₁₃	2.108	1.986	0.642	0.369	0.801	0.607	–13.662	–14.400	–1.47
x ₁₄	22.692	22.494	19.046	18.439	19.477	19.174	–9.336	–9.375	–2.38
x ₁₅	–57.041	–53.268	–47.482	–43.461	–56.837	–52.609	–94.236	–84.658
x ₁₆	7.340	7.291	1.866	1.780	1.888	1.924	–7.077	–6.700
x ₂₂	–1.539	–1.788	–1.325	–1.460	–1.376	–1.534	–75.185	–77.386	–4.32
x ₂₃	0.187	–0.034	–0.328	–0.321	–0.188	–0.203	–9.218	–9.384	–3.66
x ₂₄	–5.861	–6.488	–6.418	–6.425	–6.966	–6.991	–65.988	–67.927	–4.18
x ₂₅	–16.606	–16.975	–14.663	–15.036	–15.314	–15.720	6.523	6.184
x ₂₆	–0.270	–0.738	–1.512	–1.955	–1.389	–1.835	0.259	–1.043
x ₃₃	–4.200	–4.217	–4.333	–4.285	–4.388	–4.341	–1.193	–3.467	–5.03
x ₃₄	–13.333	–13.341	–12.689	–12.416	–13.880	–13.454	2.459	1.375	–12.12
x ₃₅	1.252	1.096	0.046	–0.292	0.146	–0.095	–11.910	–13.100
x ₃₆	–2.035	–2.174	–1.287	–1.378	–1.336	–1.422	–3.860	–4.644
x ₄₄	4.483	4.387	5.158	4.607	5.701	5.531	–5.795	–5.946	5.00
x ₄₅	19.550	19.337	16.242	15.582	16.457	16.105	–0.902	–0.885
x ₄₆	–3.084	–3.473	4.291	2.801	2.888	2.011	–0.759	–0.951
x ₅₅	–16.928	–16.030	–14.656	–13.715	–16.889	–15.899	–23.598	–21.430
x ₅₆	6.840	6.779	1.371	1.318	1.404	1.433	–8.057	–7.898
x ₆₆	0.900	0.804	1.615	1.246	1.291	1.013	–0.238	–0.414

Table 6

Calculated vibration-rotation interaction constants of H₂AsO (MHz)

Parameter	B3LYP		B3P86		B3PW91		MP2
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
$α_{1}^{A} \times 10^{- 3}$	1.171	1.154	1.301	1.280	1.274	1.254	1.646	1.673
$α_{2}^{A} \times 10^{- 3}$	–1.260	–1.242	–1.371	–1.355	–1.347	–1.328	1.872	1.906
$α_{3}^{A} \times 10^{- 3}$	1.616	1.597	1.752	1.730	1.720	1.697	2.682	2.720
$α_{4}^{A}$	753.760	750.898	690.814	686.495	688.156	684.427	–2442.728	–2483.030
$α_{5}^{A}$	20.857	18.149	114.901	110.750	107.809	104.162	416.502	430.685
$α_{6}^{A}$	–286.173	–275.770	–122.516	–119.065	–146.040	–139.251	–3568.855	–3654.317
$α_{1}^{B}$	–5.351	–5.580	–0.883	–1.170	–1.316	–1.600	3.624	3.619
$α_{2}^{B}$	2.140	2.622	0.898	1.198	0.613	1.015	8.638	8.951
$α_{3}^{B}$	–11.139	–11.359	–5.355	–5.649	–6.087	–6.378	–1.266	–1.429
$α_{4}^{B}$	–43.667	–43.828	–44.514	–44.837	–44.260	–44.550	–106.295	–108.142
$α_{5}^{B}$	98.226	97.912	100.656	100.434	101.361	101.132	–39.833	–37.725
$α_{6}^{B}$	89.381	89.265	90.908	90.718	93.804	93.684	74.520	74.170
$α_{1}^{C}$	–4.835	–5.050	–1.299	–1.555	–1.646	–1.898	2.010	2.104
$α_{2}^{C}$	12.725	13.145	11.477	11.753	11.357	11.715	22.553	22.767
$α_{3}^{C}$	–7.343	–7.577	–2.683	–2.972	–3.294	–3.578	1.208	1.209
$α_{4}^{C}$	–27.083	–27.199	–26.283	–26.508	–26.418	–26.623	–84.396	–85.860
$α_{5}^{C}$	82.413	82.081	83.995	83.736	84.560	84.302	–19.834	–18.739
$α_{6}^{C}$	77.754	77.636	77.391	77.250	80.243	80.148	48.636	48.847

Table 7

Calculated equilibrium quartic centrifugal distortion constants of H₂AsO (MHz)

Parameter	B3LYP		B3P86		B3PW91		MP2
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
D_J	13.934	13.942	13.161	13.180	13.430	13.448	8.111	8.160
D_JK	361.441	360.314	366.066	364.878	370.120	368.948	427.635	425.255
D_K×10^–3	2.725	2.715	2.857	2.845	2.852	2.839	3.815	3.805
d₁×10	–5.687	–5.691	–5.631	–5.640	–5.756	–5.764	–4.526	–4.561
d₂×10²	3.245	3.251	3.243	3.254	3.297	3.307	0.074	–0.026

Table 8

Calculated equilibrium sextic centrifugal distortion constants of H₂AsO (Hz)

Parameter	B3LYP		B3P86		B3PW91		MP2
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
10²H_J	–3.141	–3.109	–2.541	–2.525	–2.873	–2.855	–2.438	–2.422
10^-2H_K	3.793	3.764	3.965	3.932	4.040	4.005	–2.039	–1.972
H_JK	–2.546	–2.545	–2.303	–2.301	–2.512	–2.511	3.284	3.248
10^-1H_KJ	–7.025	–7.033	–8.615	–8.580	–8.386	–8.363	–14.641	–14.586
10⁴h₁	–4.118	–3.891	–6.613	–6.432	–7.264	–7.072	–41.837	–41.561
10⁴h₂	4.276	4.236	3.872	3.834	4.349	4.312	–12.280	–12.166
10⁵h₃	5.355	5.375	5.918	5.939	5.975	5.998	–7.009	–7.031

Table 9

Calculated cubic force constants of H₂AsO in normal coordinates (cm^-1)

Parameter	B3LYP		B3P86		B3PW91		MP2
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
f ₃₁₁	–793.548	–791.431	–793.680	–791.358	–791.464	–788.682	–970.988	–977.417
f ₃₂₁	4.715	6.265	–9.359	–7.524	–7.134	–5.643	36.087	37.020
f ₃₂₂	239.401	238.363	251.237	249.362	249.570	247.928	314.144	312.710
f ₃₃₃	–822.493	–820.011	–823.245	–820.626	–819.771	–816.692	–1020.573	–1024.089
f ₄₁₁	–16.078	–17.006	–18.706	–19.587	–19.025	–19.647	–39.244	–38.787
f ₄₂₁	–92.978	–92.651	–105.592	–104.871	–103.710	–103.061	52.152	52.868
f ₄₂₂	–38.181	–37.692	–35.980	–35.819	–36.784	–36.442	–13.649	–10.978
f ₄₃₃	50.719	49.044	45.376	43.795	45.482	44.188	–32.230	–31.066
f ₄₄₃	97.240	97.208	105.601	105.090	104.668	104.290	–34.434	–33.459
f ₄₄₄	131.362	131.272	130.022	130.247	127.922	128.244	1021.646	1037.253
f ₅₁₁	–44.980	–44.409	–48.356	–47.788	–47.883	–47.363	–69.097	–68.796
f ₅₂₁	90.216	90.172	80.293	80.038	83.165	82.940	–182.886	–180.248
f ₅₂₂	52.705	52.201	49.545	49.439	50.454	50.136	–60.824	–63.734
f ₅₃₃	–44.120	–43.509	–49.606	–48.952	–48.722	–48.124	–19.726	–16.907
f ₅₄₃	–4.745	–4.677	–8.634	–8.403	–7.961	–7.730	7.727	7.256
f ₅₄₄	–4.223	–4.191	–5.283	–5.126	–4.694	–4.572	61.045	60.177
f ₅₅₃	10.127	10.240	2.009	2.012	4.211	4.234	120.414	110.207
f ₅₅₄	23.310	23.088	27.679	27.328	26.594	26.243	18.878	19.187
f ₅₅₅	198.480	197.731	216.198	215.483	211.675	210.959	129.470	117.531
f ₆₁₁	–11.689	–10.580	–32.874	–31.355	–29.153	–27.815	–51.973	–51.936
f ₆₂₁	257.472	256.548	267.111	265.504	267.419	266.026	148.354	147.700
f ₆₂₂	27.339	25.585	26.919	26.066	28.453	27.059	48.538	50.524
f ₆₃₃	10.864	11.913	–13.034	–11.530	–9.217	–7.906	–50.676	–50.292
f ₆₄₃	18.416	18.667	14.134	14.511	15.307	15.648	84.048	84.258
f ₆₄₄	16.935	17.042	14.140	14.764	14.560	15.068	269.106	273.164
f ₆₅₃	107.392	107.433	91.388	91.401	96.630	96.684	19.769	19.071
f ₆₅₄	4.141	4.270	0.531	0.665	1.380	1.568	93.566	92.349
f ₆₅₅	–91.658	–91.466	–93.734	–93.446	–94.559	–94.333	13.872	11.951
f ₆₆₃	321.879	320.844	341.986	340.250	343.216	341.744	214.374	212.185
f ₆₆₄	79.639	79.780	81.815	82.034	81.859	82.125	–88.817	–85.000
f ₆₆₅	108.294	107.223	102.611	102.222	106.924	106.276	60.263	60.120
f ₆₆₆	–85.530	–86.347	–94.684	–94.345	–97.962	–98.254	152.160	155.159

Table 10

Calculated quartic force constants of H₂AsO in normal coordinates (cm^-1)

Parameter	B3LYP		B3P86		B3PW91		MP2
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
f ₁₁₁₁	238.493	249.875	273.035	284.704	235.104	246.996	334.354	380.376
f ₂₁₁₁	15.681	6.786	23.562	10.525	35.510	22.775	–19.517	–19.418
f ₂₂₁₁	–108.244	–107.408	–136.492	–135.091	–135.534	–133.855	–200.805	–200.904
f ₂₂₂₁	–33.702	–29.500	–34.329	–30.451	–31.062	–27.691	9.308	7.414
f ₂₂₂₂	128.903	126.035	147.444	139.766	141.849	135.664	157.580	154.400
f ₃₃₁₁	277.322	289.372	311.235	323.965	271.781	284.776	333.276	381.758
f ₃₃₂₁	7.750	–1.114	12.128	–0.827	25.530	12.791	–5.420	–5.763
f ₃₃₂₂	–106.518	–105.574	–134.957	–133.613	–133.779	–132.019	–216.330	–215.460
f ₃₃₃₃	325.988	337.955	358.812	372.079	317.160	330.644	332.845	380.443
f ₄₃₁₁	–28.274	–15.557	–0.266	11.491	–16.725	–4.664	17.040	19.723
f ₄₃₂₂	19.760	18.210	23.241	21.931	19.777	18.569	0.695	0.962
f ₄₃₃₃	–32.699	–20.209	–4.214	7.311	–21.299	–9.380	32.195	32.994
f ₄₄₁₁	–144.890	–146.261	–142.199	–143.360	–144.095	–145.382	–8.210	–10.205
f ₄₄₂₁	17.032	17.323	7.435	8.073	11.906	12.167	–58.974	–59.862
f ₄₄₂₂	19.880	17.813	19.658	17.493	19.634	17.491		–2.410
f ₄₄₃₁	–0.061	–0.086	0.082	–	–	–
f ₄₄₃₃	–114.527	–115.215	–113.701	–113.960	–115.343	–115.886	–38.530	–39.798
f ₄₄₄₃	–21.883	–19.873	–10.264	–9.133	–17.411	–15.784	149.081	149.100
f ₄₄₄₄	47.141	42.881	50.984	48.440	49.249	46.454	71.579	78.631
f ₅₂₂₂							–0.326	0.219
f ₅₃₁₁	12.839	10.658	19.050	15.397	21.448	17.758	29.637	32.784
f ₅₃₂₂	–28.495	–26.953	–27.450	–26.078	–26.757	–25.524	–1.955	–0.727
f ₅₃₃₃	11.675	9.577	16.689	13.105	19.377	15.8350	18.589	20.054
f ₅₄₁₁	17.584	17.957	25.413	25.228	24.521	24.362	12.635	12.241
f ₅₄₂₂	–15.070	–14.485	–13.826	–13.084	–13.777	–12.945	–14.013	–13.890
f ₅₄₃₃	13.177	13.566	20.677	20.482	19.870	19.796	11.291	9.211
f ₅₄₄₃	–4.514	–4.131	–7.237	–6.820	–6.126	–5.831	–10.539	–9.732
f ₅₄₄₄	–1.886	–1.486	–2.514	–1.905	–2.440	–1.724	141.042	141.939
f ₅₅₁₁	–13.881	–14.590	–12.065	–13.533	–13.107	–14.165	–157.102	–156.672
f ₅₅₂₁	–16.479	–15.174	–15.105	–13.650	–15.217	–14.035	23.035	22.057
f ₅₅₂₂	14.558	14.098	13.681	13.352	14.221	13.938	42.921	38.873
f ₅₅₃₁	0.184	–	–	–	–0.211	–
f ₅₅₃₃	–12.157	–12.740	–10.984	–12.214	–11.893	–12.786	–138.833	–134.821
f ₅₅₄₃	3.960	3.456	5.205	4.334	4.630	3.806	–0.216	1.133
f ₅₅₄₄	0.667	–0.253	–0.715	–0.809	–0.310	–0.477	10.046	7.127
f ₅₅₅₃	–10.772	–10.369	–9.255	–8.842	–9.594	–9.252	–38.927	–35.205
f ₅₅₅₄	4.946	4.830	8.380	8.228	7.522	7.466	13.536	14.240
f ₅₅₅₅	40.611	39.596	51.100	51.036	48.156	48.119	51.491	5.362
f ₆₂₂₁							0.234	–0.254
f ₆₂₂₂	–	–	–	–	–	0.508	–0.300	0.488
f ₆₃₁₁	–0.496	–2.507	27.909	20.406	30.617	23.647	21.234	24.601
f ₆₃₂₂	–36.189	–32.480	–36.317	–32.106	–34.497	–31.329	–12.753	–13.073
f ₆₃₃₃	0.612	–1.360	24.432	16.958	28.465	21.245	38.321	40.645
f ₆₄₁₁	–0.786	–1.363	17.702	15.826	15.738	14.019	–54.906	–54.855
f ₆₄₂₂	–28.010	–26.394	–29.636	–27.695	–27.862	–25.900	29.293	26.529
f ₆₄₃₃	0.116	–0.338	17.207	15.532	15.702	14.133	–78.085	–78.576
f ₆₄₄₃	1.832	3.592	–1.953	0.157	–1.464	–	81.041	80.537
f ₆₄₄₄	–1.048	–1.486	–0.520	–	–0.916	–0.381	–486.973	–490.111
f ₆₅₁₁	–35.098	–34.674	–36.929	–36.948	–38.063	–37.837	–11.369	–11.662
f ₆₅₂₂	38.498	38.373	44.312	41.746	43.918	41.714	–34.884	–34.965
f ₆₅₃₃	–30.408	–30.021	–33.504	–33.534	–34.298	–34.182	–5.276	–5.704
f ₆₅₄₄	9.486	9.492	6.430	6.100	7.289	6.719	62.806	62.719
f ₆₅₅₃	–11.653	–10.751	–10.957	–9.822	–11.272	–10.877	–9.288	–7.581
f ₆₅₅₄	–10.606	–10.458	–11.127	–11.122	–10.943	–10.886	–6.301	–9.208
f ₆₅₅₅	–24.358	–23.740	–27.351	–27.564	–26.527	–26.885	17.663	11.016
f ₆₆₁₁	–93.827	–93.850	–112.274	–113.839	–112.545	–112.837	–134.588	–134.756
f ₆₆₂₁	–30.799	–26.863	–33.086	–27.309	–31.326	–26.456	–9.403	–9.502
f ₆₆₂₂	101.543	99.211	138.155	130.819	132.691	128.003	56.192	55.512
f ₆₆₃₁	0.288	–	–0.187	–	0.427	–	–0.081
f ₆₆₃₃	–82.825	–82.793	–102.895	–104.190	–102.294	–102.366	–137.791	–137.242
f ₆₆₄₃	8.457	6.2450	4.788	2.724	4.358	2.578	8.256	8.140
f ₆₆₄₄	26.496	23.625	23.337	22.968	24.262	23.862	–251.103	–256.057
f ₆₆₅₃	–15.843	–14.529	–17.196	–15.195	–16.815	–15.084	–22.349	–21.066
f ₆₆₅₄	–4.173	–3.960	–5.785	–5.729	–4.668	–4.398	–20.280	–20.641
f ₆₆₅₅	37.474	36.485	34.588	34.974	36.509	37.408	19.406	14.179
f ₆₆₆₃	–17.155	–14.746	–23.885	–18.232	–21.749	–18.039	–39.234	–39.968
f ₆₆₆₄	4.780	5.028	–2.724	–2.549	1.696	1.621	–55.841	–58.597
f ₆₆₆₅	35.860	36.063	44.736	41.228	44.921	41.841	–45.065	–46.468
f ₆₆₆₆	254.448	252.635	290.808	280.324	299.140	295.367	51.009	48.286

Table 11

Calculated Coriolis coupling constants of H₂AsO

Parameter	B3LYP		B3P86		B3PW91		MP2
	QZ	5Z	QZ	5Z	QZ	5Z	QZ	5Z
$ζ_{21}^{(a)}$	0.463	0.463	0.454	0.455	0.456	0.456	0.324	0.323
$ζ_{31}^{(a)}$	0.007	0.007	0.007	0.007	0.007	0.007	0.013	0.012
$ζ_{32}^{(a)}$	–0.458	–0.458	–0.462	–0.462	–0.461	–0.461	–0.515	–0.516
$ζ_{41}^{(a)}$	0.298	0.298	0.308	0.308	0.307	0.308	–0.212	–0.211
$ζ_{42}^{(a)}$	0.258	0.258	0.246	0.246	0.248	0.248	0.212	0.213
$ζ_{43}^{(a)}$	–0.044	–0.045	–0.043	–0.044	–0.044	–0.044	0.256	0.254
$ζ_{51}^{(a)}$	–0.185	–0.186	–0.168	–0.169	–0.173	–0.173	0.416	0.417
$ζ_{52}^{(a)}$	–0.126	–0.126	–0.141	–0.141	–0.137	–0.137	0.172	0.171
$ζ_{53}^{(a)}$	0.213	0.213	0.184	0.185	0.192	0.192	0.003	0.003
$ζ_{54}^{(a)}$	0.289	0.290	0.254	0.255	0.263	0.264	–0.333	–0.334
$ζ_{61}^{(a)}$	–0.316	–0.316	–0.322	–0.322	–0.320	–0.319	–0.228	–0.229
$ζ_{62}^{(a)}$	–0.207	–0.208	–0.205	–0.206	–0.207	–0.207	0.053	0.052
$ζ_{63}^{(a)}$	0.436	0.435	0.445	0.445	0.443	0.442	0.399	0.398
$ζ_{64}^{(a)}$	0.569	0.569	0.589	0.589	0.584	0.584	–0.232	–0.231
$ζ_{65}^{(a)}$	0.110	0.110	0.102	0.103	0.104	0.104	0.517	0.518
$ζ_{21}^{(b)}$	–0.335	–0.335	–0.329	–0.329	–0.330	–0.330	–0.235	–0.234
$ζ_{31}^{(b)}$	0.010	0.010	0.009	0.009	0.009	0.009	0.018	0.017
$ζ_{32}^{(b)}$	–0.633	–0.633	–0.638	–0.638	–0.637	–0.637	–0.712	–0.712
$ζ_{41}^{(b)}$	0.412	0.412	0.426	0.426	0.425	0.425	–0.293	–0.292
$ζ_{42}^{(b)}$	0.357	0.357	0.340	0.340	0.342	0.342	0.293	0.294
$ζ_{43}^{(b)}$	0.032	0.032	0.031	0.032	0.032	0.032	–0.185	–0.184
$ζ_{51}^{(b)}$	–0.256	–0.256	–0.233	–0.233	–0.239	–0.239	0.575	0.576
$ζ_{52}^{(b)}$	–0.175	–0.174	–0.195	–0.194	–0.190	–0.189	0.238	0.236
$ζ_{53}^{(b)}$	–0.154	–0.154	–0.133	–0.134	–0.139	–0.139	–0.002	–0.002
$ζ_{54}^{(b)}$	–0.209	–0.210	–0.184	–0.185	–0.191	–0.191	0.241	0.241
$ζ_{61}^{(b)}$	–0.437	–0.436	–0.445	–0.444	–0.441	–0.441	–0.316	–0.317
$ζ_{62}^{(b)}$	–0.286	–0.287	–0.284	–0.284	–0.286	–0.286	0.073	0.072
$ζ_{63}^{(b)}$	–0.315	–0.315	–0.322	–0.322	–0.320	–0.320	–0.289	–0.288
$ζ_{64}^{(b)}$	–0.412	–0.412	–0.427	–0.426	–0.423	–0.423	0.168	0.167
$ζ_{65}^{(b)}$	–0.079	–0.080	–0.074	–0.074	–0.075	–0.076	–0.374	–0.375
$ζ_{31}^{(c)}$	–0.024	–0.024	–0.025	–0.025	–0.024	–0.024	–0.042	–0.042
$ζ_{32}^{(c)}$	0.002	0.002	–0.006	–0.006	–0.005	–0.005	–0.122	–0.121
$ζ_{41}^{(c)}$	0.849	0.848	0.837	0.836	0.838	0.837	0.252	0.254
$ζ_{42}^{(c)}$	–0.222	–0.222	–0.228	–0.228	–0.227	–0.227	–0.138	–0.138
$ζ_{51}^{(c)}$	0.090	0.091	0.060	0.061	0.068	0.070	0.693	0.692
$ζ_{52}^{(c)}$	–0.052	–0.053	–0.046	–0.046	–0.048	–0.049	–0.242	–0.242
$ζ_{61}^{(c)}$	0.439	0.440	0.459	0.460	0.457	0.457	0.523	0.524
$ζ_{62}^{(c)}$	0.171	0.171	0.186	0.186	0.184	0.184	–0.344	–0.344

3.1 Molecular structure

It has been theoretically and experimentally shown that ground state H₂AsO is a nonplanar, pyramidal molecule of C_s point group symmetry [2, 7]. Employing the analytic gradients of molecular energy, the H₂AsO geometries were optimized by MP2, B3LYP, B3P86, and B3PW91 methods with aug-cc-pVQZ and aug-cc-pV5Z basis sets considering the C_s point group symmetry. The geometries of H₂AsO can be described by five parameters: two bond lengths of As–O (R_As–O) and As–H (R_As–H), two bond angles of H–As–O (Φ_HAsO) and H–As–H (Φ_HAsH), and a dihedral angel or out-of-plane angle (Θ_opp). In order to compare with the existing experimental or theoretical data, we choose the out-of-plane angle to represent the nonplanar structure. Of course, the dihedral angel can be easily derived from the corresponding out-of-plane angle.

The obtained equilibrium geometries, dipole moments and total energies of H₂AsO are listed in Table 1, as well as the experimental data [7] and previous theoretical results [9]. In this work, the B3PW91/aug-cc-pV5Z results are in accord with the experimental data which can be derived from the ground-state rotational constants of Table 3. The discrepancy is only 0.003 Å, 0.013Å, 1.065 Å, 1.618°, and 1.328° for R_As–O, R_As–H, Φ_HAsO, Φ_HAsH, and Θ_opp, respectively. The comparison between the equilibrium molecular geometries and effective r₀ structure should be noticeable for the same reason with the reference [18]. The values of the dipole moments and total energies of the H₂AsO molecule at the B3PW91/aug-cc-pV5Z theoretical level are also listed in Table 1, which are 2.97 Debye and –2312.3 a.u., respectively. The optimized equilibrium geometry of the H₂AsO molecule at the B3PW91/aug-cc-pV5Z level can be found in Fig. 1.

Fig.1

The optimized geometry of H₂AsO at B3PW91/aug-cc-pV5Z theoretical level.

The optimized equilibrium geometry of H₂XO (X = As, P, N) are showed in Table 2. The experimentally derived HXH (X = As, P, N) bond angles of H₂AsO and H₂PO as well as the theoretical bond angles of H₂NO are 101.8°, 102.56° and ∼121° [2 , 29–33]. There are four groups around the central atom X: a double bond XO, two single bonds HX, and an unpaired electron of the X atom in H₂XO molecules. According to Valence shell electron pair repulsion (VSEPR) theory [34], the bond angle of the H₂XO molecule should be less than 120° [19]. The bond angle of φ_HXO (X = N, P, As) markedly diminishes and the bond length of r_HX and r_XO (X = N, P, As) distinctly enlarges. Therefore, the covalent bond of the H₂AsO molecule is the weakest one.

3.2 Rotational constants

The rotational constants of the H₂AsO molecule are showed in Table 3. The relationship between ground-state rotational constants values (A₀, B₀, C₀) and equilibrium rotational constants (A_e, B_e, C_e) can be expressed in Equation (2.1).

The difference between the ground-state rotational constants of the H₂AsO molecule at the B3PW91/aug-cc-pV5Z and the experimental values are 0.57%, 0.04%, and 0.26%, respectively. Therefore, one can easily conclude from Equation (2.1) that the ground-state equilibrium rotational constants (A_e = 3.989, B_e = 0.427, C_e = 0.412) of H₂AsO at the B3PW91/aug-cc-pV5Z level are reliable.

3.3 Vibrational frequencies

Molecular vibrational effects play a key role in electron scattering and various molecular properties such as the dipole moment [35 –37]. The H₂AsO molecule has six vibrational modes: AsH symmetric stretch ν₁, HAsH symmetric bend ν₂, AsO stretch ν₃, HAsH wag ν₄, AsH antisymmetric stretchν₅, and HAsH antisymmetric bend or rock ν₆.

The ω₂ of H₂AsO at B3PW91/aug-cc-pV5Z is fairly in agreement with the corresponding experimental value with the errors higher than 2.828 cm^–1 and better than previous higher-level theories B3LYP, QCISD, CCSD(T), and CCSD with 6–31G**, 6–31++G, and aug-cc-pVTZ basis sets [7], respectively. The deviations between ω₁, ω₃, and ω₄ of H₂AsO at the B3PW91/aug-cc-pV5Z and the corresponding experimental data are just 4.4034%, 1.0711%, and 4.5618%, respectively.

3.4 Anharmonic constants

Table 5 summarizes the anharmonic constants of H₂AsO, most of which can be regarded as the predicted values since the corresponding experiment data have not been observed. The experimental anharmonic constant of H₂AsO is yielded from the assignments of the observed energy levels from the emission spectra [38, 39]. The anharmonic corrections seem to be estimated empirically, for example, χ₃₃ = (ν₃–ω₃)/2. When one substitutes the BPW91/aug-cc-pV5Z result in Table 5 to this empirical expression, χ₃₃ =−7.9825 cm^–1. However, when taking $\frac{1}{4} (χ_{31} + χ_{32} + χ_{34} + χ_{35} + χ_{36})$ into account in Equation (2.1), χ₃₃ should be –4.341 cm^–1. The neglect of $\frac{1}{4} (χ_{31} + χ_{32} + χ_{34} + χ_{35} + χ_{36})$ may cause a large error. Hence, it should be careful when the empirical anharmonic correction is used.

3.5 Vibration-rotation interaction constants

Table 6 collects the vibration–rotation interaction constants $α_{i}^{X}$ (X = A, B, C; i = 1–6). To our knowledge, the theoretical and experimental studies of vibration-rotation interaction constants of the H₂AsO molecule have not been reported. Comparing the calculated results of DFT methods with that of MP2 method, the results of DFT methods generally yield vibration–rotation constants with the same sign and magnitude. It is needed to be pointed out that the calculated vibration–rotation interaction constants results by the MP2 method show the obvious gap with the DFT data. Based on the above calculation and analysis of spectroscopic constants for H₂AsO, the results using the BPW91/aug-cc-pV5Z can be expected to be accurate.

3.6 Centrifugal distortion constants

The equilibrium quartic and sextic centrifugal distortion constants of the H₂AsO molecule are listed in Tables 7 and 8. There are no corresponding experimental and theoretical values of centrifugal distortion constants of the H₂AsO molecule as yet. The calculated equilibrium quartic and sextic centrifugal distortion constants of the H₂AsO molecule at BPW91/aug-cc-pV5Z level are expected to provide the useful information for the future experiment.

3.7 Force constants

The cubic and quartic force fields of H₂AsO showed in Tables 9 and 10 can be produced by vibration–rotation interaction constants, Coriolis coupling constants and centrifugal distortion constants [19]. There are also no corresponding experimental or theoretical reports up to now. The force constant values from the B3P86 and B3PW91 methods employing aug-cc-pVQZ and aug-cc-pV5Z basis sets are very close to each other. The cubic and quartic force constants of the H₂AsO molecule at B3PW91/aug-cc-pV5Z theoretical level are expected to be trustworthy.

3.8 Coriolis coupling constants

The Coriolis coupling plays an important role in understanding the energy distribution, molecular structure, and dynamics processes of molecules in the micro-level. It especially needs to point out that the Coriolis coupling causes energy transfer between different vibration modes that are originally independent of each other, which will lead to an important influence on the infrared spectrum and the Raman spectrum behavior of the molecule. The calculated Coriolis coupling constants of H₂AsO in Table 11 gives an index of the coupling strengths between the normal coordinates Q_i and Q_j rotating along the a (x), b(y) and c (z) axis. It can be found from Table 11 that all the values obtained from B3LYP, B3PW91 and B3P86 methods, especially B3PW91 and B3P86 methods have the same order of magnitude and close to each other.

4 Conclusion

We have calculated the anharmonic force fields and spectroscopic constants of H₂AsO employing the B3P86, B3PW91, B3LYP and MP2 methods with aug-cc-pVQZ and aug-cc-pV5Z basis sets. The rotational constants, harmonic frequencies, and anharmonic constants of H₂AsO calculated at B3PW91/aug-cc-pV5Z theoretical level well produced the corresponding experimental values. The calculated fundamental vibrational frequencies, vibration–rotation interaction constants, equilibrium quartic and sextic centrifugal distortion constants, Coriolis coupling constants, cubic and quartic force constants of H₂AsO at the B3PW91/aug-cc-pV5Z level are expected to be regarded as the predicted values. The obtained anharmonic effects on the spectroscopic constants and the cubic and quartic force fields of H₂AsO will help to study the high-resolution rotational spectrum of H₂AsO in the future.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11474142), Natural Science Foundation of Shandong Province (Grant No. ZR2014AM 0005) as well as the Taishan Scholars project of Shandong Province (ts201511055). All calculation data were carried out in the Shuguang Super Computer Center (SSCC) of Ludong University.

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