DFT anharmonic force field,and spectroscopic constants for phosphaethene,CH 2 PH

1 Introduction

The molecules containing C = N or C = P double bond play an important role in organic chemistry [1]. Their geometry structures and chemical characters are affected by the nitrogen or phosphorus atom. Like their nitrogen analogs, the C = P double bond is unstable too [2]. Although the CX₂ = NY and CX₂ = PY (X, Y = H, F, Cl, Br) are two series of the unstable molecules, these molecules are interesting from the geometry structural, NMR, infrared spectroscopic, and the theoretical points of view [2–19]. The simplest CX₂ = PY molecule, CH₂PH, one of the unstable molecules, has been studied extensively [3–8, 19].

Some attentions have been paid on molecular geometry and rotational spectroscopic constants that a lot of experimental investigations have been reported for CH₂PH. In 1976, Kroto et al. reported their first detecting of CH₂PH in pyrolysis products of (CH₃)₂PH [3]. Five years later, they carried out an accurate analysis of microwave spectrum for CH₂PH [4, 5] and derived rotational constants and five quartic centrifugal distortion coefficients. They also determined dipole moment by measuring two Stark shifts (1₀₁ ← 0₀₀ and 3₀₃ ← 2₁₂ transitions) for CH₂PH. In 1981, Brown et al. improved the microwave spectra with some measurements in the region 5–125 GHz for phosphaethene [6]. They confirmed the molecular structure by least-squares fit for CH₂PH and CD₂PH. They confirmed dipole moment components which were obtained by the analysis of the four Stark effects (1₀₁ ← 0₀₀, 2₀₂ ← 1₀₁, 2₁₂ ← 3₀₃, and 3₁₂ ← 3₁₃ transitions). They also measured the rotational and distortion constants for ¹³CH₂PH, ¹²CD₂PH, and ¹²CD₂PD isotopes. Their experimental values were reproduced by some ab initio calculations. In 1985, the isovalent molecules (H₂CNH, H₂SiNH, H₂CPH, and H₂SiPH) were investigated employing large-scale MRD-CI method by Bruna et al. [8]. They calculated the dipole moments, charge distributions, and the molecular geometries in ground states for these four molecules. The vertical excitation energies were also reported as predictions. In 1988, Dyall et al. measured the spin-rotation constants and compared them with the theoretical values from COLUMBO and GAUSSIAN82 programs employing the Hartree-Fock method [9]. Some of these studies were experimental, in which all the CH₂PH were obtained by pyrolysis. Until Lacombe and his coworkers synthesized phosphaethene molecule by the VGSR method in 1988, [10] which made the measurement of rotational spectroscopic constants much easier. In 2006, Margulès et al. used this synthesize method to reinvestigate the rotational spectrum by measuring the submillimeter-wave spectrum for phosphaethene [18]. They measured 119 new lines in submillimeter region 525–650 GHz. The measurement of ground state rotational constants and quartic centrifugal distortion constants was improved significantly. They also reported the equilibrium structure calculated at the high level of theory, CCSD(T), using cc-pVnZ and cc-pwCVQZ basis sets, respectively. In 2009, Woon and Herbst reported the molecular geometries and the dipole moments using the RCCSD(T) theory with basis set aug-cc-pVTZ for a number of neutral molecules [19].

With the evolvement of analytic second derivatives, DFT predictions of ro-vibrational spectroscopic constants are reliable and cost-effective [20–26]. But as stated above, these theoretical studies [8, 19] just calculated molecular geometry, spin-rotation constants, and the dipole moment for CH₂PH. However, those works did not give the calculated anharmonic force field and spectroscopic constants which are useful for detection of CH₂PH in planetary atmosphere or interstellar space [18] Thus the goals of this work are, first, to calculate spectroscopic constants with DFT method and check them with experimental ones; second, to discuss the isotopic effects on some rotational spectroscopic constants and vibrational frequencies for 5 isotopomers.

2 Computational methods

All the quantum-chemical calculations presented below are carried out with the GAUSSIAN03 [27], and the density functional theory [28] is used. Two methods are employed: the first one is B3LYP denoted by Becke’s three-parameter functions [29] and Lee-Yang-Parr functions [30]. The second one is B3PW91 denoted by Becke’s [29] and Perdew-Wang 91’s [31] functions.

Optimized geometries of CH₂PH are calculated using analytic gradients. Then, the associated harmonic force field is calculated analytically at optimized geometry in Cartesian coordinate. The harmonic spectroscopic constants are derived by the usual manner [32, 33] The anharmonic spectroscopic data are obtained by theoretical force fields using DFT [34, 35]. No orbital has been kept frozen during these calculations.

The electronic configuration describes the distribution of electrons in atomic orbitals. Considering the descriptions of ground electronic configuration for P, H, and C are 1s²2s²2p⁶3s²3p³, 1s¹ and 1s²2s²2p², respectively, two correlation consistent polarized valence basis sets are used. One is cc-pVTZ (triple-zeta) [36]. The other is cc-pVQZ (quadruple-zeta) [36]. The quadruple-zeta basis set maybe sufficient in calculating spectroscopic properties, because basis set extension beyond cc-pVQZ does not improve calculation significantly in such applications. In this work below, VTZ and VQZ are the abbreviated descriptions of cc-pVTZ and cc-pVQZ, respectively.

3 Results and discussion

The spectroscopic constants, geometry structure and full quartic force field for CH₂PH are contained in Tables 1–8. The calculated results are compared with the available previous, empirical or experimental data [3–8, 19]. While it is usual to compare them with experimental data and predict some spectroscopic ones [37].

The computed equilibrium structures of CH₂PH and experimentally derived results [5, 18] are shown in Table 1. The molecule structure of CH₂PH optimized within the constraint of C _s symmetry is illustrated in Fig. 1. By comparing our calculated equilibrium geometries to the experimental results, [18] a good agreement can be found: most of them agree within uncertainties. Exactly, the discrepancies of calculated results can be found: 0.0001Å (–0.0106Å in the worst case) for bond lengths, –0.0384° (–0.5188° in the worst case) for bond angles. Geometry structures are nearly converged at the VTZ basis set: [38, 39] improvements from VTZ to VQZ shorten the bond lengths (about 0.003Å) and increase the bond angles (about 0.1°). The calculated results of HPC bond angle are relatively too large (by about 0.39°). It can be explained that the P and C atoms are close to both the mass center and the a principal inertial axis (see Fig. 1), which makes it extremely difficult to measure precise structure using rotational spectroscopy [40].

OPEN IN VIEWER

Fig.1

Molecular structure of CH₂PH. The horizontal and vertical axes are the a and b principal inertial axes, respectively.

Turning attention to the dipole moment, μ, the B3LYP results agree within 0.04 Debye between the experimental values [5] which were determined by Stark shifts. From the experimental and calculated dipole moment data, it is possible to obtain the rotational angle of principal inertial axes systems for CH₂PH molecule [40]. The angles formed by μ ⇀ vector with the a principal inertial axis are 32.7° and 34.2° for the experimental [5] and the B3LYP/VTZ results, respectively.

The equilibrium and ground states rotational constants for 5 isotopic species in Table 2 are compared with experimental data [5, 18]. The relationship between ground state rotational constants and equilibrium ones are: [41]

A 0 v = A e - ∑ i α i A ( v i + 1 2 ) + ⋯(1)

Where the summation covers all normal modes, α i A is vibration-rotation interaction constant (see Table 6), and ν _I is vibrational quantum number for the i ^th normal mode. Similar definitions hold for the other rotational constants B₀ and C₀. There is a suitable agreement between experimental and theoretical data, the discrepancy between them reflects the degree of accuracy for harmonic force field and molecular geometry [16]. For the molecule, ¹²CH₂PH, the B3LYP/VQZ equilibrium rotational constants are about only 0.02% lower than experimental values for A _e , and about 0.06% higher for B _e and C _e . Besides, the other levels also reproduce observations suitable: relative errors between calculated values and experimental ones are below 0.7%. For these isotopic molecules, the deviations of calculated results between different basis sets are very tiny. The DFT predictions of the spectroscopic constants are frequently as good or better than CCSD results, [21] and the B3LYP performs better than B3PW91. Most of the B3LYP/VQZ results reproduce the experimental values [5, 18] satisfactory (within 0.13%). Based on the results, it can be possible for us to analysis the isotopic effects for CH₂PH. The isotopic effect for ¹³CH₂PH is much weaker, because the C atom in question is slightly heavier and near the mass center [42]. Contrarily, the replacement of H by D introduces a large isotope shift for the rotational constants A _e and A₀. The A _e and A₀ for CD₂PD are only about half of that for CH₂PH. That’s because the mass difference of the H isotope is very distinct and the distance between H and mass center is slightly larger, which made the inertia moment, I, much larger [42]. However, the obvious isotopic effect cannot be observed on going from CD₂PH to CD₂PD.

Theoretical fundamental frequencies ν _I are obtained from related harmonic ones ω _I by including anharmonic constants x _ij (see Table 7) according to: [34]

ν i = ω i + 2 x ii + 1 2 ∑ i ≠ j x ij + . . . .(2)

As the B3LYP predictions of fundamental vibrational frequencies are very accurate and cost-effective, [21, 43] Table 3 contains nine fundamental ν _I and harmonic vibrational wave numbers ω _I for phosphaethene using B3LYP/VQZ level. It can be found that the anharmonicity effect is quite small for fundamental frequencies corresponding to the bending modes, especially for the value of ν₇, which is about 4 cm^–1 lower than ω₇. While for the stretching vibrations, the anharmonicity effects appear to be larger, except for CP stretching mode. The harmonic values of PH (ω₃), the CH₂ symmetric (ω₂) and asymmetric (ω₁) frequencies are about 82, 122, and 143 cm^–1 bigger than ν₃, ν₂, and ν₁, respectively. The ω _I and ν _I for some isotopologues are also given in Table 3. Comparing the frequencies of CH₂PH with ¹³CH₂PH, it can be found that, for small mass differences the frequencies of the isotopic molecules are close to those of the ordinary molecule. And the shifts of ω₁, ω₂, ω₄, ω₅, ω₈ between CH₂PH (or ¹³CH₂PH) and CD₂PH (or CD₂PD) are remarkable. The same thing has happened to ω₃ on going from CH₂PH to CH₂PD. That’s because the atom H in question has a large amplitude in these normal modes [42]. Table 3 also shows that inverse isotopic shift is found in ω₃ (¹³CH₂PH). The shift can be attributed to a change in the specific kinematic characteristics of the vibrations [12]. As far as we know, these parameters have no related experimental or theoretical values. The calculated results provide the reliable predictions of the fundamental and harmonic vibrational wave numbers for phosphaethene.

Table 4 presents A-reduction centrifugal distortion constants and observed [5, 18] ones for CH₂PH. The discrepancies between observed [18] ground-state quartic values and calculated equilibrium ones are less than about 7% both at B3PW91/VQZ and B3LYP/VQZ levels. The available experimental sextic centrifugal distortion constants are for Φ _K , Φ _JK , Φ _KJ , and φ _jk , while the computed values of Φ _J , φ _j , and φ _k are regarded as predictions. The calculated results of Φ _JK and φ _jk are close to experimental results [18] with deviations below 3.0 and 0.67 Hz, respectively. However, the deviations of Φ _KJ and Φ _K are about 10² and 10³ Hz, respectively. It may be caused by numerical unstability of the equations employed to obtain the centrifugal distortion constants [20].

As the asymmetric top parameter, κ, of CH₂PH is –0.972 at B3LYP/VTZ level of theory, we also give the S-reduction centrifugal distortion constants along with observed ones [6, 18]. From Table 5, one can see that the DFT calculations of quartic centrifugal distortion constants are close to Refs. [6] and [18]. These results confirm that DFT calculations can give accurate S-reduction centrifugal distortion constants, and permit us to analysis the isotopic effects. Consideration of the calculated and experimental results show that the isotopic shifts of the substitution by D are particularly larger than the substitution by ¹³C for D _J , D _JK , and D _K , the same as the situation of rotational constants above. The substitution by the D atoms decreases all the five quartic centrifugal distortion constants compared with CD₂PH or CH₂PD.

From the previous data, it appears that the B3LYP results are reliable. Thus the vibration-rotation interaction constants and anharmonicity constants are shown in Tables 6 and 7 using B3LYP method for ¹²CH₂PH. To the best of our knowledge, there is no relative previous or experimental result to be given until now. These data can provide a prediction for α i X . But there are about 33 Coriolis coupling constants ζ _ij of CH₂PH larger than 0.1, which made the comparison between experimental and calculated α i X may not be meaningful, because most of them are perturbed by the Coriolis interactions [22].

Although anharmonicity constants, x _ij , are mass-dependent, [16] the experimental ones are not yet available. Table 7 just lists the B3LYP values for ¹²CH₂PH. From Table 7 it is found that the differences of x _ij are small with basis set extension from VTZ to VQZ. The prediction of x _ij can be used to confirm the location of some overtone and combination bands [13]. It is hoped that the calculated prediction in Table 7 will be meaningful in future experimental work for CH₂PH.

Table 8 contains cubic and quartic force constants of CH₂PH using B3LYP/ VQZ level. Table 8 shows that some cubic force constants including the CH₂ symmetric stretching (F₂₂₂ = –1339.12 cm^–1), the PH stretching (F₃₃₃ = 1463.05 cm^–1), and the coupling of the CH₂ asymmetric and symmetric stretching (F₂₁₁ = –1383.79 cm^–1) appear obviously large. Similarly, some diagonal quartic force constants involving CH₂ asymmetric stretching (F₁₁₁₁ = 570.43 cm^–1), and PH stretching (F₃₃₃₃ = 954.18 cm^–1) are found to be quite significant.

The molecular equilibrium structure, spectroscopic constants, and full quartic force fields for phosphaethene are obtained at B3PW91 and B3LYP methods with VTZ and VQZ basis sets, respectively. By comparing calculated data with obtainable experimental ones, it is found that B3PW91 and B3LYP methods can reproduce the reliable spectroscopic constants and equilibrium geometries suitable. Furthermore, the rotational spectrum constants for the five isotopomers are also obtained. The isotopic effects for the quartic centrifugal distortion constant D _K and rotational constants A _e , A₀ are obvious going from CH₂PH to CD₂PD. Finally, some spectroscopic constants are predicted and the inverse isotopic shift is found in ω₃ (¹³CH₂PH). The predictions for these spectroscopic constants, such as fundamental and harmonic vibrational wave numbers, cubic and quartic force constants, anharmonicity constants, vibration-rotation interaction constants are expected to guide future high resolution experimental work for phosphaethene. And these spectroscopic constants are useful for detection of phosphaethene in planetary atmosphere and interstellar space.