ARTICLE pubs.acs.org/JPCA
Anharmonic Frequencies of CX2Y2 (X, Y = O, N, F, H, D) Isomers and Related Systems Obtained from Vibrational Multiconfiguration Self-Consistent Field Theory Florian Pfeiffer and Guntram Rauhut* Institut f€ur Theoretische Chemie, Universit€at Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
bS Supporting Information ABSTRACT: Accurate anharmonic frequencies are provided for molecules of current research, i.e., diazirines, diazomethane, the corresponding fluorinated and deuterated compounds, their dioxygen analogs, and others. Vibrational-state energies were obtained from state-specific vibrational multiconfiguration self-consistent field theory (VMCSCF) based on multilevel potential energy surfaces (PES) generated from explicitly correlated coupled cluster, CCSD(T)-F12a, and double-hybrid density functional calculations, B2PLYP. To accelerate the vibrational structure calculations, a configuration selection scheme as well as a polynomial representation of the PES have been exploited. Because experimental data are scarce for these systems, many calculated frequencies of this study are predictions and may guide experiments to come.
I. INTRODUCTION Diazirine and its derivatives constitute a class of strained compounds with C2v symmetry, the characteristic feature being the three-membered ring.1 Diazirines are the most popular precursors for the generation of carbenes because they can produce carbenes by thermolysis or photolysis at short irradiation times.2 By reversible photochromic valence isomerization, elimination and readdition of nitrogen under ring closure or ringopening processes are possible. Because carbenes are high energy species, the thermochemical driving force for these reactions is provided by the formation of molecular nitrogen. In contrast to the diazirines the isomeric diazomethane is unstrained and thus significantly more stable than the former species. Diazomethane (CH2N2) is of particular interest because of its large number of isomeric forms and is widely used in analytical chemistry. For a long time, the assignment of its IR bands has been sensitive due to overlapping bands, notably in the mid- and far IR regions. A number of studies312 has already been published on its IR spectra including band wavenumbers and assignments to vibrational modes; e.g., Khlifi et al.12 have experimentally studied the IR spectra in the gas phase at room temperature in the 2504300 cm1 region. Although diazomethane has been known since the 1920s, diazirine was synthesized for the first time in the 1960s using the Graham reaction, starting from the corresponding amidine.13 An alternative method is the oxidation of diazirine. The quality of theoretical studies during the early period of diazirine chemistry has been too low to provide reliable information.14,15 For example, Moffat14 examined the relative electronic energies of the seven isomers of diazomethane on the basis of HartreeFock calculations with minimal STO-3G and 6-31G basis sets. As the quality of such calculations is not sufficient according to current standards, we do not refer to the results of Moffat any further. With the availability of high-level r 2011 American Chemical Society
electronic structure computer codes, a renewed effort to elucidate the electronic structure of diazirines and diazo compounds and their decomposition mechanisms was initiated in the 1990s.16 Consequently, these systems have been studied extensively by EOM-CCSD and B3LYP calculations as well as twophoton absorption spectroscopy to elucidate the mechanism of their decomposition.1719 Recently, it has been possible to produce stable molecular beams of diazirine and diazomethane.18 Thus to identify and characterize these species reliably there is considerable demand to provide accurate vibrational frequencies for this class of molecules. Likewise, studies on its photophysics and photochemistry in highly excited states have begun, promoted by high-level electronic structure calculations.18 On the basis of the general empirical formulas CX2Y2 and cyc-CX2Y2 permutations in which X represents a hydrogen, a deuterium or a fluorine atom and Y a nitrogen or an oxygen atom were calculated. The molecules with a diazirine-type structure will be labeled cyc-CX2Y2, those with diazomethanetype structures by CX2Y2 (cf. Figure 1). Within the context of diazirines an additional compound of interest that has been examined previously is [3,30 ] biazirinylidene (cf. Figure 2). This molecule is metastable with respect to its dissociation products but electronically and geometrically closely related to the monocyclic diazirines.20 This type of molecule is a possible high energy carrier and laser excitation source because of the long-lived ground state. Hoffmann et al.1 investigated the ground and low-lying excited electronic states of C2N4 using second-order generalized Van Vleck perturbation theory (GVVPT2),21,22 a variant of multireference perturbation theory. Received: July 7, 2011 Revised: September 2, 2011 Published: September 06, 2011 11050
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Figure 1. Structures of diazirine cyc-CH2N2 (left) and diazomethane CH2N2 (right).
Figure 2. Structure of biazirinylidene C2N4.
In contrast to the work of Hoffmann, we used single-reference electronic structure calculations for the determination of the multidimensional potential energy surface (for a detailed discussion of this issue see below). As the size of the systems prohibits the determination of the PES in full, a multimode expansion being truncated after the 3D terms has been used.23 It is well-known that the 1D terms are of most importance and thus require highlevel ab initio methods for a proper description. We have used explicitly correlated coupled-cluster calculations with a perturbative treatment of the triple excitations, i.e., CCSD(T)-F12a, which in combination with basis sets at the triple-ζ level provide results close to the complete basis set limit.24 As explicitly correlated coupled-cluster methods are only slightly more demanding than their traditional counterparts, i.e., CCSD(T), the explicitly correlated methods are preferable in any case. However, even a truncated multimode expansion of the PES would be too expensive if all terms would have to be computed at the CCSD(T)-F12a level. For that reason we used a multilevel scheme within the expansion of the potential to speed up the calculations.25 Details concerning these aspects are provided below. The variational calculation of anharmonic vibrational frequencies of these molecules is a challenging task due to the accurate determination of high-quality potential energy surfaces (PES) and a proper inclusion of vibration correlation effects. Once modals have been computed by means of vibrational selfconsistent field theory (VSCF)2629 correlation effects need to be accounted for as can be done by a multitude of approaches. The most obvious choice are vibrational configuration interaction (VCI) calculations, which have been implemented in different ways, i.e., state-specifically or ground-state based, conventionally or configuration selective or within the framework of vibrational meanfield configuration interaction (VMFCI) theory.3037 Although the deficiencies of configuration interaction theory are well-known, VCI calculations still constitute the work horse within the calculation of vibrational-state energies.38 Alternatively, vibrational perturbation theory (VMP2) can be used to account for correlation effects.3941 However, many near-degeneracies and severe convergence problems of the VMPn series make this approach rather problematic. More accurate than the latter are vibrational coupled-cluster approaches (VCC), which have been developed by the groups of Durga-Prasad and Christiansen.4244 In particular, vibrational linear response methods based on the wave function obtained from VCC theory
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for the vibrational ground state were found to be an interesting alternative.45 Due to the occurrence of many-particle (manymode) operators in the underlying Watson-operator usually highly excited configurations need to be accounted for. As a rule of thumb, the excitation level should be higher by 1 order than the highest term in the expansion of the potential; i.e., quadruple or even quintuple excitations need to be considered. Consequently, alternative methods, which restrict the correlation space, are highly desirable. In addition to that, VSCF modals often constitute a bad basis for the correlation treatment and thus small leading coefficients in the VCI expansions appear quite frequently. A solution for these two problems is the use of vibration multiconfiguration self-consistent theory (VMCSCF), as derived for the first time by Culot and Lievin.46,47 To reduce the correlation space while maintaining the quality of the results, we recently implemented multiconfiguration self-consistent field theory (VMCSCF) with an extension to vibrational complete active space method (VCASSCF).48 Because many vibrational states inherit multiconfigurational character, the VMCSCF method reduces the number of configurations required by optimizing variationally all single mode functions and all VCI coefficients simultaneously. Our implementation of VMCSCF theory is based on the hermitecity condition of the Lagrange matrix multipliers and the resulting VMCSCF equations are solved by consecutive 2 2 Jacobi rotations of the modals.49 Moreover, we make use of an expansion of the potential energy surface in terms of incremental multimode contributions.50,51 For further details see ref 48. Benchmark calculations have shown that VMCSCF results are excellent and close to the vibrational full CI limit but the simultaneous variational optimization is a time-consuming task once grid based algorithms are used. Therefore, we have implemented a polynomial representation of the PES that allows us to calculate all the needed integrals before the contraction within the double-iterative algorithm.52 In addition, we restricted the number of configurations by a configuration selection procedure within the active space (cs-VMCSCF) because there are noninteracting configurations with negligible contributions to the energy and to other properties. The paper is organized as follows: In section II we present detailed information about the generation of the potential energy surfaces and the vibrational wave functions of the molecules under investigation. Section III discusses the results of the vibrational calculations for all molecules. Finally, conclusions and a summary is given in section IV.
II. COMPUTATIONAL DETAILS In the present work, all calculations were performed with a development version of the MOLPRO 2010.2 package of ab initio programs.53 The equilibrium geometries of all molecules under investigation were determined at the CCSD(T)-F12a level using a cc-pVTZ-F12 basis set of Peterson et al.54 In the following, this basis will be briefly denoted VTZ-F12. The MP2F12 calculations, which are the first step in CCSD(T)-F12a calculations, were performed using the MP2-F12/3C(FIX) method described in detail in refs 55 and 56. In this method the numerous two-electron integrals are computed using robust density fitting (DF) approximations57,58 (DF was not used in the HartreeFock and CCSD(T)-F12 calculations). The aug-ccpVnZ/MP2FIT basis sets of Weigend et al.59 were used as auxiliary bases, where n corresponds to the cardinal number of the orbital basis sets. For evaluating the Fock matrix (which is needed 11051
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The Journal of Physical Chemistry A in the AO and RI basis sets) the cc-pVnZ/JKFIT basis sets59 were used. Unless otherwise noted, the same basis sets59 were also used for the resolution of the identity (RI); previous work has shown that these are well suited for this purpose.55 The complementary auxiliary basis set (CABS) approach was employed; i.e., the union of the AO and RI basis sets was used to approximate the resolution of the identity. The HartreeFock reference energies were improved by addition of the complementary auxiliary basis set (CABS) singles correction. After the equilibrium structures were determined, harmonic frequencies and, more importantly, normal coordinates needed for the expansion of the PES were determined at the same level of theory. All potential energy surfaces were obtained in a fully automated and parallel fashion using the multilevel approximation within the multimode expansion; i.e., the respective one-dimensional, two-dimensional, etc. contributions within the expansion of the potential were obtained at different electronic structure levels.60 For the 1D and 2D terms the electron correlation effects were obtained from modern explicitly correlated coupled-cluster calculations including single, double, and a perturbative correction for triple excitations (CCSD(T)-F12a). Whereas a VTZ-F12 basis has been used for the 1D terms, a smaller VDZ-F12 basis set was used for the evaluation of all 2D points. As the explicitly correlated methods converge significantly faster with respect to the basis set, the quality of CCSD(T)-F12a/VDZ-F12 calculations can roughly be compared with results of conventional coupled-cluster calculations at the CCSD(T)/cc-pVQZ level. The three-dimensional terms were calculated using the B2PLYP double-hybrid functional61 with a basis set of triple-ζ quality. Within the representation of the PES, the number of grid points per dimension was set to 20. All potential surfaces were truncated after the 3D contributions; i.e., 3-mode coupling terms have be included throughout. After determination of the PES by means of grid points, it has been transformed to polynomials up to eighth order in each dimension. In a subsequent step the deviations of the fitted PES has been checked statistically by comparison of ab initio single point energies and the corresponding points on the fitted surface. Mean absolute deviations were found to be as low as 17.6 cm1 for the 3D surfaces. This deviation includes the fitting error and the intrinsic error of the multilevel approach (in particular due to the B2PLYP functional) as the reference single point energies were determined at the CCSD(T)-F12a/VTZ-F12 level. Typically, the largest deviations can be observed at the outer regions of the potential, which are not as significant for the vibrational state energies. As a consequence, deviations in the vibrational-state energies are usually much smaller. State-specific VSCF calculations provided one-mode wave functions (modals) using a mode-dependent basis of 20 nonorthogonal distributed Gaussians.29 This basis was found to be more flexible and thus more reliable than a constant basis for all modals. Vibration correlation effects were accounted for by state-specific VMCSCF calculations based on Watson’s Hamiltonian for nonlinear molecules.62 These calculations have been carried out for different correlation spaces using active spaces of three, four, and five modals with three, two, and one additional virtual modals; i.e., a constant overall space of six modals for each oscillator has been used. Extensive tests have shown that a good accuracy vs cost ratio is achieved with 4 active modals (termed [4,6]). The VCASSCF calculations include only active-virtual modal rotations whereas our configurationselective VMCSCF (cs-VMCSCF) also takes activeactive
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Table 1. Anharmonic Frequencies (cm1) Obtained from VCASSCF Calculations in Dependence on Different Active Spaces for All Modes of Diazirine [3,6] mode harm.
νi
[4,6]
[5,6]
no. of CF
νi
no. of CF
νi
no. of CF
1B2
3273.1 3166.5
660
3130.8
1552
3130.2
1898
2A1
3151.2 3015.6
876
3013.3
1664
3012.5
2185
3A1
1655.0 1631.2
876
1629.7
1664
1627.6
2185
4A1
1494.1 1456.5
876
1455.1
1664
1454.9
2185
5B2 6A1
1140.7 1128.6 1030.5 995.4
660 876
1123.2 994.1
1552 1664
1123.2 994.0
1898 2185
7B1
1003.8
980.9
660
966.6
1552
966.6
1898
8A2
990.5
970.8
529
963.3
1422
963.3
1694
9B1
834.4
812.4
660
809.5
1552
809.5
1898
rotations into account. The configuration space within the VCASSCF method only contains up to quadruple excitations and thus does not comprise a full VCI space. Therefore, the corresponding VCASSCF calculations must be considered approximate ones and would also need the inclusion of activeactive modal rotations. However, tests showed that the thresholds for the convergence are above the corrections of these rotations why they have been neglected entirely. All calculations take into account vibrational angular momentum terms (VAM) using a constant effective moment of inertia tensor; i.e., both the Watson-correction term and the correction to all matrix elements with the approximation that the μ-tensor is given as the inverse of the inertia of the equilibrium geometry are considered.63 All the calculations were performed with both the grid and the polynomial based representation of the PES.
III. RESULTS AND DISCUSSION The convergence of the VCASSCF results with respect to the size of the active space has been studied in detail for diazirine (cf. Table 1). For example, the 1B2 and 7B1 modes show clearly that the active space within a VCASSCF[3,6] calculation is too small to yield converged results. On the other hand, in a VCASSCF[5,6] calculation the improvement with respect to the [4,6] results is rather modest and typically below one wavenumber. However, at the same time the computational cost (indicated by the number of configurations in columns 4, 6, and 8 of Table 1) increases substantially and thus a [4,6] partitioning of the correlation space appears to be the preferable choice. As a consequence, all calculations presented below refer to this combination. cyc-CF2O2 and CF2O2. The main drawback of the VMCSCF approach is the fact that the computational effort grows rapidly with an increasing number of configurations. As outlined recently, a remedy to this is a selection of the most relevant configurations based on an a priori configuration selection scheme (cs). Calculated VCASSCF and cs-VMCSCF frequencies for cyc-CF2O2 are summarized in Table 2. For example, within the calculation of mode 2B2 1552 configurations have been used in the VCASSCF calculations, from which just 180 have been used in the corresponding cs-VMCSCF approach. Although this reduction leads to a significant speed-up (up to 2 orders of magnitude) of the calculations, the loss in accuracy is 11052
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Table 2. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations for All Modes of cyc-CF2O2 and CF2O2a VCASSCF mode
exp
Table 3. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations for All Modes of cyc-CF2N2a
cs-VMCSCF
VSCF [4,6] no. of CF iter
[4,6]
VCASSCF
no. of CF iter
mode
harm.
VSCF
[4,6]
[4,6]
cyc-CF2O2 1A1
1466.6 1485.8 1465.2
1664
3/4
1465.2
272
3/4
2B2
1259
1261.2 1255.8
1552
2/3
1255.8
180
2/3
3B1
1062.1 1064.2 1057.2
1552
3/4
1057.2
172
4/5
4A1
917.9 926.3 916.7
1664
5/6
916.7
210
4/5
5A1 (772) 617 6B1
660.6 658.6 616.7 615.0
1664 1552
3/4 2/3
658.7 615.0
153 133
2/3 2/3
7B2
557
558.3 557.8
1552
2/3
557.8
114
2/3
8A1
511
512.3 510.3
1664
4/5
510.3
154
2/3
9A2
383.6 383.4
1422
2/3
383.4
103
2/3
1A0
1692.6 1675.0
3634
12/15 1674.9
948
25/35
2A0
1445.4 1436.4
3634
10/11 1436.3
736
5/6
3A0 4A0
976.9 968.6 776.0 766.4
3634 3634
2/4 6/7
968.6 766.3
401 594
2/4 8/9
5A00
620.5 613.6
2556
6/7
613.6
340
6/7
6A0
613.8 612.5
3634
5/6
612.5
328
3/4
7A0
490.6 487.8
3634
4/6
487.8
373
2/4
8A0
275.0 274.0
3634
3/4
274.0
256
2/3
9A00
229.9 227.4
2556
6/7
227.3
253
2/3
cs-VMCSCF
1A1
1598.8
1580.5
1560.3
1560.3
2A1
1310.6
1289.6
1280.1
1280.1
3B2
1278.5
1256.2
1245.4
1245.4
4B1
1114.5
1089.5
1085.6
1085.6
5A1 6B1
817.2 549.1
809.8 540.8
803.0 539.7
803.0 539.7
7A1
503.4
498.6
498.1
498.1
8B2
483.1
478.4
478.1
478.1
9A2
452.9
446.7
445.6
445.6
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level.
CF2O2
Table 4. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations in Comparison with the Experimental Values for All Modes of Diazirine and cyc-CD2N2a VCASSCF Δ
[4,6]
Δ
mode
exp
harm.
VSCF
1B2
3131.9
3273.1
3113.8
3130.8
1.1
3130.7
1.2
2A1
3023.3
3151.2
3030.1
3013.3
10.0
3013.3
10.0
3A1
1628.3
1655.0
1631.1
1629.7
1.4
1629.7
1.4
4A1
1459.2
1494.1
1468.7
1455.1
4.1
1455.1
4.1
5B2
1124.9
1140.7
1132.8
1123.2
1.7
1123.1
1.8
6A1
991.8
1030.5
1007.3
994.1
2.3
994.1
2.3
7B1
967.3
1003.8
991.0
966.6
0.7
966.7
0.6
8A2 9B1
962.7 807.1
990.5 834.4
981.8 813.9
963.3 809.5
0.6 2.4
963.2 809.5
0.5 2.4
1B2
2366.9
2446.3
3113.8
2360.4
6.5
2360.4
6.5
2A1
2228.6
2277.4
3030.1
2220.2
8.4
2220.2
8.4
3A1
1610.4
1638.5
1631.1
1607.6
2.8
1607.6
2.8
4A1
1084.4
1109.5
1468.7
1081.1
3.3
1081.1
3.3
5A1
965.5
993.5
1132.8
966.4
0.9
966.4
0.9
6B1
851.9
884.8
1007.3
848.6
3.3
848.6
3.3
7B2 8A2
869.5 732.0
878.7 748.8
991.0 981.8
865.0 730.0
4.5 2.0
865.0 730.0
4.5 2.0
9B1
712.1
727.9
813.9
709.6
2.5
709.6
2.5
cyc-CH2N2
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12. and 3D terms at B2PLYP/VTZ level.
negligible. Due to the inclusion of activeactive modal rotations in the cs-VMCSCF approach, slightly different numbers of micro and macro iterations are observed for these two methods (see columns 5 and 8 in Table 2). Comparison with experimental data was only possible for cyc-CF 2 O2, 64 and to the best of our knowledge for CF 2 O2 no experimental data have yet been reported. Except for mode 5A1 the agreement between our theoretical prediction and the experimental data is excellent (the mean absolute deviation amounts to just 2.0 cm1). A possible explanation for the experimentally observed band at 772 cm1 could be that this is not the 5A1 fundamental rather than the first overtone of the 9A2 mode. cyc-CF2N2 and CF2N2. Many years ago cyc-CF2N2 and CF2N2 were studied by Schleyer and co-workers65 at the MP2/6-31G* level. These authors concluded, “Indeed, geometry optimization of difluorodiazomethane at MP2(full)/6-31G* (Cs symmetry) leads directly to dissociation products CF2 + N2.” We observed exactly the same at the CCSD(T)-F12a/vtz-f12 level and thus this species has not been considered any further within this study here. In contrast to CF2N2, the three-membered ring isomer difluorodiazirine (cyc-CF2N2) has high barriers toward dissociation. The calculated anharmonic frequencies obtained from VCASSCF and cs-VMCSCF calculations of cyc-CF2N2 are shown in Table 3. cyc-CH2N2, CH2N2, cyc-CD2N2, and CD2N2. The C2v symmetry of diazomethane has been proven and recognized since 1949.3 As can be seen from Table 4, the agreement between the experimental and the computed VCASSCF and cs-VMCSCF is
[4,6]
cs-VMCSCF
cyc-CD2N2
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level.
excellent. Larger deviations arise only for the CH and CD stretching modes. A partial loss of accuracy for the CH and CD stretching modes might be anticipated due to the importance of higher mode-coupling terms and neglected electron correlation contributions within the multilevel approximation particularly in the outer regions of the potential. In any case, this comparison shows that the computational scheme works well for predicting the fundamental transitions of the species under 11053
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Table 5. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations for All Modes of Diazomethanea VCASSCF
cs-VMCSCF
VCASSCF
cs-VaMCSCF
[4,6]
[4,6]
mode
harm.
VSCF
2.7
1A0 2A0
3302.7 3140.1
3135.9 3011.0
3150.4 3008.8
3150.0 3001.5
2107.3
5.3
3A0
1485.5
1456.6
1431.4
1431.2
2.1 4.1
1411.9 1174.2
2.1 4.2
4A0
1305.9
1269.3
1249.4
1249.6
5A0
1239.8
1225.3
1210.0
1210.0
1108.9
0.1
1109.0
0.0
6A0
957.1
937.0
930.7
930.7
580.6
566.6
2.6
566.4
2.4
7A00
862.2
880.8
852.5
852.5
412.0
433.6
417.6
3.4
417.8
3.2
8A00
636.9
654.5
618.0
617.9
367.0
447.4
398.9
7.1
398.9
7.1
9A0
536.4
533.1
523.8
523.8
1B1
3183.3
3022.4
3043.2
3043.5
2A1
3083.6
2962.4
2926.6
2926.5
3A1
1551.4
1519.8
1511.3
1511.3
4A1
1298.2
1281.5
1266.3
1266.3
5B2
1272.6
1255.8
1244.6
1244.6
6B1
1182.6
1172.1
1163.5
1163.4
7B2
1038.9
1024.4
1012.6
1012.6
8A2 9A1
917.7 751.5
895.0 738.4
890.0 737.4
890.0 737.4
exp
harm.
VSCF
[4,6]
Δ
[4,6]
Δ
1B2
3185
3338.0
3203.3
3191.4
6.4
3191.9
6.9
2A1
3077
3202.3
3081.6
3074.4
2.6
3074.3
3A1
2102
2140.8
2095.4
2102.8
0.8
4A1 5A1
1414 1170
1441.4 1186.3
1419.6 1165.9
1411.9 1174.1
6B2
1109
1119.0
1123.7
7B1
564
564.8
8B2
421
9B1
406
mode
Table 6. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations for All Modes of CH2O2 and cyc-CH2O2a
CH2O2
CH2N2
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level.
cyc-CH2O2
Figure 3. Cs equilibrium structure of CH2O2. a
investigation. In particular, the cs-VMCSCF data do not differ substantially from the computationally more demanding VCASSCF results and the B2PLYP double hybrid density functional appears to be a reliable computational approach for representing the 3D terms within the multimode expansion of the potential. A comparison of the results for diazirine with its deuterated analog shows that the modes 4A1, 5B2, and 8A2 are significantly shifted by the mass effect, whereas only moderate shifts can be seen for modes 3A1 and 6A1. This of course had to be expected as the latter two vibrations essentially describe ringbreathing modes whereas the first three involve the hydrogen atoms directly. All these conclusions can also be transferred to diazomethane as shown in Table 5 (frequencies for the deuterated analog are provided in Table S1 in the Supporting Information). cyc-CH2O2, CH2O2, cyc-CD2O2, and CD2O2. In contrast to CH2N2 the corresponding oxygen analog CH2O2 shows a bent Cs structure (cf. Figure 3). A C2v structure indeed does exist as a stationary point on the potential energy surface but refers to a transition state, which connects the two Cs minima. After correction for the zero-point vibrational energy the barrier height was determined to be 39.3 kcal/mol. Consequently, it is fully sufficient to determine the fundamental transitions of the bent equilibrium structure by considering just one minimum instead of both of them. The calculated anharmonic frequencies obtained from VCASSCF and cs-VMCSCF calculations for these molecules are shown in Table 6 (for the frequencies of the deuterated species cf. Table S2 in the Supporting Information). The corresponding cyc-CH2O2 and cyc-CD2O2 isomers of course show C2v symmetry. [3,30 ] Biazirinylidene C2N4. No experimental data are available for C2N4. However, this molecule has recently been
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level.
investigated by Hoffmann et al.1 by means of modern computational methods. Using second-order generalized Van Vleck perturbation theory (GVVPT2), these authors showed that this molecule should be stable enough to be synthesized. However, according to the T1 diagnostic of our coupled cluster calculations, we found that this molecule can still be treated by singlereference methods and thus we have applied the same multilevel scheme as described above. Our predictions for the fundamental modes as shown in Table 7 may thus help to identify this species in experiments to come. CO4. Averyanov et al. studied the potential energy surface of the CO4 molecule and concluded “that tetrahedral (Td) and planar square (D4h) structures of the CO4 molecule had to be unstable because of the first-order and the second-order JahnTeller effects”.66 In agreement with our results they found a D2d local minimum and provided harmonic frequencies at the MP2/6-31G* level. These results are in qualitative agreement with our values. Our calculated anharmonic frequencies obtained from VCASSCF and cs-VMCSCF calculations are shown in Table 8. CON2. Diazirinone is a molecule at the border of stability that has been predicted theoretically by Korkin et al. in 199467 and it was assumed to be synthesized eleven years later by Moss et al.68 However, in a more recent study Shaffer et al. question the results of Moss.69 Finally, Zeng et al. completed the long story of the discovery of diazirinone.72 Their measured IR spectra are in excellent agreement with our theoretically predictions and those of Toffoli et al. (cf. Table 9).70 Toffoli et al. studied this molecule by means of VCI calculations based on a multilevel potential energy obtained from CCSD(T)/cc-pCVQZ and 11054
dx.doi.org/10.1021/jp2064062 |J. Phys. Chem. A 2011, 115, 11050–11056
The Journal of Physical Chemistry A
ARTICLE
Table 7. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations for All Modes of C2N4a VCASSCF
cs-VMCSCF
mode
harm.
VSCF
[4,6]
[4,6]
1Ag
2051.8
2003.5
2001.8
2001.9
2B1u
1558.2
1539.5
1526.9
1527.1
3Ag
1459.7
1435.1
1429.6
1429.7
4B1u
1134.4
1117.9
1111.8
1111.8
5B3g 6B2u
914.5 857.5
892.3 840.1
888.4 840.5
888.4 840.5
7Ag
599.7
592.8
602.3
602.4
8B3g
453.1
452.1
447.2
447.2
9Au
364.9
358.5
355.0
355.0
10B2g
252.9
253.1
248.4
248.4
11B3u
244.4
245.2
241.0
241.0
12B2u
169.6
174.1
166.9
166.8
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level.
Table 8. Calculated Anharmonic Frequencies (cm1) Obtained from VCASSCF and cs-VMCSCF Calculations for All Modes of CO4a VCASSCF
cs-VMCSCF
which is partly compensated by high-order correlation effects in the coupled-cluster treatment,71 which have not been accounted for in the study of Toffoli et al. This fortuitous error compensation would readily explain the slightly better agreement of our results with the experimental data.
IV. CONCLUSIONS AND SUMMARY The fundamental vibrational transitions for a set of molecules belonging to the general formula CX2Y2 have been studied by VCASSCF and configuration selective VMCSCF calculations based on multilevel potential energy surfaces obtained from explicitly correlated coupled-cluster, CCSD(T)-F12a/cc-pVnZ-f12, and double-hybrid density functional, B2PLYP, calculations. For those species, for which experimental data are available, the agreement is excellent; i.e., maximum deviations did not exceed 10 wavenumbers, and mean absolute deviations were found to be as low as 3 cm1. Consequently, all other frequencies provided are considered reliable predictions. From a computational point of view the more economical cs-VMCSCF approach was found to yield results of equal accuracy with respect to standard VCASSCF calculations. However, deviations in the subwavenumber regime must be expected arising from the reduction of the configuration space. A space of 4 active modals per mode were found to be sufficient for the molecules studied here. ’ ASSOCIATED CONTENT
bS
Supporting Information. Tables containing VCASSCF and cs-VMCSCF frequencies for CD2N2, cyc-CD2O2, and CD2O2. This material is available free of charge via the Internet at http:// pubs.acs.org.
mode
harm.
VSCF
[4,6]
[4,6]
1B2
1661.4
1640.4
1614.4
1614.5
2E
1048.9
1027.3
1020.1
1020.1
3A1
992.9
984.8
969.9
969.9
4B2
678.9
662.4
659.1
659.1
Corresponding Author
5A1
565.0
555.4
550.0
550.0
*Electronic mail:
[email protected].
6E
542.3
538.0
537.0
537.0
7B1
341.5
335.3
335.1
335.1
’ AUTHOR INFORMATION
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level.
Table 9. Calculated Anharmonic Frequencies (cm1) Obtained from cs-VMCSCF Calculations for All Modes of CON2 Compared with the Value of Toffoli et al.70a mode
exp
1A1
2033.6
2A1
harm.
VSCF
VCIb
’ REFERENCES
VMCSCF
Δ 7.1
2037.0
2003.9
2056.9
2040.7
1350.7
1329.0
1337.3
1325.1
’ ACKNOWLEDGMENT Financial support by the Deutsche Forschungsgemeinschaft is kindly acknowledged.
3B2
959.6
990.0
965.2
967.6
958.5
1.1
4A1
902.1
923.7
913.5
909.4
903.1
1.0
5B1 6B2
564.4 528.7
567.5 533.2
563.4 527.6
566.4 530.7
562.3 526.0
3.1 2.7
a
1D terms computed at the CCSD(T)/VTZ-F12, 2D terms at CCSD(T)/VDZ-F12, and 3D terms at B2PLYP/VTZ level. b Taken from ref 70.
CCSD(T)/cc-pVTZ calculations.70 Most likely the inclusion of core correlation effects in their 1D calculations is responsible for the upshift of their frequencies in comparison to ours. As we showed recently, core correlation effects often lead to a blue shift,
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