Ground state of naphthyl cation: Singlet or triplet? Achintya Kumar Dutta, Prashant U. Manohar, Nayana Vaval, and Sourav Pal Citation: The Journal of Chemical Physics 140, 114312 (2014); doi: 10.1063/1.4868485 View online: http://dx.doi.org/10.1063/1.4868485 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Photoelectron imaging of NCCCN : The triplet ground state and the singlet-triplet splitting of dicyanocarbene J. Chem. Phys. 132, 224301 (2010); 10.1063/1.3436717 Triplet states of cyclopropenylidene and its isomers J. Chem. Phys. 132, 044308 (2010); 10.1063/1.3273321 A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes J. Chem. Phys. 131, 224321 (2009); 10.1063/1.3270190 The triplet state of cytosine and its derivatives: Electron impact and quantum chemical study J. Chem. Phys. 121, 11668 (2004); 10.1063/1.1812533 The ground state ( 1 A 1 ) and the lowest triplet state ( 3 B 1 ) of the phenyl cation C 6 H 5 + revisited J. Chem. Phys. 106, 7541 (1997); 10.1063/1.473757 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 81.84.43.137 On: Fri, 02 May 2014 07:24:27
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Ground state of naphthyl cation: Singlet or triplet?Achintya Kumar Dutta, Prashant U. Manohar, Nayana Vaval, and Sourav Pal
Citation: The Journal of Chemical Physics 140, 114312 (2014); doi: 10.1063/1.4868485 View online: http://dx.doi.org/10.1063/1.4868485 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Photoelectron imaging of NCCCN : The triplet ground state and the singlet-triplet splitting of dicyanocarbene J. Chem. Phys. 132, 224301 (2010); 10.1063/1.3436717 Triplet states of cyclopropenylidene and its isomers J. Chem. Phys. 132, 044308 (2010); 10.1063/1.3273321 A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linearacenes J. Chem. Phys. 131, 224321 (2009); 10.1063/1.3270190 The triplet state of cytosine and its derivatives: Electron impact and quantum chemical study J. Chem. Phys. 121, 11668 (2004); 10.1063/1.1812533 The ground state ( 1 A 1 ) and the lowest triplet state ( 3 B 1 ) of the phenyl cation C 6 H 5 + revisited J. Chem. Phys. 106, 7541 (1997); 10.1063/1.473757
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The polycyclic aromatic hydrocarbons (PAHs), due totheir abundant occurrence in the interstellar environment,hold an important role in the interstellar chemistry.1 In con-trast to their terrestrial analogues, the transient forms of PAHare important in the low-density interstellar environment,2
with properties that are yet to be identified. An importantfraction of the gas phase PAH is ionized in the astrophys-ical conditions3 and their properties are strongly dependenton the spin multiplicity of the electronic state. The univer-sally observed mid-infrared emissions at 3.3, 6.2, 7.7, 8.6, and11.3 μm (known as the unidentified infrared emission bands(IUR)),4 coming from a wide variety of astronomical sources,provide the key evidence of existence of PAH in the space.5
The understanding of the electronic structure and propertiesof PAH holds the key to an insight into the interstellar carboncycle.
Experimental characterization of interstellar PAH6 ischallenging because of their transient nature, owing to thepresence of the highly reactive carbocation centre. Experi-mental studies in the solution phase or even in the rare gasmatrix may be of little astrophysical significance and experi-ments in complete isolation are necessary to mimic the inter-stellar PAH chemistry, which is difficult to perform in reality.Ab initio quantum chemical methods can, therefore, be usedas efficient tools for investigation of the electronic structureand properties of the PAH.
The simplest in the family of PAH, discovered in theinterstellar cloud, is naphthyl cation.7 The naphthyl cationhas two possible constitutional isomers, namely, 1- and 2-naphthyl cations. The subject of spin multiplicity of theground state of the naphthyl cation has been a matter ofdebate.8 Previous theoretical studies9–12 have shown that thelow-lying states of 1- and 2-naphthyl cataion are quite differ-
ent from each other. The two lowest lying states of 1-naphthylcation are a closed shell singlet with both electrons miss-ing from one carbon σ orbital, and an open-shell triplet withsingly occupied σ and π orbitals. However, there can be an-other open-shell singlet state of (σ ,π ) type with singly oc-cupied σ and π orbitals, which has been not considered inthe previous theoretical studies. The 2-naphthyl cation, on theother hand, has a closed shell singlet with both electrons miss-ing from one carbon σ orbital and an open-shell triplet withtwo singly occupied σ orbitals. There also exists a (σ ,σ ′) typeopen shell singlet in 2-naphthyl cation.
The previous studies have reported significant scatter inthe results, favouring a singlet9, 10 or a triplet11, 12 groundstate with a wide range of S-T gap values. To the best ofour knowledge, no quantitative experimental data are avail-able for the S-T gap in naphthyl cation. Recently, Galué andOomens,13 from their quantitative spectroscopic evidence (in-frared photon dissociation spectroscopy) coupled with pre-liminary theoretical calculations (using DFT-B3LYP methodin 6-311g++(d,p) basis set), predicted a triplet ground statefor naphthyl cation with a very small S-T gap of 0.47 kJ/mol.The gap is too small to be accurately predicted by the DFT-B3LYP method and thus, more sophisticated electron cor-relation calculations are necessary for reliable results. Al-though some previous reports of coupled cluster calculationson naphthyl cations are available,8, 9 these are performed us-ing DZP basis set, which is too small to be used in a reliableS-T gap calculation. It is necessary to use a sufficiently largebasis set for a systematic recovery of the correlation effect anda reliable prediction of the S-T gaps.
In this paper, we present our electronic structure analy-sis of 1 and 2-naphthyl cations, using single reference CCSDmethod with perturbative triples correction in cc-pVQZ ba-sis set. We also present the calculations using smaller basissets and discuss the basis set effect on the ground state mul-tiplicity of the molecules. Spin flip equation of motion cou-pled cluster (SF-EOMCC) method14, 15 has been used to in-vestigate the open-shell singlet state, which is not possible to
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114312-2 Dutta et al. J. Chem. Phys. 140, 114312 (2014)
study in single-reference coupled cluster method. The paperis organized as follows. Section II gives computational de-tails of the calculations. The trends in the numerical results forthe geometry, IR frequencies and relative energies of singletand triplet state of 1- and 2-naphthyl cation are discussed inSec. III. Section IV contains the conclusions.
II. COMPUTATIONAL DETAILS
The DFT-B3LYP calculations have been carried out forthe closed-shell (MS = 0) state using restricted Kohn-ShamMethod. The triplet state (MS = 1) is calculated using un-restricted orbitals. The use of unrestricted orbital may leadto spin-contamination. However, Andzelm and co-workers16
have shown that the Kohn-Sham method is less susceptibleto spin-contamination, even when the unrestricted Hartree–Fock wave-function is heavily spin contaminated. All theDFT-B3LYP calculations on the singlet and triplet stateof 1-naphthyl and 2-naphthyl cation are performed usingGausssian0917 in a hierarchy of Dunning’s correlation con-sistent cc-pVXZ (X = D,T,Q) basis sets.18 Adiabatic S-Tgap calculations in DFT-B3LYP method are performed on theDFT-B3LYP optimized geometries.
The coupled cluster calculations for the closed-shell sin-glet (MS = 0) and open-shell triplet (MS = 1) state are per-formed in a hierarchy of Dunning’s correlation consistentcc-pVXZ (X = D,T,Q) basis sets,18 using geometries opti-mized at CCSD(T)/cc-pVDZ level of theory. The CCSD andCCSD(T) calculations for closed-shell singlet (MS = 0) areperformed using RHF based coupled cluster method. Thetriplet states (MS = 1) were studied using coupled clustermethod based on the ROHF reference19, 20 and and the in-clusion of partial triples is considered using the scheme de-veloped by Bartlett and co-workers.21 All the computed ge-ometries of the 1- and 2-naphthyl cations are local minima, asconfirmed by the frequency calculations. The zero point en-ergy (ZPE) corrections for the closed-shell singlet (MS = 0)and open-shell triplet (MS = 1) state are computed by doingfrequency calculation at CCSD/cc-pVDZ level of theory.
The open-shell singlet state is obtained by using spin-flip EOMCC in singles and doubles approximation (SF-EOM-CCSD). Krylov and co-workers14, 15 have shown that the SF-EOM-CC method provides an efficient approach for accuratecalculation of energies of open-shell singlet states. The spinflip EOMCC calculation for an open shell singlet involvesan unrestricted or restricted open-shell coupled cluster cal-culation on an MS = 1 triplet reference state, followed by anEOM calculation involving flipping of the spin of the elec-trons. We have used the ROHF orbitals for reference state(MS = 1 triplet) coupled cluster calculations. However, itis well-known that the energies in SF-EOM-CCSD methodare insensitive to the reference wave function. The open-shellsinglet geometries are optimized using SF-EOM-CCSD/cc-pVDZ method.
The core electrons are frozen for all the correlated calcu-lations. Total energies of the singlet and triplet state have beenextrapolated to obtain the S-T gap at the complete basis-set(CBS) limit,22–24 using following formula,25 used by Kamyia
and Hirata26 in their benchmark study:
E (n) = E (∞) + η1e−(n−1) + η2e
−(n−1)2, (1)
where E(∞) is the energy at the CBS limit, and n = 2, 3, 4corresponds to the cc-pVDZ, cc-pVTZ, and cc-pVQZ basissets, respectively. E(n) are the corresponding energies, and η1
and η2 are parameters that are used to fit the energies.For comparison with experiment, the computed stick
spectra are convoluted with a 20 cm−1 full width at half max-imum (FWHM) Lorentzian function. The single referencecoupled cluster calculations are performed using CFOUR.27
Q-Chem28 is used for the SF-EOM-CCSD calculations.
III. RESULTS AND DISCUSSIONS
From computational point of view, 1-naphthyl and 2-naphthyl cation are challenging systems as they have veryclosely lying singlet and triplet states. Therefore, the elec-tronic structural predictions can be badly affected by use ofinappropriate basis or computational method.
A. DFT calculations
Combined experimental and DFT-B3LYP/6-311G++(d,p) investigation by Galué and Oomens13 havepredicted a triplet ground state for both 1- and 2-naphthylcation with the S-T gap of 0.47 kJ/mol and 0.44 kJ/mol,respectively. However, Galué and Oomens13 have used6-311G++(d,p) basis set, which is not sufficient to correctlyreproduce S-T gap of such a small magnitude. Therefore, wehave reinvestigated the problem by using larger basis setsat the DFT-B3LYP level. Table I presents the adiabatic S-Tgaps for 1- and 2-naphthyl cation in DFT-B3LYP methodand a hierarchy of Dunning’s correlation consistent cc-pVXZ(X = D,T,Q) basis sets.18 In the cc-pVDZ basis, the groundstate of 1-naphthyl cation remains triplet with a S-T gap(including ZPE correction) of 3.23 kJ/mol. However, therelative ordering of singlet and triplet state flips in cc-pVTZbasis set, where the singlet becomes the ground state of1-naphthyl cation with a S-T gap of 4.53 kJ/mol. The
TABLE I. Adiabatic S-T gaps (kJ/mol) calculated using DFT-B3LYPmethod in different basis sets.a
aNegative value of the S-T gap indicates, triplet is the ground state.bThe triplet state is (σ ,π) type.cThe triplet state is (σ ,σ ′) type.dValues taken from work of Galué and Oomens (Ref. 13).
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114312-3 Dutta et al. J. Chem. Phys. 140, 114312 (2014)
TABLE II. Basis set dependence of S-T gap (in kJ/mol) for 1-and 2-naphthyl cation in DFT-B3LYP method.a–d
1-naphthyl cation 2-naphthyl cation
Basis Singlet Tripletc S-T gap TotalZPE correctione Singlet Tripletd S-T gap Total ZPE correctione
aThe increase in the energy from the previous basis set is given in parenthesis.bNegative value of the S-T gap indicates, triplet is the ground state.cThe triplet state is (σ ,π) type.dThe triplet state is (σ ,σ ′) type.eThe absolute ZPE correction values are provided.
results seem to converge as we go from cc-pVTZ basis tocc-pVQZ basis and 1-naphthyl cation has a singlet groundstate with a S-T gap of 4.63 kJ/mol in cc-pVQZ basis set.Augmentation of the basis set with diffuse function has anegligible effect on the S-T gap. Similar trend is observed for2-naphthyl cation (Table I), where the ground state is a tripletin cc-pVDZ basis set, and it flips to singlet as we go to alarger cc-pVTZ basis set. The result seems to have convergedwith respect to the basis set in cc-pVQZ basis set, and ourDFT-B3LYP/cc-pVQZ calculation predicts a singlet groundstate with a S-T gap of 3.45 kJ/mol, which is in contrast tothe triplet ground state reported by Galué and Oomens13 intheir DFT-B3LYP/6-311G++(d,p) study, as well as in thesmaller cc-pVDZ calculation performed by us.
Table II presents the basis set dependence of S-T gapof both 1- and 2-naphthyl cation in DFT-B3LYP method.In case of singlet 1-naphthyl cation, the energy increases by280.70 kJ/mol on going from cc-pVDZ to cc-pVTZ basis set.On the other hand, the energy of 1-naphthyl triplet increasesby 272.91 kJ/mol from cc-pVDZ to cc-pVTZ basis set. Thepreferential stabilization of the singlet state compared to thetriplet state with the increase in basis set leads to lowering ofthe S-T gap in favour of a singlet ground state. The increasein energy of the singlet state from cc-pVTZ to cc-pVQZ ba-sis is 69.38 kJ/mol. The corresponding increase in energy intriplet 1-naphthyl cation is 69.08 kJ/mol. The nearly identi-cal increase in energy for both singlet and triplet state in 1-naphthyl cation leads to convergence of S-T gap with respectto the basis set from cc-pVTZ to cc-pVQZ basis. Same trendis observed for 2-naphthyl cation, where the singlet and tripletstate energy increase by 279.53 kJ/mol and 273.25 kJ/mol, re-spectively, from cc-pVDZ to cc-pVTZ basis. It leads to low-ering of S-T gaps in favour of a singlet state. The increase inenergy from cc-pVTZ to cc-pVQZ basis set is nearly iden-tical for singlet and triplet state in 2-naphthyl cation and theS-T gap seems to converge with respect to basis set. It is inter-esting to note that the ZPE correction in DFT-B3LYP methodis independent of the basis set, and leads to preferential stabi-lization of the singlet state in both 1- and 2-naphthyl cation.
In both 1- and 2-naphthyl cation, improvement of the ba-sis set leads to preferential stabilization of singlet state com-pared to triplet state. Therefore, the triplet ground state ob-tained by Galué and Oomens13 is an artifact of the small ba-sis set used in their DFT-B3LYP calculations. The small S-T gap in DFT-B3LYP method demands more accurate the-
oretical calculations to obtain quantitative accuracy in S-Tgaps. Therefore, we have performed coupled cluster calcula-tions on 1- and 2-naphthyl cation using the same hierarchy ofDunning’s correlation consistent cc-pVXZ (X = D,T,Q) basissets.
B. Coupled cluster calculations
1. Geometries and electronic structure
Figures 1 and 2 present the C–C bond lengths of the low-est singlet and triplet states for 1- and 2-naphthyl cations us-ing DFT and CCSD(T) method. The bond lengths in DFT-B3LYP/cc-pVDZ level of theory are constantly underesti-mated compared to that obtained in CCSD(T)/cc-pVDZ levelof theory for singlet and triplet state of 1- and 2-naphthylcation. However, the bond angles and out of plane dihedralangles are very similar in both methods. All the bond lengths,bond angles, and out of plane dihedral angles are given in thesupplementary material.29
a. 1-naphthyl cation. The frontier molecular orbitals of 1-naphthyl cation are presented in Figure 3. The dominant elec-tronic configurations of the singlet and triplet state in all thethree basis sets (cc-pVXZ, X = D,T,Q) are as follows:
Singlet: (core)(5a′′)2(29a′)0 and
Triplet: (core)(5a′′)1(29a′)1,
where 29a′ is a σ type orbital and 5a′′ is a π type orbital.The closed shell singlet state is formed by removal of twoelectrons from the σ type 29a′ orbital, keeping the (4n + 2)π electrons (here n = 2) intact and thereby retaining its aro-maticity, though to a lesser extent compared to the naphtha-lene molecule because of the ring deformation. The emptyσ type orbital on the dehydrogenated carbon leads to a con-traction and deformation of the remaining σ framework tocompensate and it is particularly more prominent in the ringcontaining the dehydrogenated carbon, making the C9-C1-C2angle 148.76◦ (Figure 1).
The lowest triplet state((σ ,π ) type) is obtained by excit-ing one electron from the doubly occupied 5a′′ to the vacant29a′, which involves a π → σ charge transfer to the ring con-taining the dehydrogenated carbon, as seen in the Figure 3.Now, the π electron count in the triplet has one electron less
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114312-4 Dutta et al. J. Chem. Phys. 140, 114312 (2014)
FIG. 1. Singlet and triplet state geometries of 1- naphthtyl cation (bond lengths are in Å).
than that required to satisfy (4n + 2) rule, and that leads toloss of aromaticity. The singly occupied σ type 29a′ orbitalleads to less contraction of the σ framework compared to thatcaused by unoccupied 29a′ orbital in singlet. This results instretching of the C9–C1 and C1–C2 bonds in the triplet stateby 0.05 Å and 0.08 Å, respectively, relative to the singletgeometry. The C9–C1–C2 bond angle in the triplet state is126.24◦, which is also very close to the hexagonal bond angleof 120 (Figure 1).
It is interesting to note that the planarity of the moleculeis not disturbed in the singlet as well as in the triplet state.
There exists a possibility of another singlet state for 1-naphthyl cation, which is of open shell (σ ,π ) type, originatingfrom a linear combination of more than one configuration.The energy for this state is calculated using SF-EOM-CCSD/cc-pVTZ level of theory and presented the Table III,along with the energies of the closed shell singlet and tripletstate, calculated using RHF and ROHF based CCSD method,respectively. It can be seen that the open shell singlet stateis 17.26 kJ/mol higher in energy than the closed shell one,and the lowest singlet state is closed shell type. Therefore,the open shell singlet state is not further discussed in thispaper.
We have studied the effect of correlation and basis seton the relative stability of triplet and closed shell singlet stateusing single reference coupled cluster method.
In Table IV, we report the vertical S-T gaps for 1-naphthyl cation at the singlet geometry in cc-pVDZ and cc-pVTZ basis set. The S-T gap is positive in singlet geometry,which indicates that for 1-naphthyl cation the ground state, inthat particular geometry, is singlet in nature. It can be seenfrom our results that the improvement of both basis set fromcc-pVDZ to cc-pVTZ or correlation treatment from CCSD toCCSD(T) result in the increase in S-T gap. This indicates thatuse of better basis set or higher level of correlation results inpreferential stabilization of the singlet state compared to thetriplet state, i.e., singlet energy is lowered much more com-pared to the triplet energy, which results in widening of theS-T gap (see Figure 4).
The adiabatic S-T gaps in coupled cluster method showbasis set dependence similar to that of the DFT results.Table V reports adiabatic S-T gap, with and without zeropoint correction, in coupled cluster method for 1-naphthylcation. In CCSD/cc-pVDZ level of theory, 1-naphthyl cationshows a triplet ground state with adiabatic S-T gap (includingZPE correction) of 6.30 kJ/mol. We observe that the use of
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114312-5 Dutta et al. J. Chem. Phys. 140, 114312 (2014)
FIG. 2. Singlet and triplet state geometries of 2- naphthtyl cation (bond lengths are in Å).
improved basis set dramatically alters the relative ordering ofthe states. In cc-pVTZ basis set, the ground state flips to sin-glet with the S-T gap of 5.95 kJ/mol (with ZPE correction).The ground state is a singlet in cc-pVQZ basis and the S-T
FIG. 3. Frontier molecular orbitals of 1-naphthyl cation obtained in Hartree–Fock method (RHF for singlet and ROHF for triplet state).
gap increases to 8.30 kJ/mol (with ZPE correction). The pref-erential stabilization of singlet state with the increase in basisset, as seen in the vertical S-T gap, is also observed in adia-batic S-T gap. The change of basis set from cc-pVDZ to cc-pVTZ leads to large change in S-T gap, even alteration of signfrom negative to positive is observed. However, the change inS-T gap, as we go from cc-pVTZ to cc-pVQZ basis is smalland the S-T gap value seems to approach the basis set conver-gence limit. In CCSD extrapolated complete basis set limit,the 1-naphthyl cation has a singlet ground state with a S-Tgap of 9.33 kJ/mol (with ZPE correction).
TABLE III. Relative stability (kJ/mol) of open shell singlet and triplet staterelative to the closed shell singlet state in coupled cluster methoda for 1-naphthyl cation.
acc-pVDZ basis used for hydrogen.bCalculated using RHF based CCSD method.cCalculated using SF-EOM-CCSD method.dCalculated using ROHF based CCSD method.
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TABLE IV. Vertical S-T gapsa (in kJ/mol) of 1-naphthyl cation.
Method 1-naphthyl cation
S-T gap at CCSD/cc-pVDZ 97.04S-T gap at CCSD/cc-pVTZ 98.31S-T gap at CCSD(T)/cc-pVDZ 103.83S-T gap at CCSD(T)/cc-pVTZ 106.74
aThe triplet state is (σ ,π) type.
However, to get quantitatively accurate S-T gaps, it isnecessary to include the effect of partial triples in coupledcluster calculations. Table V also reports the CCSD(T) cal-culated S-T gap, with and without ZPE correction, for 1-naphthyl cation. In cc-pVDZ basis set, 1-naphthyl cationshows a singlet ground state, in contrast to the triplet groundstate shown by DFT-B3LYP and CCSD method in the samebasis set. However, the energy difference between singlet andtriplet state is very small and in CCSD(T)/cc-pVDZ level oftheory, the S-T gap with ZPE correction is only 2.29 kJ/mol.However, as we go to cc-pVTZ basis set, the singlet statebecomes more stabilized and the S-T gap (with ZPE cor-rection) increases to 16.49 kJ/mol. In CCSD(T) level, thechange of basis set from cc-pVDZ to cc-pVTZ basis accom-panies huge change in S-T gap for 1-naphthyl cation and thechange is larger than that observed at CCSD method. Here,it should be noted that the Dunning’s correlation consistentcc-pVXZ basis sets are designed to properly take care ofthe correlation effect and CCSD(T) method takes care of thecorrelation effect in a more robust manner than the CCSDmethod. Therefore, the change in S-T gap with basis set ismore prominent in CCSD(T) level than in CCSD level. Onthe other hand, the variation in adiabatic S-T gaps with ba-sis set in DFT-B3LYP method (Table I) is much smallerthan that shown by adiabatic S-T gap in both CCSD andCCSD(T) method. However, it is well known that energy in
FIG. 4. Change of vertical S-T gaps with change in basis set and/or level ofcorrelation.
TABLE V. Adiabatic S-T gaps (kJ/mol) of 1-naphthyl cation in coupledcluster method.a,b
aNegative value of the S-T gap indicates, triplet is the ground state.bThe triplet state is (σ ,π) type.
methods based on density functional theory converges morequickly with basis set than the wave-function based meth-ods, which is reflected in the DFT-B3LYP results of Table I.The S-T gap obtained in CCSD(T) calculations shows verysmall change from cc-pVTZ to cc-pVQZ basis and the resultsconverge with inclusion of g functions in the basis set (seeTable V). The S-T gap with ZPE correction for 1-naphthylcation in CCSD(T)/cc-pVQZ level of theory is 19.15 kJ/mol.The benchmark CCSD(T)/CBS calculations, predict a singletground state for 1-naphthyl cation and the triplet states is15.46 kJ/mol higher in energy (without ZPE correction) thanthe singlet state. The S-T gap in CCSD(T)/CBS level of the-ory with ZPE correction for 1-naphthyl cation is 20.46 kJ/mol.The findings of Table V are also consistent with the qualita-tive inference drawn from molecular orbital analysis in thebeginning of Sec. III B 1 a, which implies that the singlet 1-naphthyl cation, being aromatic, is more stabilized comparedto the non-aromatic triplet state.
Table VI presents the basis set and correlation depen-dence of S-T gap for 1-naphthyl cation. The triplet stateis 67.07 lower in energy than the singlet state in Hartree–
TABLE VI. Basis set and correlation dependence of S-T gap (in kJ/mol) of1-naphthyl cationa,b in coupled cluster method.
Correlation CorrelationBasis contribution at contribution atset State SCF CCSD level CCSD(T) level
cc-pVDZ Singlet 0.00 0.00 0.00Tripletc − 67.06 55.76 64.36S-T gap − 67.06 55.76 64.36
cc-pVTZ Singlet − 234.63 − 620.05 − 688.50(234.63) (620.05) (688.50)
aNegative value of the S-T gap indicates, triplet is the ground state.bThe increase in the energy from the previous basis set is given in parenthesis.cThe triplet state is (σ ,π) type.
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Fock (HF) method in cc-pVDZ basis set. However, the CCSDmethod recovers higher amount of correlation energy forthe singlet state than the triplet state and correlation contri-bution to the S-T gap is 55.76 kJ/mol in favour of a sin-glet ground state in CCSD/cc-pVDZ level of theory. TheCCSD(T) method recovers even a higher amount of corre-lation energy for the singlet state than the triplet state in thesame basis set and correlation contribution to the S-T gap is64.36 kJ/mol, in favour of a singlet state. On going to cc-pVTZ basis set, the energy of the singlet state increases by234.63 kJ/mol in HF level, whereas, the energy of the tripletstate increases by 225.35 kJ/mol in HF level. The preferentialstabilization of the singlet state compared to triplet state leadsto decrease in S-T gap in HF level and the S-T gap is now57.77 kJ/mol with a triplet ground state in HF/cc-pVTZ levelof theory. The increase in correlation energy from cc-pVDZto cc-pVTZ is much larger than the increase in the HF energyfor both singlet and triplet state. In CCSD level, the correla-tion energy for the singlet state increases by 620.05 kJ/molfrom cc-pVDZ to cc-pVTZ basis set. The correlation energyof the triplet state increases by 617.09 kJ/mol from cc-pVDZto cc-pVTZ basis set. Therefore, the singlet state recovers3.96 kJ/mol more correlation energy than the triplet state ongoing from cc-pVDZ to cc-pVTZ basis set. The preferentialstabilization of the singlet state from cc-pVDZ to cc-pVTZbasis, both in HF and CCSD correlation treatment, leads tothe change in relative ordering of the singlet and triplet stateand results in a singlet ground state in CCSD/cc-pVTZ levelof theory. The CCSD(T) method shows even larger stabiliza-tion of singlet state (4.90 kJ/mol) compared to the triplet statefrom cc-pVDZ to cc-pVTZ basis set. The difference in HFenergy between the singlet and triplet state seem to convergefrom cc-pVTZ to cc-pVQZ basis set. On the other hand, thedifference of correlation energy still changes with change of
basis set from cc-pVTZ to cc-pVQZ, though the magnitude isvery small. The preferential increase in correlation energy ofthe singlet state compared to the triplet state, from cc-pVTZto cc-pVQZ basis, is 1.70 kJ/mol in CCSD method and2.01 kJ/mol in CCSD(T) method. However, the trend is clearthat with the increase basis set, both Hartree–Fock and corre-lation treatment lead to preferential stabilization of the singletstate compared to the triplet state.
b. 2-naphthyl cation. The bonding patterns, and hence,the geometrical parameters of the 2-naphthyl cation arestrongly responsive to the multiplicity of the electronic states.In the triplet state, the C1-C2-C3 bond angle is 126.17◦,which is similar to the C9–C1–C2 bond angle of the 1-naphthyl triplet. In this state, the 2-naphthyl cation is perfectlyplaner with the dominant mean field electronic configuration:(core)(28a′)1(29a′)1. As seen in the Figure 5, both the orbitals28a′ and 29a′ are σ type orbitals. The highest doubly occu-pied orbital is π type (5a′′). De-excitation of the electron fromσ type 29a′ orbital into the σ type 28a′ orbital, accompaniespseudo-Jahn-Teller (PJT) distortion, resulting in loss of pla-narity of the molecule in the singlet state with C1-C2-C3-C4dihedral angle of −19.09◦. Consequently, the additional elec-tron in the σ type 28a orbital causes lowering of 28a orbitalenergy in the singlet state. On the other hand, the planarityof the π type 5a′′ orbital gets partially broken in the singletstate due to the pseudo-Jahn-Teller distortion at the dehydro-genated carbon. The resulting orbital (33a) now becomes theHOMO in the singlet 2-naphthyl cation. On the other hand,the σ type 29a′ orbital in the triplet is now empty in the sin-glet state, which leads to increase in its energy. Accordingly,the resulting orbital (34a) becomes the LUMO of singlet 2-naphthyl cation. A qualitative picture of the change in the
FIG. 5. Frontier molecular orbitals of 2-naphthyl cation obtained in Hartree–Fock method (RHF for singlet and ROHF for triplet state).
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114312-8 Dutta et al. J. Chem. Phys. 140, 114312 (2014)
FIG. 6. A qualitative depiction of the relative ordering of frontier molecularorbitals in 2-naphthyl cation in Hartree–Fock method (RHF for singlet andROHF for triplet state).
relative ordering of the orbitals is presented Figure 6. Thenon-dehydrogenated ring is planer and the 33a is π type inthis region. Consequently, the (4n + 2) electrons in π typeorbitals leads to preferential stabilization of the singlet statecompared to the triplet, due to retention of aromaticity.
In the following paragraph, we have studied the effect ofcorrelation and basis set on the relative stability of triplet andclosed shell singlet state for 2-naphthyl cation using singlereference coupled cluster method.
In Table VII, we report the vertical S-T gaps for 2-naphthyl cation at the singlet geometry in cc-pVDZ and cc-pVTZ basis set. The S-T gap is positive in the singlet ge-ometry, which indicates that the ground state is a singlet inthat geometry for 2-naphthyl cation, similar to that in the 1-naphthyl cation. However, the improvement of basis set fromcc-pVDZ to cc-pVTZ at CCSD level has a negligible effecton the vertical S-T gap of 2-naphthyl cation, unlike in thecase of 1-naphthyl cation, where the S-T gap increases withthe basis set. On the other hand, improvement in correlationtreatment from CCSD to CCSD(T), results in the increasein vertical S-T gaps, similar to that in 1-naphthyl cation.The CCSD(T) method shows an increase in vertical S-T gapwith the increase in basis set, in contrast to that in CCSDmethod.
The adiabatic S-T gaps for 2-naphthyl cation, in CCSDmethod, show basis set dependence, unlike the vertical S-Tgaps. Table VIII reports adiabatic S-T gap, with and with-out zero point correction, in coupled cluster methods for2-naphthyl cation. In CCSD/cc-pVDZ level of theory, 2-naphthyl cation shows a triplet ground state. The adiabaticS-T gaps, with ZPE correction, at the CCSD/cc-pVDZ levelis 6.24 kJ/mol. We observe that the use of improved basis setdramatically alters the relative ordering of the states. In cc-
TABLE VII. Vertical S-T gapsa (in kJ/mol) of 2-naphthyl cation.
Method 2-naphthyl cation
S-T gap at CCSD/cc-pVDZ 88.63S-T gap at CCSD/cc-pVTZ 88.47S-T gap at CCSD(T)/cc-pVDZ 98.91S-T gap at CCSD(T)/cc-pVTZ 100.39
aThe triplet state is (σ ,σ ′) type.
TABLE VIII. Diabatic S-T gaps(kJ/mol) of 2-naphthyl cation in coupledcluster method.a,b
aNegative value of the S-T gap indicates, triplet is the ground state.bThe triplet state is (σ ,σ ′) type.
pVTZ basis set, the ground state of 2-naphthyl cation flipsto singlet, similar to that in 1-naphthyl cation. However, theS-T gap for 2-naphthyl cation in CCSD/cc-pVTZ level oftheory is only 1.95 kJ/mol (with ZPE correction), which issmaller than that in 1-naphthyl cation (5.95 kJ/mol) at thesame level of theory. The ground state for 2-naphthyl cationis a singlet in cc-pVQZ basis set and the S-T gap increases to2.99 kJ/mol (with ZPE correction). The preferential stabiliza-tion of singlet state with the increase in basis set, as seen inthe 1-naphthyl cation, is also observed in 2-naphthyl cation.The change of basis set, from cc-pVDZ to cc-pVTZ, leads tolarge change (7.39 kJ/mol) in S-T gap of 2-naphthyl cation,even alteration of sign from negative to positive is observed.However, the change in S-T gap is slightly smaller than thatin 1-naphthyl cation (8.59 kJ/mol). On moving from cc-pVTZto cc-pVQZ basis, the S-T gap for 2-naphthyl cation showsvery small change and values seem to approach the basis setconvergence limit. In CCSD extrapolated complete basis setlimit, 2-naphthyl cation has a singlet ground state with S-Tgap of 3.98 kJ/mol (with ZPE correction).
The results of CCSD(T) method, necessary to get thequantitative accuracy in S-T gaps, are also presented inTable VIII. In CCSD(T)/cc-pVDZ method, 2-naphthyl cationshows a triplet ground state, which is in accordance withthe DFT-B3LYP and CCSD result. However, the result is incontrary to that in the case of 1-naphthyl cation, where theCCSD(T)/cc-pVDZ level of theory predicts a singlet groundstate with a S-T gap of 2.29 kJ/mol (with ZPE correction).The 2-naphthyl cation shows a triplet ground state with S-T gap of 1.17 kJ/mol in CCSD(T)/cc-pVDZ level of theory(with ZPE correction). However, the S-T gaps for both the1- and 2-naphthyl cation in CCSD(T)/cc-pVDZ level of the-ory are very small. The ground state for 2-naphthyl cationflips from triplet to singlet, as we go from cc-pVDZ to cc-pVTZ basis set in CCSD(T) method. The 2-naphthyl cationshows a S-T gap of 15.19 kJ/mol at CCSD(T)/cc-pVTZ levelof theory with ZPE correction, which is slightly smaller thanthat in 1-naphthyl cation (16.49 kJ/mol) at the same levelof theory. However, the change in S-T gap (including ZPEcorrection) in 2-naphthyl cation with change in basis setfrom cc-pVDZ to cc-pVTZ in CCSD(T) method is larger(16.36 kJ/mol) than that in 1-naphthyl cation (14.20 kJ/mol).The trend is just opposite to that of CCSD method. The S-T gap obtained in CCSD(T) method for 2-naphthyl cation
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TABLE IX. Basis set and correlation dependence of S-T gap of 2-naphthylcationa,b in coupled cluster method.
Basis set State SCF CCSD CCSD(T)
cc-pVDZ Singlet 0.00 0.00 0.00Tripletc − 72.21 63.53 75.82S-T gap − 72.21 63.53 75.82
cc-pVTZ Singlet − 231.49 − 618.94 − 687.19(231.49) (618.94) (687.19)
aNegative value of the S-T gap indicates, triplet is the ground state.bThe increase in the energy from the previous basis set is given in parenthesis.cThe triplet state is (σ ,σ ′) type.
shows very small change from cc-pVTZ basis to cc-pVQZbasis and results converge with inclusion of g functions in thebasis set. The S-T gap with ZPE correction for 2-naphthylcation in CCSD(T)/cc-pVQZ level of theory is 16.29 kJ/mol.The benchmark CCSD(T)/CBS calculation also predicts a sin-glet ground state for 2-naphthyl cation. The triplet state is15.96 kJ/mol higher in energy (without ZPE correction) thanthe singlet state. The S-T gap in CCSD(T)/CBS level of the-ory with ZPE correction for 2-naphthyl cation is 18.40 kJ/mol,which is slightly smaller than that obtained in 1-naphthylcation (20.46kJ/mol). Here it should be noted that the groundstate of 1-naphthyl cation is 5.05 kJ/mol lower in energy (withZPE correction) than the ground state of 2-naphthyl cation(see the supplementary material29 for their respective energyvalues). The results are consistent with the qualitative infer-ence drawn from molecular orbital analysis in Secs. III B 1 aand III B 1 b, which implies that the singlet state in both1- and 2-naphthyl cation, being aromatic, is more stabilizedcompared to the non-aromatic triplet state. However, the ringdistortion induced loss of planarity of the π type HOMO re-duces the stabilization effect in the singlet 2-naphthyl cation.Consequently, the S-T gap in 2-naphthyl cation is smaller thanthat in completely planner 1-naphthyl cation.
Table IX presents the basis set and correlation depen-dence of S-T gap for 2-naphthyl cation. The trends in 2-naphthyl cation are similar to that of 1-naphthyl cation. Theground state of 2-naphthyl cation is a triplet in HF/cc-pVDZlevel of theory with the S-T gap of -72.21 kJ/mol. However,the correlation energy favours the singlet state compared tothe triplet state in both CCSD(by 63.53 kJ/mol) and CCSD(T)(by 75.82 kJ/mol) method. On going from cc-pVDZ to cc-pVTZ basis, both HF and correlation energy leads to pref-erential stabilization of singlet state compared to the tripletstate. The S-T gap at HF level converges from cc-pVTZ tocc-pVQZ. However, the preferential stabilization of singletstate by the correlation energy increases from cc-pVTZ to cc-pVQZ basis set, although by a very small amount.
TABLE X. Relative stability (kJ/mol) of open shell singlet and triplet staterelative to the closed shell singlet state in coupled cluster methoda for 2-naphthyl cation
acc-pVDZ basis used for hydrogen.bCalculated using RHF based CCSD method.cCalculated using SF-EOM-CCSD method.dCalculated using ROHF based CCSD method.
It should be noted that the preferential stabilization of thesinglet state compared to the triplet state in both 1- and 2-naphthyl cation are more prominent in CCSD(T) level thanthat in CCSD level. Here, the adiabatic S-T gaps show sim-ilar behavior towards improvement in basis set and level ofcorrelation, as that seen in the case of vertical S-T gaps. Inboth cases, the improvement of basis set and correlation ef-fect lead to preferential stabilization of singlet state comparedto the triplet state. The structural reorganization plays a vitalrole in the relative ordering of S-T gaps, which is evident fromthe significant difference in the structural parameter of singletand triplet state, especially near the dehydrogenated centre.The large vertical and very small adiabatic S-T gaps highlightthe important role of reorganization energies in predicting S-Tgaps in 1- and 2-naphthyl cation.
There also exists an open shell singlet in 2-naphthylcation, similar to that in 1-naphthyl cation. However, the openshell singlet 2-naphthyl cation has a (σ ,σ ′) configuration, oncontrary to the (σ ,π ) configuration of the open-shell singlet incase of 1-naphthyl cation. Table X presents the relative ener-gies of open shell (calculated in SF-EOM-CCSD method) andclosed shell singlet (calculated in RHF based CCSD method)for 2-naphthyl cation, along with the triplet state energy (cal-culated in ROHF based CCSD method). The open shell andclosed shell singlet are near degenerate in case of 2-naphthylcation. This degeneracy is responsible for the pseudo-Jahn-Teller distortion in the ground state geometry of 2-naphthylcation. The energy gap between is two lowest energy singletis −2.16 kJ/mol. It should be noted that the gap is surpris-ingly small and the excitation energy falls in the IR range.However, the lack of computational facilities has forced usto perform SF-EOM-CC calculations in small basis set andthe effect of triples cannot be considered. As we have seenin case of S-T gaps, small basis set and neglecting the effectof triples may lead to small energy gaps. To make a conclud-ing statement about the small energy gap between S0 and S1,one needs to perform a detailed analysis using a sufficientlylarge basis set and taking account of the effect of inclusionof triples. At the same time, calculation of adiabatic S-T be-tween the lowest singlet state and triplet state, would requireconsideration of the open shell state, especially in case of 2-naphthyl cation, where the open shell singlet and closed shellsinglet are near degenerate. However, our primary motiva-tion in this paper was to verify the relative stability order-ing of the closed-shell singlet, and triplet state reported in thejoint experimental and DFT-B3LYP/6-3I1G++(d,p) study of
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TABLE XI. Comparison of experimental and CCSD/cc-pVDZ computed IR absorption bands of 1-naphthyl cation.a
580 583 147 Ring oop deformation 554 30 CH ip bend/ring breathing735 729 27 CH oop bend 749 90 CH oop bend1011 1001 22 CH ip bend/ring breathing 983 34 CH ip bend/ring breathing1196 1184 29 CH ip bend/ring deform 1170 193 CH ip bend/ring deform
1220 47 CH ip bend/ring deform 1211 41 CH ip bend/ring deform1380 1409 5 CH ip bend/ring deform 1372 25 CC stretch/CH ip bend1485 1424 31 CC stretch/CH ip bend 1478 80 CC stretch/CH ip bend
aThe triplet state is (σ ,π) type.bValues taken from work of Galué and Oomens (Ref 13).cOnly bands closer to experimental peaks are included.dFrequencies are scaled32 with factor of 0.947.eMode description: ip = in plane; oop = out of plane.
Galué and Oomens,13 using highly accurate theoretical meth-ods and big basis sets. Therefore, we restrict ourselves to per-forming benchmark calculations only on the closed shell sin-glet and triplet state in the present study. Hopefully, the openshell singlet will be studied in more details in some futurework.
2. IR frequency analysis
Previous studies30–32 have shown that the vibronic cou-pling between the low-lying electronic states results in poorcorrespondence between theoretically calculated and experi-mental spectra for PAH. Table XI presents the comparison be-tween CCSD/cc-pVDZ computed IR spectra for singlet andtriplet state of 1-naphthyl cation, and the experimental val-ues reported by Galué and Oomens. Table XII presents thesame for 2-naphthyl cation. The lower frequency region ofthe experimental spectra (upto1001 cm−1) shows excellentagreement with the computed spectra of singlet state of 1-and 2-naphthyl cation. On the other hand, the computed spec-tra of triplet 1- and 2-naphthyl cation show better agreement
with the higher frequency region (>1001 cm−1) of the ex-perimental spectra. Figure 7 shows that the computed spectraof neither the singlet nor the triplet state of 1- or 2-naphthylcation show even qualitative agreement with the entire rangeof experimental spectra. Moreover, Galué and Oomens13 havesuggested that the relative intensities of the peaks may notbe accurately reproduced by their experimental spectroscopicmethod, which is based on multiple absorption of photons.Therefore, it is not justified to use the correlation between ex-perimental and theoretically calculated IR spectra as a tool fordiagnosis of the multiplicity of the ground state of the naph-thyl cation.
IV. CONCLUSIONS
In this work, we discussed the electronic structural analy-ses of 1- and 2- naphthyl cations in terms of bonding patterns,and S-T gaps. Both these molecules have a singlet groundstate with both electrons missing from a carbon σ orbital.However, their triplet states are different from each other. Thetriplet state in 1-naphthyl cation is (π ,σ ) type, whereas the
TABLE XII. Comparison of experimental and CCSD/cc-pVDZ computed IR absorption bands of 2-naphthyl cation.a
Singlet Triplet
Experimental Frequency Intensity Frequency Intensityfrequencyb (cm−1) c,d (km mol−1) Descriptione (cm−1)c,d (km mol−1) Descriptione
580 586 27 Ring ip deformation 582 31 CH ip bend/ring breathing735 744 6 CH oop bend 766 1 CC stretch/ ring deform1011 1010 0 CH oop bend 982 0 CH oop bend1196 1190 6 CH ip bend/ring deform 1185 43 CH ip bend/ring deform
. . . . . . . . . 1208 340 CH ip bend/ring deform1380 1375 64 CH ip bend/ring deform 1390 11 CH ip bend/ring deform1485 1481 1 CC stretch/CH ip bend 1489 2 CC stretch/CH ip bend
aThe triplet state is (σ ,σ ′) type.bValues taken from work of Galué and Oomens (Ref. 13).cOnly bands closer to experimental peaks are included.dFrequencies are scaled32 with factor of 0.947.eMode description: ip = in plane; oop = out of plane.
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FIG. 7. Comparison of experimental and CCSD/cc-pVDZ computed spec-tra of naphthyl cation. *Experimental spectra taken from work of Galué andOomens (Ref. 13).
triplet state in 2-naphthyl cation is (σ ,σ ′) type. Both, the sin-glet and triplet states of 1-and 2-naphthyl cation are highlysensitive to the quality of basis-set as well as the correla-tion method. The DFT-B3LYP method is found to be un-suitable for predicting correct ordering of the states of naph-thyl cation. Even in coupled cluster method, the inclusion ofperturbative triples is necessary to get a quantitative correctordering of the states. We have found that the use of bothbetter basis set, and better correlation method lead to pref-erential stabilization of singlet state compared to the tripletstate. The benchmark CCSD(T)/CBS calculations reveal thatthe ground states of both the constitutional isomers are sin-glet in contrast to the combined experimental and theoreti-cal study reported by Galué and Oomens.13 The S-T gaps inCCSD(T)/CBS level of theory without and with ZPE correc-tion for 1-naphthyl cation are, respectively, 15.46kJ/mol and20.46 kJ/mol, whereas for 2-naphthyl cation, the values are15.96kJ/mol and 18.40 kJ/mol, respectively. Our IR frequencyanalysis shows that the correlation between computed and ex-perimental spectra cannot be used as a probe for the multi-plicity of the ground state of naphthyl cation, as opposed tothat used by Galué and Oomens13 in interpreting their experi-mental data.
The MO framework and bonding patterns in 2-naphthylcation are more sensitive to spin multiplicity leading topseudo-Jahn-Teller distortion in the singlet state, compared tothe planer geometry in the triplet state. On the other hand, therelative ordering of the MOs and the planarity in the structureof 1-naphthyl cation are undisturbed by the spin-multiplicityof the low-lying electronic states. The MO diagrams alsoshow that the lowest singlet states of both 1- and 2-naphthylcation have aromatic character and, therefore, are more stabi-lized than the non-aromatic triplets, which is reflected in ourcomputed S-T gap values.
In this work, we have studied bare naphthyl cation in gasphase. Presence of electron donating or electron withdraw-ing substituents will considerably change the molecular or-bital picture and thereby can alter the relative ordering of thesinglet triplet energy spectrum. Work is currently under wayto study the effect of substitution on the S-T gap of 1- and2-naphthyl cation.
ACKNOWLEDGMENTS
The authors acknowledge the grant from CSIR XIIthfive year plan project on Multi-scale Simulations of Material(MSM) and facilities of the Centre of Excellence in ScientificComputing at NCL. A.K.D. thanks the Council of Scientificand Industrial Research (CSIR) for a Senior Research Fel-lowship. S.P. acknowledges the DST J. C. Bose Fellowshipproject and CSIR SSB grant towards completion of the work.P.U.M. thanks DST, India, for financial support under GrantNo. SR/FT/CS-18/2011.
1T. Henning and F. Salama, Science 282, 2204 (1998).2A. G. G. M. Tielens, The Physics and Chemistry of the Interstellar Medium(Cambridge University Press, 2005).
3G. C. Sloan, T. L. Hayward, L. J. Allamandola, J. D. Bregman, B. DeVito,and D. M. Hudgins, Astrophys. J. Lett. 513, L65 (1999).
4A. Leger and L. Dhendecourt, Astron. Astrophys. 146, 81 (1985).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
114312-12 Dutta et al. J. Chem. Phys. 140, 114312 (2014)
5D. M. Hudgins, Polycyclic Aromat. Compd. 22, 469 (2002).6H. A. Galué and O. Jos, Astrophys. J. 746, 83 (2012).7S. Iglesias-Groth, A. Manchado, D. A. García-Hernández, J. I. G.Hernández, and D. L. Lambert, Astrophys. J. Lett. 685, L55 (2008).
8S. Rayne and K. Forest, Comput. Theor. Chem. 983, 69 (2012).9D. Ascenzi, D. Bassi, P. Franceschi, O. Hadjar, P. Tosi, M. Di Stefano, M.Rosi, and A. Sgamellotti, J. Chem. Phys. 121, 6728 (2004).
10S. J. Klippenstein, Int. J. Mass Spectrom. Ion Processes 167–168, 235(1997).
11K. Fujiwara, A. Harada, and J. Aihara, J. Mass Spectrom. 31, 1216 (1996).12P. Du, F. Salama, and G. H. Loew, Chem. Phys. 173, 421 (1993).13H. Alvaro Galué and J. Oomens, Angew. Chem., Int. Ed. 50, 7004
(2011).14L. V. Slipchenko and A. I. Krylov, J. Chem. Phys. 117, 4694 (2002).15A. I. Krylov, Chem. Phys. Lett. 338, 375 (2001).16J. Baker, A. Scheiner, and J. Andzelm, Chem. Phys. Lett. 216, 380 (1993).17M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 09, Revision
B.01, Gaussian, Inc., Wallingford, CT, 2009.18J. T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).19M. Rittby and R. J. Bartlett, J. Phys. Chem. 92, 3033 (1988).20G. E. Scuseria, Chem. Phys. Lett. 176, 27 (1991).21J. Gauss, W. J. Lauderdale, J. F. Stanton, J. D. Watts, and R. J. Bartlett,
Chem. Phys. Lett. 182, 207 (1991).22K. L. Bak, P. Jørgensen, J. Olsen, T. Helgaker, and W. Klopper, J. Chem.
Phys. 112, 9229 (2000).23A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper, H. Koch, J. Olsen, and
A. K. Wilson, Chem. Phys. Lett. 286, 243 (1998).24T. Helgaker, W. Klopper, H. Koch, and J. Noga, J. Chem. Phys. 106, 9639
(1997).25K. A. Peterson, D. E. Woon, and T. H. Dunning, J. Chem. Phys. 100, 7410
(1994).26M. Kamiya and S. Hirata, J. Chem. Phys. 125, 074111 (2006).27CFOUR (Coupled-Cluster Techniques for Computational Chemistry), a
quantum-chemical program package by J. Gauss, J. F. Stanton, M. E.
Harding, P. G. Szalay, and R. J. Bartlett with contributions from A. A.Auer, U. Benedikt, C. Berger, D. E. Bernholdt, Y. J. Bomble, L. Cheng, O.Christiansen, M. Heckert, O. Heun, C. Huber, T. C. Jagau, D. Jonsson, J.Jusélius, K. Klein, W. J. Lauderdale, D. A. Matthews, T. Metzroth, L. A.Mück, D. P. O’Neill, D. R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F.Schiffmann, W. Schwalbach, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang,J. D. Watts and the integral packages MOLECULE (J. Almlöf and P. R.Taylor), PROPS (P. R. Taylor), ABACUS (T. Helgaker, H. J. A. Jensen,P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. vanWüllen. For the current version, see http://www.cfour.de.
28Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown,A. T. B. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O’Neill, R. A.DiStasio, Jr., R. C. Lochan, T. Wang, G. J. O. Beran, N. A. Besley, J. M.Herbert, C. Yeh Lin, T. Van Voorhis, S. Hung Chien, A. Sodt, R. P. Steele,V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J.Baker, E. F. C. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz,A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C.-P.Hsu, G. Kedziora, R. Z. Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee,W. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y.Min Rhee, J. Ritchie, E. Rosta, C. David Sherrill, A. C. Simmonett, J. E.Subotnik, H. Lee Woodcock Iii, W. Zhang, A. T. Bell, A. K. Chakraborty,D. M. Chipman, F. J. Keil, A. Warshel, W. J. Hehre, H. F. Schaefer Iii,J. Kong, A. I. Krylov, P. M. W. Gill, and M. Head-Gordon, Phys. Chem.Chem. Phys. 8, 3172 (2006).
29See supplementary material at http://dx.doi.org/10.1063/1.4868485 for ab-solute energies, details of geometries, Lowdin population analysis, anderror analysis.
30J. A. Piest, J. Oomens, J. Bakker, G. von Helden, and G. Meijer, Spec-trochim. Acta Mol. 57(4), 717–735 (2001).
31H. Alvaro Galué, O. Pirali, and J. Oomens, Astron. Astrophys. 517, A15(2010).
32NIST Computational Chemistry Comparison and Benchmark Database,NIST Standard Reference Database Number 101, Release 16a, August2013, edited by Russell D. Johnson III, see http://cccbdb.nist.gov/.
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