Large‐scale ab initio calculations for C3

Vibrational predissociation in the bending levels of the à state of C3Ar

Vibrational predissociation (VP) has been observed in 16 bands of the C₃Ar van der Waals complex near the 0 v₂ 0 - 000 (v₂ = 2^-, 4^-, 2⁺) and 0 2^- 2 - 100 bands of the ùΠ-X̃¹Σ⁺ _g system of C₃. New higher resolution wavelength-resolved emission (WRE) spectra covering a wider spectral range have been recorded for many of these C₃Ar bands, which show that most of the features observed in fluorescence must be reassigned as emission from the C₃ fragment. Two types of VP processes have been recognized. The first type gives rise to vibrationally hot C₃ fragments, mostly following |Δv| = 1, |ΔP| = 1 propensity rules, where P is the vibronic angular momentum of C₃. The second type gives vibrationally cooled fragments. The VP processes can change abruptly from one type to the other with comparatively small differences in vibrational energy. Although the initial states are associated with both orbital components of the C₃, ùΠ_u state, most of the VP fragments belong to the lower orbital component. A dipole-induced dipole model has been used to interpret the observed ΔP- propensities. Ab initio calculations of the binding energies of the ground and excited electronic states of C₃Ar have been carried out; the calculated values are consistent with estimates of ≤144 cm^-1 and 164 cm^-1, respectively, given by the WRE spectra.

Quantum Scattering Calculations for Rotational Excitations of by Hydrogen Atom: Potential Energy Surfaces and Rate Coefficients

Ab initio calculations are performed to determine new potential energy surfaces for the ground state and low-lying excited states of C₃ induced by collision with atomic hydrogen. The calculations are performed using the multireference configuration interaction method including Davidson's correction using aug-cc-pVQZ (augmented correlation consistent polarized valence quadruple zeta) basis sets. Nonadiabatic effects leading to avoided crossings are observed between ground and excited states. The computed points of the ground-state surface are fitted to an analytical form suitable for time-independent quantum scattering calculations of the state-to-state collisional cross sections. The close-coupling calculations are performed up to 1000 cm^-1. Resonances are observed at very low energies. Among all the rotational transitions, Δj = 2 is found to be predominant for excitation. After Boltzmann thermal averaging collisional cross sections, rate coefficients for rotational levels j = 0, 2, ..., 8 are obtained and discussed covering the temperature up to 100 K. The magnitude of the state-to-state excitation rate obtained is maximum for j = 0 → 2 transition and decrease for other higher excitations. The results computed in this work will be crucially required to accurately model the abundance of carbon trimer and its hydrocarbon form in space.

Infrared spectroscopy of C3-(H2O)n and C3-(D2O)n complexes in helium droplets

The C₃ molecule is an important species with implications in combustion and astrochemistry, and much of the interest in this molecule is related to its interactions with other species found in these environments. We have utilized helium droplet beam techniques along with a recently developed carbon cluster evaporation source to assemble C₃-(H₂O)_n and C₃-(D₂O)_n complexes with n = 1-2 and to record their rovibrational spectra. We observe only a single isomer of the n = 1 complex, in agreement with theoretical predictions as well as data from earlier matrix isolation studies. The spectra of the n = 1 complex are consistent with the ab initio structure, which involves a nearly linear arrangement of CCC-HO atoms in the complex. The C₃-H₂O spectrum we obtain exhibits slight differences from the analogous C₃-D₂O spectrum, which we assign to a difference in linewidth between the two spectra. We have also examined the n = 2 species and obtained a structure that appears to be distinct from those observed in matrix isolation studies and, to our knowledge, has not been previously observed.

Stretching our understanding of C3: Experimental and theoretical spectroscopy of highly excited nν1 + mν3 states (n ≤ 7 and m ≤ 3)

We present the high resolution infrared detection of fifteen highly vibrationally excited nν₁ + mν₃ combination bands (n ≤ 7 and m ≤ 3) of C₃ produced in a supersonically expanding propyne plasma, of which fourteen are reported for the first time. The fully resolved spectrum, around 3 μm, is recorded using continuous wave cavity ring-down spectroscopy. A detailed analysis of the resulting spectra is provided by ro-vibrational calculations based on an accurate local ab initio potential energy surface for C₃ (X̃¹Σ_g⁺). The experimental results not only offer a significant extension of the available data set, extending the observed number of quanta v₁ to 7 and v₃ to 3, but also a vital test to the fundamental understanding of this benchmark molecule. The present variational calculations give remarkable agreement compared to experimental values with typical accuracies of ∼0.01% for the vibrational frequencies and ∼0.001% for the rotational parameters, even for high energy levels around 10 000 cm^-1.

Multiple conical intersections in small linear parameter Jahn-Teller systems: the DMBE potential energy surface of ground-state C3 revisited

A new single-sheeted DMBE potential energy surface for ground-state C3 is reported. The novel analytical form accurately describes the three symmetry-equivalent C2v disjoint seams, in addition to the symmetry-required D3h one, over the entire configuration space. The present formalism warrants by built-in construction the confluence of the above crossings, and the rotation-in-plane of the C2v seams when the perimeter of the molecule fluctuates. Up to 1050 ab initio energies have been employed in the calibration procedure, of which 421 map the loci of intersection. The calculated energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion, and fitted analytically with chemical accuracy. The novel form is shown to accurately mimic the region defined by the 4 conical intersections, while exhibiting similar attributes to the previously reported one [J. Chem. Phys., 2015, 143, 074302] at the regions of configuration space away from the crossing seams. Despite being mainly addressed to C3, the present approach should be applicable to adiabatic PESs of any X3 system experiencing similar topological attributes, in particular the small-linear-parameter Jahn-Teller molecules.

Cn (n=2-4): current status

The major aspects of the C₂, C₃ and C₄ elemental carbon clusters are surveyed. For C₂, a brief analysis of its current status is presented. Regarding C₃, the most recent results obtained in our group are reviewed with emphasis on modelling its potential energy surface which is particularly complicated due to the presence of multiple conical intersections. As for C₄, the most stable isomeric forms of both triplet and singlet spin states and their possible interconversion pathways are examined afresh by means of accurate ab initio calculations. The main strategies for modelling the ground triplet C₄ potential are also discussed. Starting from a truncated cluster expansion and a previously reported DMBE form for C₃, an approximate four-body term is calibrated from the ab initio energies. The final six-dimensional global DMBE form so obtained reproduces all known topographical aspects while providing an accurate description of the C₄ linear-rhombic isomerization pathway. It is therefore commended for both spectroscopic and reaction dynamics studies.This article is part of the theme issue 'Modern theoretical chemistry'.

Theoretical spectroscopic parameters for isotopic variants of HCO+ and HOC. J Chem Phys 2017;147:114111. [PMID: 28938835 DOI: 10.1063/1.4998467]

Theoretical spectroscopic parameters are derived for all isotopologues of HCO⁺ and HOC⁺ involving H, D, ¹⁶O, ¹⁷O, ¹⁸O, ¹²C, and ¹³C by means of a two-step procedure. Full-dimensional rovibrational calculations are first carried out to obtain numerically exact rovibrational energies for J = 0-15 in both parities. Effective spectroscopic constants for the vibrational ground state, ν₁, ν₂, and ν₃ are determined by fitting the calculated rovibrational energies to appropriate spectroscopic Hamiltonians. Combining our vibration-rotation corrections with the available experimental ground-state rotational constants, we also derive the new estimate for the equilibrium structure of HCO⁺, r_e(CH) = 1.091 98 Å and r_e(CO) = 1.105 62 Å, and for the equilibrium structure of HOC⁺, r_e(HO) = 0.990 48 Å and r_e(CO) = 1.154 47 Å. Regarding the spectroscopic parameters, our estimates are in excellent agreement with available experimental results for the isotopic variants of both HCO⁺ and HOC⁺: the agreement for the rotational constants B_v is within 3 MHz, for the quartic centrifugal distortion constants D_v within 1 kHz, and for the effective ℓ-doubling constants q_v within 2 MHz. We thus expect that our results can provide useful assistance in analyzing expected observations of the rare isotopologues of HCO⁺ and HOC⁺ that are not yet experimentally known.

High-level theoretical rovibrational spectroscopy beyond fc-CCSD(T): The C3 molecule

An accurate local (near-equilibrium) potential energy surface (PES) is reported for the C3 molecule in its electronic ground state (X̃(1)Σg (+)). Special care has been taken in the convergence of the potential relative to high-order correlation effects, core-valence correlation, basis set size, and scalar relativity. Based on the aforementioned PES, several rovibrational states of all (12)C and (13)C substituted isotopologues have been investigated, and spectroscopic parameters based on term energies up to J = 30 have been calculated. Available experimental vibrational term energies are reproduced to better than 1 cm(-1) and rotational constants show relative errors of not more than 0.01%. The equilibrium bond length has been determined in a mixed experimental/theoretical approach to be 1.294 07(10) Å in excellent agreement with the ab initio composite value of 1.293 97 Å. Theoretical band intensities based on a newly developed electric dipole moment function also suggest that the infrared active (1, 1(1), 0)←(0, 0(0), 0) combination band might be observable by high-resolution spectroscopy.

Gas-Phase Spectroscopic Detection and Structural Elucidation of Carbon-Rich Group 14 Binary Clusters: Linear GeC3Ge

Guided by high-level quantum-chemical calculations at the CCSD(T) level of theory, the first polyatomic germanium-carbon cluster, linear Ge2C3, has been observed at high spectral resolution in the gas phase through its remarkably complex fundamental antisymmetric C-C stretching mode ν3 located at 1932 cm(-1). The observation of a total of six isotopic species permits the derivation of a highly accurate value for the equilibrium Ge-C bond length. The present study suggests that many more Ge-C species might be detectable in the future using a combination of laser-ablation techniques for production and high-resolution infrared and/or microwave techniques for spectroscopic detection.

Rotational analysis of bands of the à - X̃ transition of the C3Ar van der Waals complex

Rotational analyses have been carried out for four of the strongest bands of the Ã-X̃ transition of the C3Ar van der Waals complex, at 393 and 399 nm. These bands lie near the 02(-)0-000 and 04(-)0-000 bands of the Ã(1)Πu-X̃(1)Σ(+) g transition of C3 and form two close pairs, each consisting of a type A and a type C band of an asymmetric top, about 4 cm(-1) apart. Only K″ = even lines are found, showing that the complex has two equivalent carbon atoms (I = 0), and must be T-shaped, or nearly so. Strong a- and b-axis electronic-rotational (Coriolis) coupling occurs between the upper states of a pair, since they correlate with a (1)Πu vibronic state of C3, where the degeneracy is lifted in the lower symmetry of the complex. Least squares rotational fits, including the coupling, have given the rotational constants for both electronic states: the van der Waals bond lengths are 3.81 and 3.755 Å, respectively, in the ground and excited electronic states. For the ground state our new quantum chemical calculations, using the Multi-Channel Time-Dependent Hartree method, indicate that the C3 unit is non-linear, and that the complex does not have a rigid-molecule structure, existing instead as a superposition of arrowhead (↑) and distorted Y-shaped (Y) structures.

The C3-bending vibrational levels of the C3-Kr and C3-Xe van der Waals complexes studied by their Ã-X̃ electronic transitions and by ab initio calculations

Fluorescence excitation spectra and wavelength-resolved emission spectra of the C(3)-Kr and C(3)-Xe van der Waals (vdW) complexes have been recorded near the 2(2-)(0), 2(2+)(0), 2(4-)(0), and 1(1)(0) bands of the Ã(1)Π(u)-X̃(1)Σ(g)(+) system of the C(3) molecule. In the excitation spectra, the spectral features of the two complexes are red-shifted relative to those of free C(3) by 21.9-38.2 and 34.3-36.1 cm(-1), respectively. The emission spectra from the à state of the Kr complex consist of progressions in the two C(3)-bending vibrations (ν(2), ν(4)), the vdW stretching (ν(3)), and bending vibrations (ν(6)), suggesting that the equilibrium geometry in the X̃ state is nonlinear. As in the Ar complex [Zhang et al., J. Chem. Phys. 120, 3189 (2004)], the C(3)-bending vibrational levels of the Kr complex shift progressively to lower energy with respect to those of free C(3) as the bending quantum number increases. Their vibrational structures could be modeled as perturbed harmonic oscillators, with the dipole-induced dipole terms of the Ar and Kr complexes scaled roughly by the polarizabilities of the Ar and Kr atoms. Emission spectra of the Xe complex, excited near the Ã, 2(2-) level of free C(3), consist only of progressions in even quanta of the C(3)-bending and vdW modes, implying that the geometry in the higher vibrational levels (υ(bend) ≥ 4, E(vib) ≥ 328 cm(-1)) of the X̃ state is (vibrationally averaged) linear. In this structure the Xe atom bonds to one of the terminal carbons nearly along the inertial a-axis of bent C(3). Our ab initio calculations of the Xe complex at the level of CCSD(T)∕aug-cc-pVTZ (C) and aug-cc-pVTZ-PP (Xe) predict that its equilibrium geometry is T-shaped (as in the Ar and Kr complexes), and also support the assignment of a stable linear isomer when the amplitude of the C(3) bending vibration is large (υ(4) ≥ 4).

Linear Centrosymmetric SiC5Si: Floppy or Not?

Linear SiC5Si has been studied by the coupled cluster variant CCSD(T) and a large basis set of 393 contracted Gaussian-type orbitals. The full cubic force field was calculated, from which a variety of spectroscopic constants was obtained. The calculations indicate that linear SiC5Si behaves like a fairly normal semirigid molecule. In particular, excitation of any of its vibrations by one vibrational quantum leads to changes in the rotational constant not exceeding 0.3%.

Self-consistent field tight-binding model for neutral and (multi-) charged carbon clusters

A semiempirical model for carbon clusters modeling is presented, along with structural and dynamical applications. The model is a tight-binding scheme with additional one- and two-center distance-dependent electrostatic interactions treated self-consistently. This approach, which explicitly accounts for charge relaxation, allows us to treat neutral and (multi-) charged clusters not only at equilibrium but also in dissociative regions. The equilibrium properties, geometries, harmonic spectra, and relative stabilities of the stable isomers of neutral and singly charged clusters in the range n=1-14, for C(20) and C(60), are found to reproduce the results of ab initio calculations. The model is also shown to be successful in describing the stability and fragmentation energies of dictations in the range n=2-10 and allows the determination of their Coulomb barriers, as examplified for the smallest sizes (C(2) (2+),C(3) (2+),C(4) (2+)). We also present time-dependent mean-field and linear response optical spectra for the C(8) and C(60) clusters and discuss their relevance with respect to existing calculations.

Coupled Cluster Study of the Linear Carbon Chains C2n+1 (n = 5−9)

Making use of the coupled cluster variant CCSD(T) in conjunction with Dunning's cc-pVTZ basis set, equilibrium structures and complete harmonic force fields have been calculated for the linear carbon chains of type C2n+1 with n = 5-9. With the exception of C3, which is a well-known "floppy" molecule with an extremely shallow bending potential, all members of the C2n+1 series up to C19 appear to behave like fairly normal semirigid molecules. The IR active bending vibrations of lowest wavenumber for C17 and C19, which may be of interest to forthcoming far-infrared astronomy, are predicted to occur at 13.1 and 11.1 cm(-1), respectively, with corresponding absolute IR intensities of 6.6 and 5.9 km mol-1. Huge IR intensities are calculated for one antisymmetric stretching vibration per chain (19,948, 29,632, and 30,040 km mol(-1) for C15, C17, and C19, respectively). A quantitative description of these vibrations may require the explicit consideration of anharmonicity effects and electronic structure calculations going beyond CCSD(T).

Theoretical investigation of excited states of C(3)

In this work, we present ab initio calculations for the potential energy surfaces of C(3) in different electronic configurations, including the singlet ground state [X (1)Sigma(g) (+),((1)A(1))], the triplet ground state [a (3)Pi(u),((3)B(1), (3)A(1))], and some higher excited states. The geometries studied include triangular shapes with two identical bond lengths, but different bond angles between them. For the singlet and triplet ground states in the linear geometry, the total energies resulting from the mixed density functional--Hartree-Fock and quadratic configuration interaction methods reproduce the experimental values, i.e., the triplet occurs 2.1 eV above the singlet. In the geometry of an equilateral triangle, we find a low-lying triplet state with an energy of only 0.8 eV above the energy of the singlet in the linear configuration, so that the triangular geometry yields the lowest excited state of C(3). For the higher excited states up to about 8 eV above the ground state, we apply time-dependent density functional theory. Even though the systematic error produced by this approach is of the order of 0.4 eV, the results give different prospective to insight into the potential energy landscape for higher excitation energies.

Ab Initio calculations and vibrational energy level fits for the lower singlet potential-energy surfaces of C3

Ab initio multireference configuration interaction potential energy surfaces are computed for the eight lowest singlet surfaces of C(3). These reveal several important features, including several conical intersections in linear, nonlinear, and equilateral triangle geometries. These intersections are important because, particularly for the excited A (1)Pi(u) state, reasonable ab initio results could only be obtained by including nearby, near degenerate, (1)Sigma(u) (-) and (1)Delta(u) states that cross the A (1)Pi(u) state around 4500 cm(-1) above the equilibrium geometry, and a (1)Pi(g) state whose potential in turn crosses the other states about 2000 cm(-1) further up. These states are probably responsible for the complexity of the shorter wavelength UV absorption spectrum of C(3). The computed potential energy surface for the ground, X (1)Sigma(g) (+), state and for the lowest two excited singlet surfaces (which both correlate with the A (1)Pi(u) state in a collinear geometry) are fitted to analytic functional forms. Vibrational energy levels are calculated for both states, taking account of the Renner-Teller coupling in the excited A (1)Pi(u) state. The potential parameters for both states are then least-squares fitted to experimental data. The ground-state fit covers a range of approximately 8500 cm(-1) above the lowest level, and reproduces 100 observed vibrational levels with an average error of 2.8 cm(-1). The A (1)Pi(u) state surfaces cover a range of 3250 cm(-1) above the zero-point level, and reproduce the 44 observed levels in this range with an average error of 2.8 cm(-1).

The C3-bending levels of the C3-Ar complex studied by optical spectroscopy and ab initio calculation

The A-X electronic transition of C3-Ar, near 405 nm, has been studied by both laser-induced fluorescence and wavelength-resolved emission techniques. Emission spectra have been recorded from 14 vibrational levels of the A state of C3-Ar; these spectra consist of progressions in the ground state v2 and v4 vibrations (the in- and out-of-plane C3-bending motions, respectively). With increasing bending excitation, these ground state levels shift progressively downwards compared to those of free C3, indicating that the van der Waals complexes are becoming more tightly bound. The level structure of the two vibrations of C3-Ar has been fitted to a perturbed harmonic oscillator model, where the potential function has the form V = V1r cos theta + V2r2 cos 2theta (r is the amplitude of the C3-bending motion and theta gives the orientation of the rare gas atom relative to the plane of the bent C3 molecule). Ab initio calculations have been carried out for C3-Ar at the coupled-cluster singles, doubles (and triples)/correlation consistent polarization valence quadruple-zeta level. They predict that the C3-Ar complex is nearly T shaped at equilibrium, and that as the C3 molecule bends away from the linear configuration, the preferred orientation is "arrow" shaped. From the results of the best fit to the model and the emission spectral intensities, the relative orientation of the out-of-plane pi electron of the A-state complex and the Ar atom has been estimated. No bands of the Ar complex were found near the C3, A-X, (0,0) band, consistent with the fact that the A 1Piu, upsilon = 0 level of free C3 is strongly perturbed by triplet levels. In the excitation spectra of the Ar complex, the bands with upsilonb' > 0 show redshifts of about 16-36 cm(-1) compared to those of free C3, indicating that the A-state complex in these levels is more tightly bonded than the X-state complex.

Equilibrium Structure and Spectroscopic Constants of Difluorovinylidene: An ab Initio Study

Highly correlated ab initio calculations with large basis sets are reported for difluorovinylidene, F(2)CC. Based on CCSD(T)/aug-cc-pVQZ results and taking core correlation effects properly into account, a reliable theoretical equilibrium geometry is derived: r(e)(CC) = 134.74(10) pm, r(e)(CF) = 131.00(10) pm, and angle(e)(FCC) = 123.23(10) degrees. The error bars are estimated from analogous comparative calculations on the equilibrium structures of the CF(2), C(2), and C(3) species. Correlated harmonic [CCSD(T)/aug-cc-pVQZ] and anharmonic [CCSD(T)/TZ2Pf] force fields provide theoretical values for the fundamental vibrational wavenumbers which are in excellent agreement with those measured previously in an argon matrix. Many spectroscopic constants of F(2)CC are predicted. In addition, the energy of F(2)CC relative to difluoroethyne (FCCF) and the barrier to isomerization from F(2)CC to FCCF have been reinvestigated by means of the present high-level ab initio calculations. Copyright 2001 Academic Press.

The Effectiveness of Newton's Method for Improving Ab Initio Force Fields with Applications to CO2 and H2CO

Ab initio force field parameters are refined using modifications to Newton's method in which a figure of merit function is approximated as a Taylor Series truncated at second order. We investigate two versions of Newton's method: the Discrete Newton method where the Hessian is approximated by finite differences and the Gauss-Newton method where the Hessian is approximated as the product of first derivatives. The applicability of both rests on the capability of current ab initio methods to calculate quartic force fields that accurately reproduce experimental observables such as band centers and inertial constants. As examples, we calculate refined potential energy surfaces for CO2 and H2CO. We show that an algorithm depending solely on Newton's methods requires only a small number of iterations. Additionally, Newton-based methods provide a great deal of information about the sensitivity of the force field parameters to the observables being fit. We also demonstrate that the less computationally demanding Gauss-Newton method gives results similar to the less approximate Discrete Newton method. Copyright 1998 Academic Press. Copyright 1998Academic Press