Measurement and calculation of CO (7-0) overtone line intensities.

Intensities of 14 lines in the sixth overtone (7-0) band of carbon monoxide (12C16O) are measured in the visible range between 14 300 and 14 500 cm-1 using a frequency-stabilized cavity ring-down spectrometer. This is the first observation of such a high and weak overtone spectrum of the CO molecule. A theoretical model is constructed and tested based on the use of a high accuracy ab initio dipole moment curve and a semi-empirical potential energy curve. Accurate studies of high overtone transitions provide a challenge to both experiment and theory as the lines are very weak: below 2 × 10-29 cm molecule-1 at 296 K. Agreement between theory and experiment within the experimental uncertainty of a few percent is obtained. However, this agreement is only achieved after issues with the stability of the Davidson correction to the multi-reference configuration interaction calculations are addressed.

Subpromille Measurements and Calculations of CO (3-0) Overtone Line Intensities.

Intensities of lines in the near-infrared second overtone band (3-0) of ^{12}C^{16}O are measured and calculated to an unprecedented degree of precision and accuracy. Agreement between theory and experiment to better than 1‰ is demonstrated by results from two laboratories involving two independent absorption- and dispersion-based cavity-enhanced techniques. Similarly, independent Fourier transform spectroscopy measurements of stronger lines in this band yield mutual agreement and consistency with theory at the 1‰ level. This set of highly accurate intensities can provide an intrinsic reference for reducing biases in future measurements of spectroscopic peak areas.

Highly accurate HF dimer ab initio potential energy surface.

A highly accurate, (HF)2 potential energy surface (PES) is constructed based on ab initio calculations performed at the coupled-cluster single double triple level of theory with an aug-cc-pVQZ-F12 basis set at about 152 000 points. A higher correlation correction is computed at coupled-cluster single double triple quadruple level for 2000 points and is considered alongside other more minor corrections due to relativity, core-valence correlation, and Born-Oppenheimer failure. The analytical surface constructed uses 500 constants to reproduce the ab initio points with a standard deviation of 0.3 cm-1. Vibration-rotation-inversion energy levels of the HF dimer are computed for this PES by variational solution of the nuclear-motion Schrödinger equation using the program WAVR4. Calculations over an extended range of rotationally excited states show very good agreement with the experimental data. In particular, the known empirical rotational constants B for the ground vibrational states are predicted to better than about 2 MHz. B constants for excited vibrational states are reproduced several times more accurately than by previous calculations. This level of accuracy is shown to extend to higher excited inter-molecular vibrational states v and higher excited rotational quantum numbers (J, Ka).

Absolute 13C/12C Isotope Amount Ratio for Vienna Pee Dee Belemnite from Infrared Absorption Spectroscopy.

Measurements of isotope ratios are predominantly made with reference to standard specimens that have been characterized in the past. In the 1950s, the carbon isotope ratio was referenced to a belemnite sample collected by Heinz Lowenstam and Harold Urey1 in South Carolina's Pee Dee region. Due to the exhaustion of the sample since then, reference materials that are traceable to the original artefact are used to define the Vienna Pee Dee Belemnite (VPDB) scale for stable carbon isotope analysis2. However, these reference materials have also become exhausted or proven to exhibit unstable composition over time3, mirroring issues with the international prototype of the kilogram that led to a revised International System of Units4. A campaign to elucidate the stable carbon isotope ratio of VPDB is underway5, but independent measurement techniques are required to support it. Here we report an accurate value for the stable carbon isotope ratio inferred from infrared absorption spectroscopy, fulfilling the promise of this fundamentally accurate approach6. Our results agree with a value recently derived from mass spectrometry5, and therefore advance the prospects of SI-traceable isotope analysis. Further, our calibration-free method could improve mass balance calculations and enhance isotopic tracer studies in CO2 source apportionment.

Use of the complete basis set limit for computing highly accurate ab initio dipole moments.

Calculating dipole moments with high-order basis sets is generally only possible for the light molecules, such as water. A simple, yet highly effective strategy of obtaining high-order dipoles with small, computationally less expensive basis sets is described. Using the finite field method for computing dipoles, energies calculated with small basis sets can be extrapolated to produce dipoles that are comparable to those obtained in high order calculations. The method reduces computational resources by approximately 50% (allowing the calculation of reliable dipole moments for larger molecules) and simultaneously improves the agreement with experimentally measured infrared transition intensities. For atmospherically important molecules, which are typically too large to consider the use of large basis sets, this procedure will provide the necessary means of improving calculated spectral intensities by several percent.

A highly accurate ab initio dipole moment surface for the ground electronic state of water vapour for spectra extending into the ultraviolet.

A new global and highly accurate ab initio dipole moment surface (DMS) for water vapour is presented. This DMS is based on a set of 17 628 multi-reference configuration interaction data points that were calculated with the aug-cc-pCV6Z basis set with the Douglas-Kroll-Hess Hamiltonian; tests are performed at several other levels of ab initio theory. This new "CKAPTEN" DMS improves agreement with recent experimental measurements compared with previous models that poorly predicted some bands in the infrared while also maintaining or improving on the agreement for all remaining strong lines. For high overtones located in both the visible and the near ultraviolet regions, our predicted intensities all lie within 10% of recent atmospheric observations. A crossing of energy levels in the ν1 fundamental and 2ν2 states is seen to offset transition intensities in the ν1 fundamental band; residual inaccuracies within the potential energy surface used is the cause of this problem.

High-accuracy water potential energy surface for the calculation of infrared spectra.

Transition intensities for small molecules such as water and CO2 can now be computed with such high accuracy that they are being used to systematically replace measurements in standard databases. These calculations use high-accuracy ab initio dipole moment surfaces and wave functions from spectroscopically determined potential energy surfaces (PESs). Here, an extra high-accuracy PES of the water molecule (H216O) is produced starting from an ab initio PES which is then refined to empirical rovibrational energy levels. Variational nuclear motion calculations using this PES reproduce the fitted energy levels with a standard deviation of 0.011 cm-1, approximately three times their stated uncertainty. The use of wave functions computed with this refined PES is found to improve the predicted transition intensities for selected (problematic) transitions. A new room temperature line list for H216O is presented. It is suggested that the associated set of line intensities is the most accurate available to date for this species.This article is part of the theme issue 'Modern theoretical chemistry'.

High Accuracy ab Initio Calculations of Rotational-Vibrational Levels of the HCN/HNC System.

Highly accurate ab initio calculations of vibrational and rotational-vibrational energy levels of the HCN/HNC (hydrogen cyanide/hydrogen isocyanide) isomerising system are presented for several isotopologues. All-electron multireference configuration interaction (MRCI) electronic structure calculations were performed using basis sets up to aug-cc-pCV6Z on a grid of 1541 geometries. The ab initio energies were used to produce an analytical potential energy surface (PES) describing the two minima simultaneously. An adiabatic Born-Oppenheimer diagonal correction (BODC) correction surface as well as a relativistic correction surface were also calculated. These surfaces were used to compute vibrational and rotational-vibrational energy levels up to 25 000 cm-1 which reproduce the extensive set of experimentally known HCN/HNC levels with a root-mean-square deviation σ = 1.5 cm-1. We studied the effect of nonadiabatic effects by introducing opportune radial and angular corrections to the nuclear kinetic energy operator. Empirical determination of two nonadiabatic parameters results in observed energies up to 7000 cm-1 for four HCN isotopologues (HCN, DCN, H13CN, and HC15N) being reproduced with σ = 0.37 cm-1. The height of the isomerization barrier, the isomerization energy and the dissociation energy were computed using a number of models; our best results are 16 809.4, 5312.8, and 43 729 cm-1, respectively.

Saddle point localization of molecular wavefunctions.

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.

High-Accuracy CO(2) Line Intensities Determined from Theory and Experiment.

Atmospheric CO(2) concentrations are being closely monitored by remote sensing experiments which rely on knowing line intensities with an uncertainty of 0.5% or better. Most available laboratory measurements have uncertainties much larger than this. We report a joint experimental and theoretical study providing rotation-vibration line intensities with the required accuracy. The ab initio calculations are extendible to all atmospherically important bands of CO(2) and to its isotologues. As such, they will form the basis for detailed CO(2) spectroscopic line lists for future studies.

Communication: Visible line intensities of the triatomic hydrogen ion from experiment and theory.

The visible spectrum of H3(+) is studied using high-sensitivity action spectroscopy in a cryogenic radiofrequency multipole trap. Advances are made to measure the weak ro-vibrational transitions from the lowest rotational states of H3(+) up to high excitation energies providing visible line intensities and, after normalisation to an infrared calibration line, the corresponding Einstein B coefficients. Ab initio predictions for the Einstein B coefficients are obtained from a highly precise dipole moment surface of H3(+) and found to be in excellent agreement, even in the region where states have been classified as chaotic.

Variational calculation of highly excited rovibrational energy levels of H2O2.

Results are presented for highly accurate ab initio variational calculation of the rotation-vibration energy levels of H2O2 in its electronic ground state. These results use a recently computed potential energy surface and the variational nuclear-motion programs WARV4, which uses an exact kinetic energy operator, and TROVE, which uses a numerical expansion for the kinetic energy. The TROVE calculations are performed for levels with high values of rotational excitation, J up to 35. The purely ab initio calculations of the rovibrational energy levels reproduce the observed levels with a standard deviation of about 1 cm(-1), similar to that of the J = 0 calculation, because the discrepancy between theory and experiment for rotational energies within a given vibrational state is substantially determined by the error in the vibrational band origin. Minor adjustments are made to the ab initio equilibrium geometry and to the height of the torsional barrier. Using these and correcting the band origins using the error in J = 0 states lowers the standard deviation of the observed-calculated energies to only 0.002 cm(-1) for levels up to J = 10 and 0.02 cm(-1) for all experimentally known energy levels, which extend up to J = 35.

Calculation of rotation-vibration energy levels of the water molecule with near-experimental accuracy based on an ab initio potential energy surface.

A recently computed, high-accuracy ab initio Born-Oppenheimer (BO) potential energy surface (PES) for the water molecule is combined with relativistic, adiabatic, quantum electrodynamics, and, crucially, nonadiabatic corrections. Calculations of ro-vibrational levels are presented for several water isotopologues and shown to have unprecedented accuracy. A purely ab initio calculation reproduces some 200 known band origins associated with seven isotopologues of water with a standard deviation (σ) of about 0.35 cm(-1). Introducing three semiempirical scaling parameters, two affecting the BO PES and one controlling nonadiabatic effects, reduces σ below 0.1 cm(-1). Introducing one further rotational nonadiabatic parameter gives σ better than 0.1 cm(-1) for all observed ro-vibrational energy levels up to J = 25. We conjecture that the energy levels of closed-shell molecules with roughly the same number of electrons as water, such as NH3, CH4, and H3O(+), could be calculated to this accuracy using an analogous procedure. This means that near-ab initio calculations are capable of predicting transition frequencies with an accuracy only about a factor of 5 worse than high resolution experiments.

Spectroscopy of H3+ based on a new high-accuracy global potential energy surface.

The molecular ion H(3)(+) is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro-vibrational spectrum of H(3)(+) is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm(-1) relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm(-1). Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro-vibrational data show that an accuracy of the order of 0.1 cm(-1) is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.

Calibration-quality adiabatic potential energy surfaces for H3(+) and its isotopologues.

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion H(3)(+). The underlying Born-Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born-Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41,655 ab initio points is presented which gives a standard deviation better than 0.1 cm(-1) when restricted to the points up to 6000 cm(-1) above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for H(3)(+), H(2)D(+), and HD(2)(+) are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the H(3)(+) isotopologues considered to better than 0.2 cm(-1). This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the H(3)(+) isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of H(3)(+) resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16,000 cm(-1), and (c) results suggest that we can predict accurately the lines of H(3)(+) towards dissociation and thus facilitate their experimental observation.

Global spectroscopy of the water monomer.

Given the large energy required for its electronic excitation, the most important properties of the water molecule are governed by its ground potential energy surface (PES). Novel experiments are now able to probe this surface over a very extended energy range, requiring new theoretical procedures for their interpretation. As part of this study, a new, accurate, global spectroscopic-quality PES and a new, accurate, global dipole moment surface are developed. They are used for the computation of the high-resolution spectrum of water up to the first dissociation limit and beyond as well as for the determination of Stark coefficients for high-lying states. The water PES has been determined by combined ab initio and semi-empirical studies. As a first step, a very accurate, global, ab initio PES was determined using the all-electron, internally contracted multi-reference configuration interaction technique together with a large Gaussian basis set. Scalar relativistic energy corrections are also determined in order to move the energy determinations close to the relativistic complete basis set full configuration interaction limit. The electronic energies were computed for a set of about 2500 geometries, covering carefully selected configurations from equilibrium up to dissociation. Nuclear motion computations using this PES reproduce the observed energy levels up to 39 000 cm(-1) with an accuracy of better than 10 cm(-1). Line positions and widths of resonant states above dissociation show an agreement with experiment of about 50 cm(-1). An improved semi-empirical PES is produced by fitting the ab initio PES to accurate experimental data, resulting in greatly improved accuracy, with a maximum deviation of about 1 cm(-1) for all vibrational band origins. Theoretical results based on this semi-empirical surface are compared with experimental data for energies starting at 27 000 cm(-1), going all the way up to dissociation at about 41 000 cm(-1) and a few hundred wavenumbers beyond it.

Precision measurements and computations of transition energies in rotationally cold triatomic hydrogen ions up to the midvisible spectral range.

First-principles computations and experimental measurements of transition energies are carried out for vibrational overtone lines of the triatomic hydrogen ion H(3)(+) corresponding to floppy vibrations high above the barrier to linearity. Action spectroscopy is improved to detect extremely weak visible-light spectral lines on cold trapped H(3)(+) ions. A highly accurate potential surface is obtained from variational calculations using explicitly correlated Gaussian wave function expansions. After nonadiabatic corrections, the floppy H(3)(+) vibrational spectrum is reproduced at the 0.1 cm(-1) level up to 16600 cm(-1).

A global, high accuracy ab initio dipole moment surface for the electronic ground state of the water molecule.

A highly accurate, global dipole moment surface (DMS) is calculated for the water molecule using ab initio quantum chemistry methods. The new surface is named LTP2011 and is based on all-electron, internally contracted multireference configuration interaction, including size-extensivity corrections in the aug-cc-pCV6Z basis set. Dipoles are computed as energy derivatives and small corrections due to relativistic effects included. The LTP2011 DMS uses an appropriate functional form that guarantees qualitatively correct behaviour even for most high energies configuration (up to about 60,000 cm(-1)), including, in particular, along the water dissociation channel. Comparisons with high precision experimental data show agreement within 1% for medium-strength lines. The new DMS and all the ab initio data are made available in the supplementary material.

State-selective spectroscopy of water up to its first dissociation limit.

A joint experimental and first-principles quantum chemical study of the vibration-rotation states of the water molecule up to its first dissociation limit is presented. Triple-resonance, quantum state-selective spectroscopy is used to probe the entire ladder of water's stretching vibrations up to 19 quanta of OH stretch, the last stretching state below dissociation. A new ground state potential energy surface of water is calculated using a large basis set and an all-electron, multireference configuration interaction procedure, which is augmented by relativistic corrections and fitted to a flexible functional form appropriate for a dissociating system. Variational nuclear motion calculations on this surface are used to give vibrational assignments. A total of 44 new vibrational states and 366 rotation-vibration energy levels are characterized; these span the region from 35,508 to 41,126 cm(-1) above the vibrational ground state.

Collisionally assisted spectroscopy of water from 27,000 to 34,000 cm(-1).

We report here an experimental approach that enables measurement of weak transitions to a wide range of rovibrational levels of water in the energy region 27,000-34,200 cm(-1). We have previously demonstrated the use of laser double-resonance overtone excitation to access highly excited vibrational levels from single rovibrational states. Although this approach simplifies the assignment of the spectra, it strongly reduces the number of observed transitions and hence our ability to test theoretical predictions. Here, we increase significantly the number of observed transitions by allowing rotational relaxation of H2O at intermediate levels of the double-resonance excitation scheme to the levels of the same nuclear spin (ortho or para). Our recently developed semiempirical potential energy surface PES12 enables assignment of the resulting complex spectra and reproduction of the measured transitions with accuracy better than 1 cm(-1).