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.

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.

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.

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.

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).

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).

A new ab initio ground-state dipole moment surface for the water molecule.

A valence-only (V) dipole moment surface (DMS) has been computed for water at the internally contracted multireference configuration interaction level using the extended atom-centered correlation-consistent Gaussian basis set aug-cc-pV6Z. Small corrections to these dipole values, resulting from core correlation (C) and relativistic (R) effects, have also been computed and added to the V surface. The resulting DMS surface is hence called CVR. Interestingly, the C and R corrections cancel out each other almost completely over the whole grid of points investigated. The ground-state CVR dipole of H(2) (16)O is 1.8676 D. This value compares well with the best ab initio one determined in this study, 1.8539+/-0.0013 D, which in turn agrees well with the measured ground-state dipole moment of water, 1.8546(6) D. Line intensities computed with the help of the CVR DMS shows that the present DMS is highly similar to though slightly more accurate than the best previous DMS of water determined by Schwenke and Partridge [J. Chem. Phys. 113, 16 (2000)]. The influence of the precision of the rovibrational wave functions computed using different potential energy surfaces (PESs) has been investigated and proved to be small, due mostly to the small discrepancies between the best ab initio and empirical PESs of water. Several different measures to test the DMS of water are advanced. The seemingly most sensitive measure is the comparison between the ab initio line intensities and those measured by ultralong pathlength methods which are sensitive to very weak transitions.

Approaching the full set of energy levels of water.

We report here the measurements of rovibrational levels in the electronic ground state of water molecule at the previously inaccessible energies above 26,000 cm(-1). The use of laser double-resonance overtone excitation extends this limit to 34,200 cm(-1), which corresponds to 83% of the water dissociation energy. We use experimental data to generate a semiempirical potential energy surface that now allows prediction of water levels with sub-cm(-1) accuracy at any energy up to the new limit.

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule.

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.

Continuous-wave cavity ringdown spectroscopy of the 8nu polyad of water in the 25,195-25,340 cm(-1) range.

State-of-the-art experiments and calculations are used to record and assign the data obtained in the weakly absorbing blue energy region of the H2O spectrum. Continuous-wave cavity ringdown absorption spectroscopy with Doppler resolution is used to probe the range from 25,195 to 25,470 cm(-1) with an absorption sensitivity of approximately 1 parts per 10(9) (ppb)/cm. 62 lines of the polyad nu(OH)=8 are reported, of which 43 are assigned using variational nuclear calculations. The study includes absorption line intensities (in the range of 10(-28)-10(-26) cmmolecule) for all lines and self-broadening pressure coefficient for a few lines. The newly obtained energy levels are also reported.

On equilibrium structures of the water molecule.

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .

A 3000 K laboratory emission spectrum of water.

An emission spectrum of hot water with a temperature of about 3000 K is obtained using an oxy-acetylene torch. This spectrum contains a very large number of transitions. The spectrum, along with previous cooler laboratory emission spectra and an absorption spectrum recorded from a sunspot, is analyzed in the 500-2000 cm(-1) region. Use of a calculated variational linelist for water allows significant progress to be made on assigning transitions involving highly excited vibrational and rotational states. In particular emission from rotationally excited states up to J=42 and vibrational levels with up to eight quanta of bending motion are assigned.

Analysis of hot D2O emission using spectroscopically determined potentials.

Fourier transform emission spectra of D2O vapor were recorded at a temperature of 1500 degrees C in the wavenumber range 380-1880 cm(-1). 15 346 lines were measured, of which the majority were identified as belonging to D2O. The spectrum was analyzed using variational nuclear motion calculations based on spectroscopically determined potential-energy surfaces. Initial assignments were made using a potential surface obtained by fitting a high accuracy ab initio potential. The new assignments were used to refine the potential surface, resulting in additional assignments. A total of 6400 D2O transitions were assigned and 2144 new D2O energy levels were obtained. Transitions involving the 4nu2 and 5nu2 bending states, with band origins of 4589.30 (+/-0.02) and 5679.6 (+/-0.1) cm(-1), respectively, were assigned for the first time.

High-accuracy ab initio rotation-vibration transitions for water.

The spectrum of water vapor is of fundamental importance for a variety of processes, including the absorption and retention of sunlight in Earth's atmosphere. Therefore, there has long been an urgent need for a robust and accurate predictive model for this spectrum. In our work on the high-resolution spectrum of water, we report first-principles calculations that approach experimental accuracy. To achieve this, we performed exceptionally large electronic structure calculations and considered a variety of effects, including quantum electrodynamics, which have routinely been neglected in studies of small many-electron molecules. The high accuracy of the resulting ab initio procedure is demonstrated for the main isotopomers of water.