Diagonal Born-Oppenheimer Correction Research Articles

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules.

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Fulminic acid: a quasibent spectacle.

Fulminic acid (HCNO) played a critical role in the early development of organic chemistry, and chemists have sought to discern the structure and characteristics of this molecule and its isomers for over 200 years. The mercurial nature of the extremely flat H-C-N bending potential of fulminic acid, with a nearly vanishing harmonic vibrational frequency at linearity, remains enigmatic and refractory to electronic structure theory, as dramatic variation with both orbital basis set and electron correlation method is witnessed. To solve this problem using rigorous electronic wavefunction methods, we have employed focal point analyses (FPA) to ascertain the ab initio limit of optimized linear and bent geometries, corresponding vibrational frequencies, and the HCN + O(3P) → HCNO reaction energy. Electron correlation treatments as extensive as CCSDT(Q), CCSDTQ(P), and even CCSDTQP(H) were employed, and complete basis set (CBS) extrapolations were performed using the cc-pCVXZ (X = 4-6) basis sets. Core electron correlation, scalar relativistic effects (MVD1), and diagonal Born-Oppenheimer corrections (DBOC) were all included and found to contribute significantly in determining whether vibrationless HCNO is linear or bent. At the all-electron (AE) CCSD(T)/CBS level, HCNO is a linear molecule with ω5(H-C-N bend) = 120 cm-1. However, composite AE-CCSDT(Q)/CBS computations give an imaginary frequency (51i cm-1) at the linear optimized geometry, leading to an equilibrium structure with an H-C-N angle of 173.9°. Finally, at the AE-CCSDTQ(P)/CBS level, HCNO is once again linear with ω5 = 45 cm-1, and inclusion of both MVD1 and DBOC effects yields ω5 = 32 cm-1. A host of other topics has also been investigated for fulminic acid, including the dependence of re and ωi predictions on a variety of CBS extrapolation formulas, the question of multireference character, the N-O bond energy and enthalpy of formation, and issues that give rise to the quasibent appellation.

Introducing MPEC: Massively parallel electron correlation.

We have developed a new program for carrying out improved internally contracted Multi-reference Configuration Interaction Singles and Doubles (i2cMRCISD) calculations. It is designed from the ground up to be used on distributed memory parallel computers. Tests show good scaling properties with the number of cores per node and the number nodes. This program features Gaussian basis sets with ℓ > 6; scalar special relativity via the spin-free method; convergence to C∞v, D∞v, or spherical electronic states; special code to determine Rydberg orbitals; both uncontracted and contracted MRCISD wavefunctions; one and two electron properties, including full spin-orbit matrix elements with the Breit interaction; analytic calculation of Born-Oppenheimer diagonal correction for multi-configuration Hartree-Fock wavefunctions; and analytic calculation of second order Born-Oppenheimer corrections for Hartree-Fock wavefunctions. The program can be obtained from software.nasa.gov.

Ro-vibrational levels and their (e-f) splitting of acetylene molecule calculated from new potential energy surfaces

Ro-vibrational energy levels of acetylene are reported using variational nuclear motion calculations from new ab initio and empirically optimized full six-dimensional potential energy surfaces in the ground electronic state of the acetylene molecule. The calculations account for the triple, quadruple and quintuple excitations as well as relativistic and diagonal Born-Oppenheimer corrections. Variational nuclear motion calculations were performed using the exact kinetic energy operator in orthogonal coordinates. The convergence of energy levels calculations versus the size of the vibrational basis set functions was verified. Our best ab initio potential energy surface that includes the above-mentioned contributions provides the RMS (obs.-calc.) errors of 0.95 cm−1 for five fundamental energy levels. The largest contribution to the RMS error is caused primarily by a significant deviation of the ν4 fundamental frequency. Experimental values of 120 vibrational band origins were used to empirically adjust few lower-order parameters of the potential energy surface. The average error drops down to 0.45 cm−1 or 0.25 cm−1 for empirically optimized potential energy function with two or seven adjusted parameters corresponding to quadratic force field terms and one third order term. The splitting of (e – f) rovibrational doublets and their J dependence were calculated with high accuracy due to the full account of Coriolis interactions. Computed (e – f) splittings allow one to check the correctness of the assignment of empirical energy levels. The estimation of the accuracy for the calculated vibrational levels in an extended range up to 9500 cm−1 shows that the set of ab initio vibrational levels can be used for future assignments of empirically not observed ro-vibrational energy levels. The comparison of the calculated and experimental ro-vibrational energy levels of the C2D2 and 13C2H2 isotopologues is also reported.

ATOMIC-2 Protocol for Thermochemistry.

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2um analyses.

The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics.

The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born-Oppenheimer corrections (DBOCs) are non-integrable, and the geometric phase effect on the nuclear wavepackets cannot be accounted for unless a model is available. To circumvent these difficulties, the moving crude adiabatic (MCA) representation was proposed and successfully tested in low energy dynamics where the wavepacket skirts the conical intersection. We assess the MCA representation in the case of non-adiabatic transitions through conical intersections. First, we show that using a Gaussian basis in the adiabatic representation indeed exhibits the aforementioned difficulties with a special emphasis on the possibility to regularize the DBOC terms. Then, we show that MCA is indeed able to properly model non-adiabatic transitions. Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Analytic calculation of the Berry curvature and diagonal Born-Oppenheimer correction for molecular systems in uniform magnetic fields.

The diagonal nonadiabatic term arising from the Born-Oppenheimer wave function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the latter, known as the diagonal Born-Oppenheimer correction (DBOC), is typically small in magnitude. Therefore, unless high accuracy is sought, the diagonal nonadiabatic term is usually neglected when calculating molecular properties. In the presence of a magnetic field, the wave function is generally complex, and the geometric vector potential gives rise to a screening force that is qualitatively important for molecular dynamics. This screening force is written in terms of the Berry curvature and is added to the bare Lorentz force acting on the nuclei in the presence of the field. In this work, we derive analytic expressions for the Berry curvature and DBOC using both first- and second-quantization formalisms for the case of generalized and restricted Hartree-Fock theories in a uniform magnetic field. The Berry curvature and DBOC are calculated as a function of the magnetic field strength and the bond distance for the ground-state singlets of H2, LiH, BH, and CH+. We also examine the stability and time-reversal symmetry of the underlying self-consistent field solutions. The character of the DBOC and Berry curvature is found to depend on the magnetic field and varies between molecules. We also identify instances of broken time-reversal symmetry for the dissociation curves of BH and CH+.

Role of post-CCSD(T) corrections in predicting the energetics and kinetics of the OH˙ + O3 reaction.

The present work investigates the OH˙ +O3 reaction by means of chemical kinetics and quantum chemical calculations. To estimate the reaction barrier height and reaction energy, we have included various corrections, like zero point energy corrections, contribution from full triple excitations and partial quadratic excitations at the coupled-cluster level, core corrections, diagonal Born-Oppenheimer corrections and spin-orbit coupling corrections. The reaction barrier and reaction energy were estimated to be 1.64 kcal mol-1 and -39.97 kcal mol-1, respectively, which are in good agreement with the experimental results. Using this barrier height, we have estimated the rate constants using transition state theory augmented with zero curvature tunneling (TST/ZCT) in the temperature range of 220-450 K and the thus obtained rate constants were compared with available experimental results.

New Ab Initio Potential Energy Surfaces for NH3 Constructed from Explicitly Correlated Coupled-Cluster Methods.

Accurate calculation of ab initio potential energy surfaces (PESs) for the NH3 molecule is a difficult task because of the poor convergence of the standard CCSD(T) method with respect to the basis size. Currently, the best available NH3 PESs contain empirically refined parameters. In this paper, we show that CCSD(T)/aug-cc-pCV6Z calculations are not sufficient to properly describe the PES over a large range of nuclear configurations. However, the PES obtained by the extrapolation of the CCSD(T)/aug-cc-pCVXZ (X = T, Q, 5, and 6) energies to the complete basis set limit is closer to that based on the explicitly correlated CCSD(T)-F12a method using the cc-pCVQZ-F12 orbital basis set. All of the ab initio PESs constructed in this work include the following corrections: one electron relativistic effects, diagonal Born-Oppenheimer correction, and high-order electronic correlations (CCSDT, CCSDTQ, and CCSDTQP). Finally, the root-mean-square deviation between the predicted band centers obtained from our final "pure" ab initio PES and the experimental ones in the spectral region [0-7000] cm-1 is divided by two compared to the most accurate ab initio PES available in the literature.

Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning.

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.

Precise equilibrium structure of thiazole (c-C3H3NS) from twenty-four isotopologues.

The pure rotational spectrum of thiazole (c-C3H3NS, Cs) has been studied in the millimeter-wave region from 130 to 375GHz. Nearly 4800 newly measured rotational transitions for the ground vibrational state of the main isotopologue were combined with previously reported measurements and least-squares fit to a complete sextic Hamiltonian. Transitions for six singly substituted heavy-atom isotopologues (13C, 15N, 33S, 34S) were observed at natural abundance and likewise fit. Several deuterium-enriched samples were prepared, which gave access to the rotational spectra of 16 additional isotopologues, 14 of which had not been previously studied. The rotational spectra of each isotopologue were fit to A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The experimental values of the ground-state rotational constants (A0, B0, and C0) from each isotopologue were converted to determinable constants (A0″, B0″, and C0″), which were corrected for effects of vibration-rotation interactions and electron-mass distributions using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The moments of inertia from the resulting constants (Ae, Be, and Ce) of 24 isotopologues were used to determine the precise semi-experimental equilibrium structure (re SE) of thiazole. As a basis for comparison, a purely theoretical equilibrium structure was estimated by an electronic structure calculation [CCSD(T)/cc-pCV5Z] that was subsequently corrected for extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born-Oppenheimer correction. The precise re SE structure is compared to the resulting "best theoretical estimate" structure. Some, but not all, of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the re SE results. The possible origin of the discrepancies between the best theoretical estimate re and semi-empirical re SE structures is discussed.

Precise equilibrium structure determination of thiophene (c-C4H4S) by rotational spectroscopy-Structure of a five-membered heterocycle containing a third-row atom.

The rotational spectrum of thiophene (c-C4H4S) has been collected between 8 and 360GHz. Samples of varying deuterium-enrichment were synthesized to yield all possible deuterium-substituted isotopologues of thiophene. A total of 26 isotopologues have been measured and least-squares fit using A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The resultant rotational constants (A0, B0, and C0) from each reduction were converted to determinable constants (A″, B″, and C″) to remove the impact of centrifugal distortion. The computed vibrational and electron mass corrections [CCSD(T)/cc-pCVTZ] were applied to the determinable constants to obtain semi-experimental equilibrium rotational constants (Ae, Be, and Ce) for 24 isotopologues. A precise semi-experimental equilibrium (re SE) structure has been achieved from a least-squares fit of the equilibrium moments of inertia. The combination of the expanded isotopologue rotational data with high-level computational work establishes a precise re SE structure for this sulfur-containing heterocycle. The CCSD(T)/cc-pCV5Z structure has been obtained and corrected for the extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born-Oppenheimer correction. The precise re SE structure is compared to the resulting "best theoretical estimate" structure. Several of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the re SE results. The possible origin of the discrepancies for the computed parameters that fall outside the statistical uncertainties is discussed.

Thermophysical properties of low-density neon gas from highly accurate first-principles calculations and dielectric-constant gas thermometry measurements.

New interatomic potential energy and interaction-induced polarizability curves for two ground-state neon atoms were developed and used to predict the second density, acoustic, and dielectric virial coefficients and the dilute gas shear viscosity and thermal conductivity of neon at temperatures up to 5000 K. The potential energy curve is based on supermolecular coupled-cluster (CC) calculations at very high levels up to CC with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. Scalar and spin-orbit relativistic effects, the diagonal Born-Oppenheimer correction, and retardation of the dispersion interactions were taken into account. The interaction-induced polarizability curve, which in this work is only needed for the calculation of the second dielectric virial coefficient, is based on supermolecular calculations at levels up to CCSDT and includes a correction for scalar relativistic effects. In addition to these first-principles calculations, highly accurate dielectric-constant gas thermometry (DCGT) datasets measured at temperatures from 24.5 to 200 K were analyzed to obtain the difference between the second density and dielectric virial coefficients with previously unattained accuracy. The agreement of the DCGT values with the ones resulting from the first-principles calculations is, despite some small systematic deviations, very satisfactory. Apart from this combination of two virial coefficients, the calculated thermophysical property values of this work are significantly more accurate than any available experimental data.

Theoretical calculation of position-specific carbon and hydrogen isotope equilibriums in butane isomers

Position-specific isotope analysis has shown its potential to reveal information regarding formation, migration, and conversion procesess of hydrocarbons. The intramolecular isotope compositions of butane are promising to serve as a new thermometer and tracer. Therefore, position-specific isotope signatures in butane at equilibrium are needed for calibrating experimental measurements, establishing new geothermometers, and recognizing kinetic isotope effects. Here we conduct quantum chemistry modeling with corrections beyond the harmonic approximation and the Born-Oppenheimer approximation to obtain accurate intramolecular and intermolecular carbon and hydrogen isotope fractionation factors for butane isomers at equilibrium. Temperature dependences of these equilibrium isotope effects are presented for the range from 0 °C to 726.85 °C. The contribution of higher-order energy terms to 1000lnα values beyond the Bigeleisen-Mayer equation is found to be comparable to the magnitude of current experimental precisions. In addition to the significance of anharmonicity, the contribution of hindered internal rotation and diagonal Born-Oppenheimer correction is found to be important for accurate predictions of position-specific hydrogen isotope equilibriums. The abundance ratio of n-butane to i-butane at equilibriums is also calculated at various temperatures. Our results provide fundamental understanding of equilibrium properties for studying position-specific isotope effects in butane.

Vibrational levels of formaldehyde: Calculations from new high precision potential energy surfaces and comparison with experimental band origins

Vibrational energy levels of H2CO are reported using variational nuclear motion calculations from new ab initio and empirically optimized full 6-dimensional ab initio potential energy surfaces in the ground electronic state of the formaldehyde molecule. Ab initio calculations were carried out using extended electronic structure coupled-cluster calculations accounting for dynamic electron correlations including triple and quadruple excitations as well as relativistic and diagonal Born-Oppenheimer corrections. Variational nuclear motion calculations are compared in different sets of coordinates with exact kinetic energy operator and in normal coordinates with Watson-Eckart kinetic energy operator. Our best ab initio potential energy surface including the above mentioned contributions provides the RMS (obs.-calc.) errors of 0.25 cm−1 for fifteen vibrational band origins without empirically adjusted parameters. The average error drops down to 0.08 cm−1 for an empirically optimized potential energy function with six adjusted parameters corresponding to quadratic force field terms. The estimation of the accuracy for the calculated vibrational levels in an extended range up to 4500 cm−1 shows that the set of ab initio vibrational levels could be more consistent than experimental levels obtained from earlier studies of low resolution spectra. The comparison of the calculated and experimental vibrational energy levels of the D2CO isotopologue is also reported.

State-of-the-Art Quantum Chemistry Meets Variable Reaction Coordinate Transition State Theory to Solve the Puzzling Case of the H2S + Cl System.

The atmospheric reaction of H2S with Cl has been reinvestigated to check if, as previously suggested, only explicit dynamical computations can lead to an accurate evaluation of the reaction rate because of strong recrossing effects and the breakdown of the variational extension of transition state theory. For this reason, the corresponding potential energy surface has been thoroughly investigated, thus leading to an accurate characterization of all stationary points, whose energetics has been computed at the state of the art. To this end, coupled-cluster theory including up to quadruple excitations has been employed, together with the extrapolation to the complete basis set limit and also incorporating core–valence correlation, spin–orbit, and scalar relativistic effects as well as diagonal Born–Oppenheimer corrections. This highly accurate composite scheme has also been paralleled by less expensive yet promising computational approaches. Moving to kinetics, variational transition state theory and its variable reaction coordinate extension for barrierless steps have been exploited, thus obtaining a reaction rate constant (8.16 × 10–11 cm3 molecule–1 s–1 at 300 K and 1 atm) in remarkable agreement with the experimental counterpart. Therefore, contrary to previous claims, there is no need to invoke any failure of the transition state theory, provided that sufficiently accurate quantum-chemical computations are performed. The investigation of the puzzling case of the H2S + Cl system allowed us to present a robust approach for disclosing the thermochemistry and kinetics of reactions of atmospheric and astrophysical interest.

Hartree-Fock instabilities and the diagonal Born-Oppenheimer correction

The NO and NO radicals are used to demonstrate how instabilities in Hartree-Fock wavefunctions can result in unsatisfactory, or even unphysical, values of the diagonal Born-Oppenheimer correction (DBOC). For NO, an avoided crossing between two UHF solutions of symmetry results in a nearly 1 kJ/mol (80 cm) defect in the SCF-level DBOC just beyond the equilibrium bond distance. In that case, CCSD is able to recover essentially correct behaviour. For ground-state () NO, a second-order CPHF pole is observed in the dependence of the DBOC on the bending angle at a geometry rather far from the true conical intersection between the and states, an artifact that cannot be completely ameliorated by any method short of full CI. These effects arise from well-known problems associated with (near) instabilities of Hartree-Fock solutions, though there is little in the literature about this in the current context. The goal of this paper is to raise awareness of these potential problems, as the DBOC (adiabatic correction) is now an essential part of many modern protocols for high-accuracy calculations, and to provide some comments of the causes of these phenomena.

Diagonal Born-Oppenheimer corrections to the ground electronic state potential energy surfaces of ozone: improvement of ab initio vibrational band centers for the 16O3, 17O3 and 18O3 isotopologues.

Mass-dependent diagonal Born-Oppenheimer corrections (DBOCs) to the ab initio electronic ground state potential energy surface for the main 16O3 isotopologue and for homogeneous isotopic substitutions 17O3 and 18O3 of the ozone molecule are reported for the first time. The system being of strongly multiconfigurational character, multireference configuration interaction wave function ansatz with different complete active spaces was used. The reliable DBOC calculations with the targeted accuracy were possible to carry out up to about half of the dissociation threshold D0. The comparison with the experimental band centers shows a significant improvement of the accuracy with respect to the best Born-Oppenheimer (BO) ab initio calculations reducing the total root-mean-squares (calculated-observed) deviations by about a factor of two. For the set of 16O3 vibrations up to five bending and four stretching quanta, the mean (calculated-observed) deviations drop down from 0.7 cm-1 (BO) to about 0.1 cm-1, with the most pronounced improvement seen for bending states and for mixed bending-stretching polyads. In the case of bending band centers directly observed under high spectral resolutions, the errors are reduced by more than an order of magnitude down to 0.02 cm-1 from the observed levels, approaching nearly experimental accuracy. A similar improvement for heavy isotopologues shows that the reported DBOC corrections almost remove the systematic BO errors in vibrational levels below D0/2, though the scatter increases towards higher energies. The possible reasons for this finding, as well as remaining issues are discussed in detail. The reported results provide an encouraging accuracy validation for the multireference methods of the ab initio theory. New sets of ab initio vibrational states can be used for improving effective spectroscopic models for analyses of the observed high-resolution spectra, particularly in the cases of accidental resonances with "dark" states requiring accurate theoretical predictions.

Estimating Systematic Error and Uncertainty in Ab Initio Thermochemistry. I. Atomization Energies of Hydrocarbons in the ATOMIC(hc) Protocol.

Research in ab initio quantum chemistry has produced an increasing number of thermochemistry protocols, serving different needs from benchmark-level accuracy for small molecules to "chemical accuracy" for larger molecules. While in experimental thermochemistry it is accepted standard to report results complete with intervals of 95% confidence, so far few of the most advanced theoretical approaches have followed suit, based on either statistical comparison to well-established experimental data or careful assessment of high level theoretical results for individual molecules. Here we report on the development of intrinsic uncertainty estimates for the ATOMIC protocol in applications to hydrocarbons. ATOMIC is a theoretical procedure geared toward larger molecules and based on the ab initio implementation of bond separation reactions (BSRs) to reduce errors of midlevel composite approaches. Each of the components contributing to the bottom-of-the-well atomization energy (EA,e) is scrutinized for possible error by comparison to a large number of very high-level results, including complete-basis-set estimates of CCSDT(Q) bond separation energies for 83 hydrocarbons up to the size of naphthalene. Some of the observations are the following: Post-CCSD(T) effects are sizable even for saturated aliphatic compounds but well-represented in a BSR model summing over bond contributions, while conjugated systems pose more problems. Another significant source of error is the complete-basis-set extrapolation of all-electron CCSD(T) contributions, which still carries an uncertainty of a few tenths of a kcal/mol for midsize molecules like benzene, even if based on large basis-set calculations (cc-pCV5Z, cc-pCV6Z). Scalar relativistic terms and diagonal Born-Oppenheimer corrections are of less concern, the former because they are well represented in a BSR model and the latter because they are small in general. Observations are cast into simple expressions that separate obvious bias from nonsystematic error, formulating the former as correction to and the latter as uncertainty of an ATOMIC result. The updated protocol, complete with uncertainties and termed ATOMIC(hc) ("hc" for hydrocarbons), is validated in comparisons with both experimental data from the Active Thermochemical Tables and high-level theoretical data generated in this work. Analysis of lower-level ATOMIC models and of further components needed to convert EA,e into enthalpies of formation will be reported separately.

Diagonal Born-Oppenheimer Corrections within the Nuclear-Electronic Orbital Framework.

The nuclear-electronic orbital (NEO) method treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons. This approach invokes the Born-Oppenheimer separation between the quantum and classical nuclei, as well as the conventional separation between the electrons and classical nuclei. To test the validity of this additional adiabatic approximation, herein the diagonal Born-Oppenheimer correction (DBOC) within the NEO framework is derived, analyzed, and calculated numerically for a set of eight molecules. Inclusion of the NEO DBOC is found to change the equilibrium bond lengths by only ∼10-4 Å and the heavy atom vibrational stretching frequencies by ∼1-2 cm-1 per quantum proton bonded to an atom participating in the vibrational mode. These results imply that the DBOC does not significantly impact molecular properties computed with the NEO approach, although it can be included when necessary. Understanding the physical characteristics and quantitative contributions of the DBOC has broad implications for applications of multicomponent density functional theory and wave function methods.