Model Chemistry Recommendations for Scaled Harmonic Frequency Calculations: A Benchmark Study

Despite the widespread popularity of scaled harmonic frequency calculations to predict experimental fundamental frequencies in chemistry, sparse benchmarking is available to guide users on the appropriate level of theory and basis set choices (model chemistry) or deep understanding of expected errors. An updated assessment of the best approach for scaling to minimize errors is also overdue. Here, we assess the performance of over 600 popular, contemporary, and robust model chemistries in the calculation of scaled harmonic frequencies, evaluating different scaling factor types and their implications in the scaled harmonic frequencies and model chemistry performance. We can summarize our results into three main findings: (1) Using model-chemistry-specific scaling factors optimized for three different frequency regions (low (<1,000 cm^-1), mid (1,000-2,000 cm^-1), and high (>2,000 cm^-1)) results in substantial improvements in the agreement between the scaled harmonic and experimental frequencies compared to other choices. (2) Larger basis sets and more robust levels of theory generally lead to superior performance; however, the particular model chemistry choice matters and poor choices lead to significantly reduced accuracies. (3) Outliers are expected in routine calculations regardless of the model chemistry choice. Our benchmarking results here do not consider the intensity of vibrational transitions; however, we draw upon previous benchmarking results for dipole moments that highlight the importance of diffuse functions (i.e., augmented basis sets) in high-quality intensity predictions. In terms of specific recommendations, overall, the highest accuracy model chemistries are double-hybrid density functional approximations with a non-Pople augmented triple-ζ basis set, which can produce median frequency errors down to 7.6 cm^-1 (DSD-PBEP86/def2-TZVPD), which is very close to the error in the harmonic approximation, i.e., the anharmonicity error. Double-ζ basis sets should not be used with double-hybrid functionals as there is no improvement compared to hybrid functional results (unlike for double-hybrid triple-ζ model chemistries). Note that 6-311G* and 6-311+G* basis sets perform like a double-ζ basis set for vibrational frequencies. After scaling, all studied hybrid functionals with non-Pople triple-ζ basis sets will produce median errors of less than 15 cm^-1, with the best result of 9.9 cm^-1 with B97-1/def2-TZVPD. Appropriate matching of double-ζ basis sets with hybrid functionals can produce high-quality results, but the precise choice of functional and basis set is more important. The B97-1, TPSS0-D3(BJ), or ωB97X-D hybrid density functionals with 6-31G*, pc-1, or pcseg-1 are recommended for fast routine calculations, all delivering median errors of 11-12 cm^-1. Note that dispersion corrections are not easily available for B97-1; given its strong performance here, we recommend these be added to major programs in coming updates.

VIBFREQ1295: A New Database for Vibrational Frequency Calculations

High-throughput approaches for producing approximate vibrational spectral data for molecules of astrochemistry interest rely on harmonic frequency calculations using computational quantum chemistry. However, model chemistry recommendations (i.e., a level of theory and basis set pair) for these calculations are not yet available and, thus, thorough benchmarking against comprehensive benchmark databases is needed. Here, we present a new database for vibrational frequency calculations (VIBFREQ1295) storing 1295 experimental fundamental frequencies and CCSD(T)(F12*)/cc-pVDZ-F12 ab initio harmonic frequencies from 141 molecules. VIBFREQ1295's experimental data was complied through a comprehensive review of contemporary experimental data, while the ab initio data was computed here. The chemical space spanned by the molecules chosen is considered in-depth and is shown to have good representation of common organic functional groups and vibrational modes. Scaling factors are routinely used to approximate the effect of anharmonicity and convert computed harmonic frequencies to predicted fundamental frequencies. With our experimental and high-level ab initio data, we find that a single global uniform scaling factor of 0.9617(3) results in median differences of 15.9(5) cm^-1. A far superior performance with a median difference of 7.5(5) cm^-1 can be obtained, however, by using separate scaling factors (SFs) for three regions: frequencies less than 1000 cm^-1 (SF = 0.987(1)), between 1000 and 2000 cm^-1 (SF = 0.9727(6)), and above 2000 cm^-1 (SF = 0.9564(4)). This sets a lower bound for the performance that could be reliably obtained using scaling of harmonic frequency calculations to predict experimental fundamental frequencies. VIBFREQ1295's most important purpose is to provide a robust database for benchmarking the performance of any vibrational frequency calculations. VIBFREQ1295 data could also be used to train machine-learning models for the prediction of vibrational spectra and as a reference and data starting point for more detailed spectroscopic modeling of particular molecules. The database can be found as part of the Supporting Information for this paper or in the Harvard DataVerse at https://doi.org/10.7910/DVN/VLVNU7.

Chemical property prediction under experimental biases

Predicting the chemical properties of compounds is crucial in discovering novel materials and drugs with specific desired characteristics. Recent significant advances in machine learning technologies have enabled automatic predictive modeling from past experimental data reported in the literature. However, these datasets are often biased because of various reasons, such as experimental plans and publication decisions, and the prediction models trained using such biased datasets often suffer from over-fitting to the biased distributions and perform poorly on subsequent uses. Hence, this study focused on mitigating bias in the experimental datasets. We adopted two techniques from causal inference combined with graph neural networks that can represent molecular structures. The experimental results in four possible bias scenarios indicated that the inverse propensity scoring-based method and the counter-factual regression-based method made solid improvements.

Phosphine on Venus Cannot Be Explained by Conventional Processes

The recent candidate detection of ∼1 ppb of phosphine in the middle atmosphere of Venus is so unexpected that it requires an exhaustive search for explanations of its origin. Phosphorus-containing species have not been modeled for Venus' atmosphere before, and our work represents the first attempt to model phosphorus species in the venusian atmosphere. We thoroughly explore the potential pathways of formation of phosphine in a venusian environment, including in the planet's atmosphere, cloud and haze layers, surface, and subsurface. We investigate gas reactions, geochemical reactions, photochemistry, and other nonequilibrium processes. None of these potential phosphine production pathways is sufficient to explain the presence of ppb phosphine levels on Venus. If PH₃'s presence in Venus' atmosphere is confirmed, it therefore is highly likely to be the result of a process not previously considered plausible for venusian conditions. The process could be unknown geochemistry, photochemistry, or even aerial microbial life, given that on Earth phosphine is exclusively associated with anthropogenic and biological sources. The detection of phosphine adds to the complexity of chemical processes in the venusian environment and motivates in situ follow-up sampling missions to Venus. Our analysis provides a template for investigation of phosphine as a biosignature on other worlds.

Assessment of Isoprene as a Possible Biosignature Gas in Exoplanets with Anoxic Atmospheres

The search for possible biosignature gases in habitable exoplanet atmospheres is accelerating, although actual observations are likely years away. This work adds isoprene, C₅H₈, to the roster of biosignature gases. We found that isoprene geochemical formation is highly thermodynamically disfavored and has no known abiotic false positives. The isoprene production rate on Earth rivals that of methane (CH₄; ∼500 Tg/year). Unlike methane, on Earth isoprene is rapidly destroyed by oxygen-containing radicals. Although isoprene is predominantly produced by deciduous trees, isoprene production is ubiquitous to a diverse array of evolutionary distant organisms, from bacteria to plants and animals-few, if any, volatile secondary metabolites have a larger evolutionary reach. Although non-photochemical sinks of isoprene may exist, such as degradation of isoprene by life or other high deposition rates, destruction of isoprene in an anoxic atmosphere is mainly driven by photochemistry. Motivated by the concept that isoprene might accumulate in anoxic environments, we model the photochemistry and spectroscopic detection of isoprene in habitable temperature, rocky exoplanet anoxic atmospheres with a variety of atmosphere compositions under different host star ultraviolet fluxes. Limited by an assumed 10 ppm instrument noise floor, habitable atmosphere characterization when using James Webb Space Telescope (JWST) is only achievable with a transit signal similar or larger than that for a super-Earth-sized exoplanet transiting an M dwarf star with an H₂-dominated atmosphere. Unfortunately, isoprene cannot accumulate to detectable abundance without entering a run-away phase, which occurs at a very high production rate, ∼100 times the Earth's production rate. In this run-away scenario, isoprene will accumulate to >100 ppm, and its spectral features are detectable with ∼20 JWST transits. One caveat is that some isoprene spectral features are hard to distinguish from those of methane and also from other hydrocarbons containing the isoprene substructure. Despite these challenges, isoprene is worth adding to the menu of potential biosignature gases.

Evaluating Alternatives to Water as Solvents for Life: The Example of Sulfuric Acid

The chemistry of life requires a solvent, which for life on Earth is water. Several alternative solvents have been suggested, but there is little quantitative analysis of their suitability as solvents for life. To support a novel (non-terrestrial) biochemistry, a solvent must be able to form a stable solution of a diverse set of small molecules and polymers, but must not dissolve all molecules. Here, we analyze the potential of concentrated sulfuric acid (CSA) as a solvent for biochemistry. As CSA is a highly effective solvent but a reactive substance, we focused our analysis on the stability of chemicals in sulfuric acid, using a model built from a database of kinetics of reaction of molecules with CSA. We consider the sulfuric acid clouds of Venus as a test case for this approach. The large majority of terrestrial biochemicals have half-lives of less than a second at any altitude in Venus's clouds, but three sets of human-synthesized chemicals are more stable, with average half-lives of days to weeks at the conditions around 60 km altitude on Venus. We show that sufficient chemical structural and functional diversity may be available among those stable chemicals for life that uses concentrated sulfuric acid as a solvent to be plausible. However, analysis of meteoritic chemicals and possible abiotic synthetic paths suggests that postulated paths to the origin of life on Earth are unlikely to operate in CSA. We conclude that, contrary to expectation, sulfuric acid is an interesting candidate solvent for life, but further work is needed to identify a plausible route for life to originate in it.

Phosphine as a Biosignature Gas in Exoplanet Atmospheres

A long-term goal of exoplanet studies is the identification and detection of biosignature gases. Beyond the most discussed biosignature gas O₂, only a handful of gases have been considered in detail. In this study, we evaluate phosphine (PH₃). On Earth, PH₃ is associated with anaerobic ecosystems, and as such, it is a potential biosignature gas in anoxic exoplanets. We simulate the atmospheres of habitable terrestrial planets with CO₂- and H₂-dominated atmospheres and find that PH₃ can accumulate to detectable concentrations on planets with surface production fluxes of 10¹⁰ to 10¹⁴ cm^-2 s^-1 (corresponding to surface concentrations of 10s of ppb to 100s of ppm), depending on atmospheric composition and ultraviolet (UV) irradiation. While high, the surface flux values are comparable to the global terrestrial production rate of methane or CH₄ (10¹¹ cm^-2 s^-1) and below the maximum local terrestrial PH₃ production rate (10¹⁴ cm^-2 s^-1). As with other gases, PH₃ can more readily accumulate on low-UV planets, for example, planets orbiting quiet M dwarfs or with a photochemically generated UV shield. PH₃ has three strong spectral features such that in any atmosphere scenario one of the three will be unique compared with other dominant spectroscopic molecules. Phosphine's weakness as a biosignature gas is its high reactivity, requiring high outgassing rates for detectability. We calculate that tens of hours of JWST (James Webb Space Telescope) time are required for a potential detection of PH₃. Yet, because PH₃ is spectrally active in the same wavelength regions as other atmospherically important molecules (such as H₂O and CH₄), searches for PH₃ can be carried out at no additional observational cost to searches for other molecular species relevant to characterizing exoplanet habitability. Phosphine is a promising biosignature gas, as it has no known abiotic false positives on terrestrial planets from any source that could generate the high fluxes required for detection.