Conformers of gaseous threonine

Exploring torsional conformer space with physical prior mean function-driven meta-Gaussian processes

We present a novel approach for systematically exploring the conformational space of small molecules with multiple internal torsions. Identifying unique conformers through a systematic conformational search is important for obtaining accurate thermodynamic functions (e.g., free energy), encompassing contributions from the ensemble of all local minima. Traditional geometry optimizers focus on one structure at a time, lacking transferability from the local potential-energy surface (PES) around a specific minimum to optimize other conformers. In this work, we introduce a physics-driven meta-Gaussian processes (meta-GPs) method that not only enables efficient exploration of target PES for locating local minima but, critically, incorporates physical surrogates that can be applied universally across the optimization of all conformers of the same molecule. Meta-GPs construct surrogate PESs based on the optimization history of prior conformers, dynamically selecting the most suitable prior mean function (representing prior knowledge in Bayesian learning) as a function of the optimization progress. We systematically benchmarked the performance of multiple GP variants for brute-force conformational search of amino acids. Our findings highlight the superior performance of meta-GPs in terms of efficiency, comprehensiveness of conformer discovery, and the distribution of conformers compared to conventional non-surrogate optimizers and other non-meta-GPs. Furthermore, we demonstrate that by concurrently optimizing, training GPs on the fly, and learning PESs, meta-GPs exhibit the capacity to generate high-quality PESs in the torsional space without extensive training data. This represents a promising avenue for physics-based transfer learning via meta-GPs with adaptive priors in exploring torsional conformer space.

Accurate Computation of Aqueous pKas of Biologically Relevant Organic Acids: Overcoming the Challenges Posed by Multiple Conformers, Tautomeric Equilibria, and Disparate Functional Groups with the Fully Black-Box pK-Yay Method

The use of static electronic structure calculations to compute solution-phase pKas offers a great advantage in that a macroscopic bulk property could be computed via microscopic computations involving very few molecules. There are various sources of errors in the quantum chemical calculations though. Overcoming these errors to accurately compute pKas of a plethora of acids is an active area of research in physical chemistry pursued by both computational as well as experimental chemists. We recently developed the pK-Yay method in our attempt to accurately compute aqueous pKas of strong and weak acids. The method is fully black-box, computationally inexpensive, and is very easy for even a nonexpert to use. However, the method was thus far tested on very few molecules (only 16 in all). Herein, in order to assess the future applicability of pK-Yay, we study the effect of multiple conformers, the presence of tautomers under equilibrium, and the impact of a wide variety of functional groups (derivatives of acetic acid with substituents at various positions, dicarboxylic acids, aromatic carboxylic acids, amines and amides, phenols and thiols, and fluorine bearing organic acids). Starting with more than 1000 conformers and tautomers, this study establishes that overall errors of ∼ 1.0 pKa units are routinely obtained for a majority of the molecules. Larger errors are noted in cases where multiple charges, intramolecular hydrogen bonding, and several ionizable functional groups are simultaneously present. An important conclusion to emerge from this work is that, the computed pKas are insensitive (difference <0.5) to whether we consider multiple conformers/tautomers or only choose the most stable conformer/tautomer. Further, pK-Yay captures the stereoelectronic effects arising due to differing axial vs equatorial pattern, and is useful to predict the dominant acid-base equilibrium in a system featuring several equilibria. Overall, pK-Yay may be employed in several chemical applications featuring organic molecules and biomonomers.

Protonation of serine: conformers, proton affinities and gas-phase basicities at the "gold standard" and beyond

The potential energy surfaces (PESs) of serine and its protonated counterparts are investigated to determine the structures of the minima. A total of 95 neutral serine, 15 N-(amino-) and 46 O-(carbonyl-)protonated serine conformers are found. Their relative energies, geometries and harmonic vibrational frequencies are determined at the MP2/aug-cc-pVDZ level of theory. To obtain highly accurate thermodynamic values, further computations are performed: the ten conformers with the lowest relative energies from each molecule type (neutral, N- and O-protonated) are further optimized using the explicitly correlated CCSD(T)-F12a/cc-pVDZ-F12 method (for neutral serine, harmonic vibrational frequencies were also computed). In addition, auxiliary corrections were determined: basis-set effects up to CCSD(T)-F12b/cc-pVQZ-F12, electron correlation effects up to CCSDT(Q), core correlation and second-order Douglas-Kroll relativistic effects along with zero-point energy contributions. Two important thermodynamic parameters (at 298.15 K), proton affinity (PA)/gas-phase basicity (GB) are calculated considering the two different protonation sites: 218.05 ± 0.2/209.86 ± 0.6 kcal mol^-1 and 205.87 ± 0.2/196.36 ± 0.3 kcal mol^-1 for the amino and carbonyl sites, respectively. The uncertainty of the determined values was approximated based on various sources including auxiliary corrections, basis-set effects, harmonic vibrational frequencies.

Benchmark Structures and Conformational Landscapes of Amino Acids in the Gas Phase: A Joint Venture of Machine Learning, Quantum Chemistry, and Rotational Spectroscopy

The accurate characterization of prototypical bricks of life can strongly benefit from the integration of high resolution spectroscopy and quantum mechanical computations. We have selected a number of representative amino acids (glycine, alanine, serine, cysteine, threonine, aspartic acid and asparagine) to validate a new computational setup rooted in quantum-chemical computations of increasing accuracy guided by machine learning tools. Together with low-lying energy minima, the barriers ruling their interconversion are evaluated in order to unravel possible fast relaxation paths. Vibrational and thermal effects are also included in order to estimate relative free energies at the temperature of interest in the experiment. The spectroscopic parameters of all the most stable conformers predicted by this computational strategy, which do not have low-energy relaxation paths available, closely match those of the species detected in microwave experiments. Together with their intrinsic interest, these accurate results represent ideal benchmarks for more approximate methods.

Benchmark Ab Initio Determination of the Conformers, Proton Affinities, and Gas-Phase Basicities of Cysteine

A systematic conformational mapping combined with literature data leads to 85 stable neutral cysteine conformers. The implementation of the same mapping process for the protonated counterparts reveals 21 N-(amino-), 64 O-(carbonyl-), and 37 S-(thiol-)protonated cysteine conformers. Their relative energies and harmonic vibrational frequencies are given at the MP2/aug-cc-pVDZ level of theory. Further benchmark ab initio computations are performed for the 10 lowest-lying neutral and protonated amino acid conformers (for each type) such as CCSD(T)-F12a/cc-pVDZ-F12 geometry optimizations (and frequency computations for cysteine) as well as auxiliary correction computations of the basis set effects up to CCSD(T)-F12b/cc-pVQZ-F12, electron correlation effects up to CCSDT(Q), core correlation effects, second-order Douglass-Kroll relativistic effects, and zero-point energy contributions. Boltzmann-averaged 0 (298.15) K proton affinity and [298.15 K gas-phase basicity] values of cysteine are predicted to be 214.96 (216.39) [208.21], 201.83 (203.55) [194.16], and 193.31 (194.74) [186.40] kcal/mol for N-, O-, and S-protonation, respectively, also considering the previously described auxiliary corrections.

Benchmark ab initio proton affinity and gas-phase basicity of α-alanine based on coupled-cluster theory and statistical mechanics

We determine the proton affinity (PA) and gas-phase basicity (GB) of amino acid α-alanine at a chemically accurate level by performing explicitly-correlated CCSD(T)-F12b/aug-cc-pVDZ geometry optimizations and normal mode vibrational frequency calculations as well as CCSD(T)-F12b/aug-cc-pVTZ energy computations at the possible neutral and protonated geometries. Temperature effects at 298.15 K considering translational, rotational, and vibrational enthalpy and entropy corrections are obtained via standard statistical mechanics utilizing the molecular geometries and the harmonic vibrational energy levels. Both the amino nitrogen (N) and the carbonyl oxygen (O) atoms are proven to be potential protonation sites and a systematic conformational search reveals 3 N- and 9 O-protonated conformers in the 0.00-7.88 and 25.43-30.43 kcal/mol energy ranges at 0 K, respectively. The final computed PA and GB values at (0)298.15 K in case of N-protonation are (214.47)216.80 and 207.07 kcal/mol, respectively, whereas the corresponding values for O-protonation are (189.04)190.63 and 182.31 kcal/mol. The results of the benchmark high-level coupled-cluster computations are utilized to assess the accuracy of several lower-level cost-effective methods such as MP2 and density functional theory with various functionals (SOGGA11-X, M06-2X, PBE0, B3LYP, M06, TPSS).

TorsiFlex: an automatic generator of torsional conformers. Application to the twenty proteinogenic amino acids

In this work, we introduce TorsiFlex, a user-friendly software written in Python 3 and designed to find all the torsional conformers of flexible acyclic molecules in an automatic fashion. For the mapping of the torsional potential energy surface, the algorithm implemented in TorsiFlex combines two searching strategies: preconditioned and stochastic. The former is a type of systematic search based on chemical knowledge and should be carried out before the stochastic (random) search. The algorithm applies several validation tests to accelerate the exploration of the torsional space. For instance, the optimized structures are stored and this information is used to prevent revisiting these points and their surroundings in future iterations. TorsiFlex operates with a dual-level strategy by which the initial search is carried out at an inexpensive electronic structure level of theory and the located conformers are reoptimized at a higher level. Additionally, the program takes advantage of conformational enantiomerism, when possible. As a case study, and in order to exemplify the effectiveness and capabilities of this program, we have employed TorsiFlex to locate the conformers of the twenty proteinogenic amino acids in their neutral canonical form. TorsiFlex has produced a number of conformers that roughly doubles the amount of the most complete work to date.

Integration of theory, simulation, artificial intelligence and virtual reality: a four-pillar approach for reconciling accuracy and interpretability in computational spectroscopy

The established pillars of computational spectroscopy are theory and computer based simulations. Recently, artificial intelligence and virtual reality are becoming the third and fourth pillars of an integrated strategy for the investigation of complex phenomena. The main goal of the present contribution is the description of some new perspectives for computational spectroscopy, in the framework of a strategy in which computational methodologies at the state of the art, high-performance computing, artificial intelligence and virtual reality tools are integrated with the aim of improving research throughput and achieving goals otherwise not possible. Some of the key tools (e.g., continuous molecular perception model and virtual multifrequency spectrometer) and theoretical developments (e.g., non-periodic boundaries, joint variational-perturbative models) are shortly sketched and their application illustrated by means of representative case studies taken from recent work by the authors. Some of the results presented are already well beyond the state of the art in the field of computational spectroscopy, thereby also providing a proof of concept for other research fields.

Benchmark ab initio proton affinity of glycine

A systematic conformational search reveals three N- (amino) and eight O- (carbonyl) protonated glycine conformers with benchmark equilibrium(adiabatic) relative energies in the 0.00-7.51(0.00-7.37) and 25.91-31.61(24.45-30.28) kcal mol-1 ranges, respectively. Benchmark ab initio structures of the glycine conformers and its protonated species are obtained at the CCSD(T)-F12b/aug-cc-pVTZ level of theory and the relative energy computations consider basis-set effects up to aug-cc-pVQZ with CCSD(T)-F12b, electron correlation up to CCSDT(Q), core correlation corrections, scalar relativistic effects, and zero-point energy contributions. The best predictions for Boltzmann-averaged 0(298.15) K proton affinities and [298.15 K gas-phase basicities] of glycine are 211.00(212.43)[204.75] and 186.38(187.64)[180.21] kcal mol-1 for N- and O-protonation, respectively, in excellent agreement with experiments.

Two-level stochastic search of low-energy conformers for molecular spectroscopy: implementation and validation of MM and QM models

The search for stationary points in the molecular potential energy surfaces (PES) is a problem of increasing relevance in molecular sciences especially for large, flexible systems featuring several large-amplitude internal motions.

Definitive thermochemistry and kinetics of the interconversions among conformers of n-butane and n-pentane

The focal-point analysis (FPA) technique is used for the definitive characterization of conformational interconversion parameters, including activation energy barriers, activation free energies, and kinetic rate coefficients at 298 K, of two n-alkanes, n-butane, and n-pentane, yielding the first complete analysis of their interconversion kinetics. The FPA implementation developed in this study is based on geometry optimizations and harmonic frequency computations carried out with density functional theory methods and single-point energy computations up to the CCSD(T) level of electronic structure theory using atom-centered Gaussian basis sets as large as cc-pV5Z. The anharmonic vibrational computations are carried out, at the MP2/6-31G* level of theory. Reflecting the convergence behavior of the Gibbs free-energy terms and the interconversion parameters, well-defined uncertainties, mostly neglected in previous theoretical studies, are provided. Finally, the effect of these uncertainties on the concentrations of the conformers of n-butane and n-pentane is examined via a global Monte-Carlo uncertainty analysis. © 2017 Wiley Periodicals, Inc.

Gas-phase enthalpies of formation and enthalpies of sublimation of amino acids based on isodesmic reaction calculations

Accurate gas-phase enthalpies of formation (ΔfH298°) of 20 common α-amino acids, seven uncommon amino acids, and three small peptides were calculated by combining G4 theory calculations with an isodesmic reaction approach. The internal consistency over a set of ΔfH298°(g) values was achieved by sequential adjustment of their values through the isodesmic reactions. Four amino acids, alanine, β-alanine, sarcosine, and glycine, with reliable internally self-consistent experimental data, were chosen as the key reference compounds. These amino acids together with about 100 compounds with reliable experimental data (their accuracy was supported by G4 calculations) were used to estimate the enthalpies of formation of remaining amino acids. All of the amino acids with the previously established enthalpies of formation were later used as the reference species in the isodesmic reactions for the other amino acids. A systematic comparison was made of 14 experimentally determined enthalpies of formation with the results of calculations. The experimental enthalpies of formation for 10 amino acids were reproduced with good accuracy, but the experimental and calculated values for 4 compounds differed by 11–21 kJ/mol. For these species, the theoretical ΔfH298°(g) values were suggested as more reliable than the experimental values. On the basis of theoretical results, the recommended values for the gas-phase enthalpies of formation were also provided for amino acids for which the experimental ΔfH298°(g) were not available. The enthalpies of sublimation were evaluated for all compounds by taking into account the literature data on the solid-phase enthalpies of formation and the ΔfH298°(g) values recommended in our work. A special attention was paid to the accurate prediction of enthalpies of formation of amino acids from the atomization reactions. The problems associated with conformational flexibility of these compounds and harmonic treatment of low frequency torsional modes were discussed. The surprisingly good agreement between the ΔfH298°(g) values calculated from the atomization and isodesmic reactions is largely the result of a fortuitous mutual compensation of various corrections used in the atomization reaction procedure.

DFT studies on the intrinsic conformational properties of non-ionic pyrrolysine in gas phase

B3LYP/6-31G(d,p) level of theory is used to carry out a detailed gas phase conformational analysis of non-ionized (neutral) pyrrolysine molecule about its nine internal back-bone torsional angles. A total of 13 minima are detected from potential energy surface exploration corresponding to the nine internal back-bone torsional angles. These minima are then subjected to full geometry optimization and vibrational frequency calculations at B3LYP/6-31++G(d,p) level. Characteristic intramolecular hydrogen bonds present in each conformer, their relative energies, theoretically predicted vibrational spectra, rotational constants and dipole moments are systematically reported. Single point calculations are carried out at B3LYP/6-311++G(d,p) and MP2/6-31++G(d,p) levels. Six types of intramolecular H-bonds, viz. O...H-O, N...H-O, O...H-N, N...H-N, O...H-C and N...H-C, are found to exist in the pyrrolysine conformers; all of which contribute to the stability of the conformers. The vibrational frequencies are found to shift invariably toward the lower side of frequency scale corresponding to the presence of intramolecular H-bond interactions in the conformers.

Gas phase basicities of polyfunctional molecules. Part 3: Amino acids

The present article is the third part of a general overview of the gas-phase protonation thermochemistry of polyfunctional molecules (first part: Mass Spectrom. Rev., 2007, 26:775-835, second part: Mass Spectrom. Rev., 2011, in press). This review is devoted to the 20 proteinogenic amino acids and is divided in two parts. In the first one, the experimental data obtained during the last 30 years using the equilibrium, thermokinetic and kinetic methods are presented. A general re-assignment of the values originating from these various experiments has been done on the basis of the commonly accepted Hunter & Lias 1998 gas-phase basicity scale in order to provide an homogeneous set of data. In the second part, theoretical investigations on gaseous neutral and protonated amino acids are reviewed. Conformational landscapes of both types of species were examined in order to provide theoretical protonation thermochemistry based on the truly identified most stable conformers. Proton affinities computed at the presently highest levels of theory (i.e. composite methods such as Gn procedures) are presented. Estimates of thermochemical parameters calculated using a Boltzmann distribution of conformers at 298K are also included. Finally, comparison between experiment and theory is discussed and a set of evaluated proton affinities, gas-phase basicities and protonation entropies is proposed.

Benchmarking Experimental and Computational Thermochemical Data: A Case Study of the Butane Conformers

Due to its crucial importance, numerous studies have been conducted to determine the enthalpy difference between the conformers of butane. However, it is shown here that the most reliable experimental values are biased due to the statistical model utilized during the evaluation of the raw experimental data. In this study, using the appropriate statistical model, both the experimental expectation values and the associated uncertainties are revised. For the 133-196 and 223-297 K temperature ranges, 668 ± 20 and 653 ± 125 cal mol(-1), respectively, are recommended as reference values. Furthermore, to show that present-day quantum chemistry is a favorable alternative to experimental techniques in the determination of enthalpy differences of conformers, a focal-point analysis, based on coupled-cluster electronic structure computations, has been performed that included contributions of up to perturbative quadruple excitations as well as small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. For the 133-196 and 223-297 K temperature ranges, in exceptional agreement with the corresponding revised experimental data, our computations yielded 668 ± 3 and 650 ± 6 cal mol(-1), respectively. The most reliable enthalpy difference values for 0 and 298.15 K are also provided by the computational approach, 680.9 ± 2.5 and 647.4 ± 7.0 cal mol(-1), respectively.