Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Predicting crystal form stability under real-world conditions

The physicochemical properties of molecular crystals, such as solubility, stability, compactability, melting behaviour and bioavailability, depend on their crystal form1. In silico crystal form selection has recently come much closer to realization because of the development of accurate and affordable free-energy calculations2-4. Here we redefine the state of the art, primarily by improving the accuracy of free-energy calculations, constructing a reliable experimental benchmark for solid-solid free-energy differences, quantifying statistical errors for the computed free energies and placing both hydrate crystal structures of different stoichiometries and anhydrate crystal structures on the same energy landscape, with defined error bars, as a function of temperature and relative humidity. The calculated free energies have standard errors of 1-2 kJ mol-1 for industrially relevant compounds, and the method to place crystal structures with different hydrate stoichiometries on the same energy landscape can be extended to other multi-component systems, including solvates. These contributions reduce the gap between the needs of the experimentalist and the capabilities of modern computational tools, transforming crystal structure prediction into a more reliable and actionable procedure that can be used in combination with experimental evidence to direct crystal form selection and establish control5.

Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach

Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.

A quantum computing implementation of nuclearelectronic orbital (NEO) theory: Toward an exact pre-Born-Oppenheimer formulation of molecular quantum systems

Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron-nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron-nuclear problem on near-term quantum computers, based upon the Nuclear-Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10-6 hartree and entanglement entropy to within 10-4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy.

The Global Characterisation of a Drug-Dendrimer Conjugate - PEGylated poly-lysine Dendrimer

The recent emergence of drug-dendrimer conjugates within pharmaceutical industry research and development introduces a range of challenges for analytical and measurement science. These molecules are very high molecular weight (100-200kDa) with a significant degree of structural complexity. The characteristics and quality attributes that require understanding and definition, and impact efficacy and safety, are diverse. They relate to the intact conjugate, the various building blocks of these complex systems and the level of the free and bound active pharmaceutical ingredient (API). From an analytical and measurement science perspective, this necessitates the measurement of the molecular weight, impurity characterisation, the quantitation of the number of conjugated versus free API molecules, the determination of the impurity profiles of the building blocks, primary structure and both particle size and morphology. Here we report the first example of a global characterisation of a drug-dendrimer conjugate - PEGylated poly-lysine dendrimer currently under development (AZD0466). The impact of the wide variety of analytical and measurement techniques on the overall understanding of this complex molecular entity is discussed, with the relative capabilities of the various approaches compared. The results of this study are an essential platform for the research and development of the future generations of related dendrimer-based medicines.

Does Z' equal 1 or 2? Enhanced powder NMR crystallography verification of a disordered room temperature crystal structure of a p38 inhibitor for chronic obstructive pulmonary disease

The crystal structure of the Form A polymorph of N-cyclopropyl-3-fluoro-4-methyl-5-[3-[[1-[2-[2-(methylamino)ethoxy]phenyl]cyclopropyl]amino]-2-oxo-pyrazin-1-yl]benzamide (i.e., AZD7624), determined using single-crystal X-ray diffraction (scXRD) at 100 K, contains two molecules in the asymmetric unit (Z' = 2) and has regions of local static disorder. This substance has been in phase IIa drug development trials for the treatment of chronic obstructive pulmonary disease, a disease which affects over 300 million people and contributes to nearly 3 million deaths annually. While attempting to verify the crystal structure using nuclear magnetic resonance crystallography (NMRX), we measured ¹³C solid-state NMR (SSNMR) spectra at 295 K that appeared consistent with Z' = 1 rather than Z' = 2. To understand this surprising observation, we used multinuclear SSNMR (¹H, ¹³C, ¹⁵N), gauge-including projector augmented-wave density functional theory (GIPAW DFT) calculations, crystal structure prediction (CSP), and powder XRD (pXRD) to determine the room temperature crystal structure. Due to the large size of AZD7624 (ca. 500 amu, 54 distinct ¹³C environments for Z' = 2), static disorder at 100 K, and (as we show) dynamic disorder at ambient temperatures, NMR spectral assignment was a challenge. We introduce a method to enhance confidence in NMR assignments by comparing experimental ¹³C isotropic chemical shifts against site-specific DFT-calculated shift distributions established using CSP-generated crystal structures. The assignment and room temperature NMRX structure determination process also included measurements of ¹³C shift tensors and the observation of residual dipolar coupling between ¹³C and ¹⁴N. CSP generated ca. 90 reasonable candidate structures (Z' = 1 and Z' = 2), which when coupled with GIPAW DFT results, room temperature pXRD, and the assigned SSNMR data, establish Z' = 2 at room temperature. We find that the polymorphic Form A of AZD7624 is maintained at room temperature, although dynamic disorder is present on the NMR timescale. Of the CSP-generated structures, 2 are found to be fully consistent with the SSNMR and pXRD data; within this pair, they are found to be structurally very similar (RMSD₁₆ = 0.30 Å). We establish that the CSP structure in best agreement with the NMR data possesses the highest degree of structural similarity with the scXRD-determined structure (RMSD₁₆ = 0.17 Å), and has the lowest DFT-calculated energy amongst all CSP-generated structures with Z' = 2.

Solubility prediction from first principles: a density of states approach

Solubility is a fundamental property of widespread significance. Its accurate prediction remains a major challenge. We present a novel, efficient approach to solubility prediction for molecules over a range of conditions based on density of states.

Transferable force field for crystal structure predictions, investigation of performance and exploration of different rescoring strategies using DFT-D methods

A new force field, here called AZ-FF, aimed at being used for crystal structure predictions, has been developed. The force field is transferable to a new type of chemistry without additional training or modifications. This makes the force field very useful in the prediction of crystal structures of new drug molecules since the time-consuming step of developing a new force field for each new molecule is circumvented. The accuracy of the force field was tested on a set of 40 drug-like molecules and found to be very good where observed crystal structures are found at the top of the ranked list of tentative crystal structures. Re-ranking with dispersion-corrected density functional theory (DFT-D) methods further improves the scoring. After DFT-D geometry optimization the observed crystal structure is found at the leading top of the ranking list. DFT-D methods and force field methods have been evaluated for use in predicting properties such as phase transitions upon heating, mechanical properties or intrinsic crystalline solubility. The utility of using crystal structure predictions and the associated material properties in risk assessment in connection with form selection in the drug development process is discussed.

Experimental and Quantum Chemical Evaluations of Pyridine Oxidation Under Drug Development Stress Test Conditions

The oxidation reaction of pyridine by hydrogen peroxides in water media was investigated by combining quantum chemical calculations and laboratory experiments. Pyridine was selected as a model system for aromatic amines that frequently occurs in drug molecules. Several different reaction conditions, commonly used in stress testing of drug molecules during drug development, were investigated to increase mechanistic insight to this class of oxidation reactions. Of special interest is to note that small amounts of acetonitrile, a regularly used cosolvent to keep poorly soluble drug molecules in water solution, could catalyze the oxidation reaction in the presence of hydrogen peroxide. Consequently, attention needs to be taken when comparing data from different stress test studies of amine oxidation by hydrogen peroxides at different pH, and with and without acetonitrile. In particular, they need to be controlled when identifying the proper intrinsic stability of the drug molecule.

A qualitative method for prediction of amine oxidation in methanol and water

We have developed a predictive method, based on quantum chemical calculations, that qualitatively predicts N-oxidation by hydrogen peroxides in drug structures. The method uses linear correlations of two complementary approaches to estimate the activation barrier without calculating it explicitly. This method can therefore be automated as it avoids demanding transition state calculations. As such, it may be used by chemists without experience in molecular modeling and provide additional understanding to experimental findings. The predictive method gives relative rates for N,N-dimethylbenzylamine and N-methylmorpholine in good agreement with experiments. In water, the experimental rate constants show that N,N-dimethylbenzylamine is oxidized three times faster than N-methylmorpholine and in methanol it is two times faster. The method suggests it to be two and five times faster, respectively. The method was also used to correlate experimental with predicted activation barriers, linear free-energy relationships, for a test set of tertiary amines. A correlation coefficient R(2) = 0.74 was obtained, where internal diagnostics in the method itself allowed identification of outliers. The method was applied to four drugs: caffeine, azelastine, buspirone, and clomipramine, all possessing several nitrogens. Both overall susceptibility and selectivity of oxidation were predicted, and verified by experiments.

Prediction of drug candidates' sensitivity toward autoxidation: computational estimation of C-H dissociation energies of carbon-centered radicals

A method to predict a compound's sensitivity toward autoxidation using bond dissociation energies for hydrogen abstraction is described. The methodology is based on quantum mechanics and has been validated with a small molecule test set. Through this work, it has been observed that stabilization of an incipient radical by more than a single functional group is normally required to trigger autoxidation. The method has also been used to understand salt effects, wherein protonation of a basic amine stabilizes proximal C-H bonds to autoxidation. It can be used to support understanding of autoxidation processes and can form a predictive role for propensity to form potentially genotoxic and other degradation products. An automated protocol has been developed that allows the nonspecialist to perform quantum chemical calculations. The protocol is robust to enable general usage such that drug-like molecules can be handled by the tool and give an answer in hours (up to some days) depending on the size of the molecule. The efficiency of the tool makes it possible to perform risk assessment for autoxidation of small lists of molecules and could typically be used for shortlisted candidates before drug nomination, during drug formulation development, and during due diligence for in-licensing compounds.

State-of-the-art tools for computational site of metabolism predictions: comparative analysis, mechanistical insights, and future applications

In drug design, it is crucial to have reliable information on how a chemical entity behaves in the presence of metabolizing enzymes. This requires substantial experimental efforts. Consequently, being able to predict the likely site/s of metabolism in any compound, synthesized or virtual, would be highly beneficial and time efficient. In this work, six different methodologies for predictions of the site of metabolism (SOM) have been compared and validated using structurally diverse data sets of drug-like molecules with well-established metabolic pattern in CYP3A4, CYP2C9, or both. Three of the methods predict the SOM based on the ligand's chemical structure, two additional methods use structural information of the enzymes, and the sixth method combines structure and ligand similarity and reactivity. The SOM is correctly predicted in 50 to 90% of the cases, depending on method and enzyme, which is an encouraging rate. We also discuss the underlying mechanisms of cytochrome P450 metabolism in the light of the results from this comparison.

Regioselective protonation of ferrocene in superacid and formation of a C—H—Fe bond. An experimental and theoretical study of the structure and dynamics of the ferrocenonium ion

Protonation of ferrocene has been suggested to take place on carbon (exo-protonation) or iron (endo-protonation). However, experiments have not been conclusive because of interfering exchange reactions. Now low-temperature protonation of ferrocene and [2H10]-ferrocene in superacid and direct observation of the carbocation by 1H NMR at low temperature shows only primary protonation and that it exclusively takes place in an endo-fashion. Studies by DFT calculations using B3LYP hybrid functional indicate the presence of an intramolecular nonlinear C—H—Fe bond and that the proton might be delocalized between carbon and iron. Potential energy barriers for degenerate rearrangements of the hydride bridged carbocation are low, suggesting that the proton might be delocalized between all 10 carbons and iron. The NMR results are consistent with such an interpretation.Key words: regioselective, protonation, superacid, ferrocenonium ion.