Psi4: an open-source ab initio electronic structure program

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHiPSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated 18 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory

Since the original fitting of Grimme's DFT-D3 damping parameters, the number and quality of benchmark interaction energies has increased significantly. Here, conventional benchmark sets, which focus on minimum-orientation radial curves at the expense of angular diversity, are augmented by new databases such as side chain-side chain interactions (SSI), which are composed of interactions gleaned from crystal data and contain no such minima-focused bias. Moreover, some existing databases such as S22×5 are extended to shorter intermolecular separations. This improved DFT-D3 training set provides a balanced description of distances, covers the entire range of interaction types, and at 1526 data points is far larger than the original training set of 130. The results are validated against a new collection of 6773 data points and demonstrate that the effect of refitting the damping parameters ranges from no change in accuracy (LC-ωPBE-D3) to an almost 2-fold decrease in average error (PBE-D3).

Nearest-neighbor parameters for 7-deaza-adenosine·uridine base pairs in RNA duplexes

One of the major limitations in RNA structure prediction is the lack of information about the effect of nonstandard nucleotides on stability. The nonstandard nucleotide 7-deaza-adenosine (7DA) is a naturally occurring analog of adenosine that has been studied for medicinal purposes and is commonly referred to as tubercidin. In 7DA, the nitrogen in the 7 position of adenosine is replaced by a carbon. Differences in RNA duplex stability due to the removal of this nitrogen can be attributed to a possible change in hydration and a difference in base stacking interactions resulting from changes in the electrostatics of the ring. In order to determine how 7DA affects the stability of RNA, optical melting experiments were conducted on RNA duplexes that contain either internal or terminal 7DA·U pairs with all possible nearest-neighbor combinations. On average, duplexes containing 7DA·U pairs are 0.43 and 0.07 kcal/mol less stable than what is predicted for the same duplex containing internal and terminal A-U pairs, respectively. Thermodynamic parameters for all nearest-neighbor combinations of 7DA·U pairs were derived from the data. These parameters can be used to more accurately predict the secondary structure and stability of RNA duplexes containing 7DA·U pairs.

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER-HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single-point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo-bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.

Big Changes for Small Noncovalent Dimers: Revisiting the Potential Energy Surfaces of (P2)2 and (PCCP)2 with CCSD(T) Optimizations and Vibrational Frequencies

This article details the re-examination of low-lying stationary points on the potential energy surfaces (PESs) of two challenging noncovalent homogeneous dimers, (P2)2 and (PCCP)2. The work was motivated by the rather large differences between MP2 and CCSD(T) energetics that were recently reported for these systems (J. Comput. Chem. 2014, 35, 479-487). The current investigation reveals significant qualitative and quantitative changes when the CCSD(T) method is used to characterize the stationary points instead of MP2. For example, CCSD(T) optimizations and harmonic vibrational frequency computations with the aug-cc-pVTZ basis set indicate that the parallel-slipped (PS) structure is the only P2 dimer stationary point examined that is a minimum (zero imaginary frequencies, ni = 0), whereas prior MP2 computations indicated that it was a transition state (ni = 1). Furthermore, the L-shaped structure of (P2)2 was the only minimum according to MP2 computations, but it collapses to the PS structure on the CCSD(T)/aug-cc-pVTZ PES. For the larger PCCP dimer, the CCSD(T) computations reveal that four rather than just two of the six stationary points characterized are minima. A series of explicitly correlated single-point energies were computed for all of the optimized structures to estimate the MP2 and CCSD(T) electronic energies at the complete basis set limit. CCSDT(Q) computations were also performed to assess the effects of dynamical electron correlation beyond the CCSD(T) level. For both (P2)2 and (PCCP)2, dispersion remains the dominant attractive component to the interaction energy according to symmetry-adapted perturbation theory analyses, and it is also the most challenging component to accurately evaluate.

Modeling molecule-plasmon interactions using quantized radiation fields within time-dependent electronic structure theory

We present a combined cavity quantum electrodynamics/ab initio electronic structure approach for simulating plasmon-molecule interactions in the time domain. The simple Jaynes-Cummings-type model Hamiltonian typically utilized in such simulations is replaced with one in which the molecular component of the coupled system is treated in a fully ab initio way, resulting in a computationally efficient description of general plasmon-molecule interactions. Mutual polarization effects are easily incorporated within a standard ground-state Hartree-Fock computation, and time-dependent simulations carry the same formal computational scaling as real-time time-dependent Hartree-Fock theory. As a proof of principle, we apply this generalized method to the emergence of a Fano-like resonance in coupled molecule-plasmon systems; this feature is quite sensitive to the nanoparticle-molecule separation and the orientation of the molecule relative to the polarization of the external electric field.

Can density cumulant functional theory describe static correlation effects?

We evaluate the performance of density cumulant functional theory (DCT) for capturing static correlation effects. In particular, we examine systems with significant multideterminant character of the electronic wave function, such as the beryllium dimer, diatomic carbon, m-benzyne, 2,6-pyridyne, twisted ethylene, as well as the barrier for double-bond migration in cyclobutadiene. We compute molecular properties of these systems using the ODC-12 and DC-12 variants of DCT and compare these results to multireference configuration interaction and multireference coupled-cluster theories, as well as single-reference coupled-cluster theory with single, double (CCSD), and perturbative triple excitations [CCSD(T)]. For all systems the DCT methods show intermediate performance between that of CCSD and CCSD(T), with significant improvement over the former method. In particular, for the beryllium dimer, m-benzyne, and 2,6-pyridyne, the ODC-12 method along with CCSD(T) correctly predict the global minimum structures, while CCSD predictions fail qualitatively, underestimating the multireference effects. Our results suggest that the DC-12 and ODC-12 methods are capable of describing emerging static correlation effects but should be used cautiously when highly accurate results are required. Conveniently, the appearance of multireference effects in DCT can be diagnosed by analyzing the DCT natural orbital occupations, which are readily available at the end of the energy computation.

Theoretical Characterization of the Minimum-Energy Structure of (SF6)2

MP2 and symmetry-adapted perturbation theory calculations are used in conjunction with the aug-cc-pVQZ basis set to characterize the SF6 dimer. Both theoretical methods predict the global minimum structure to be of C2 symmetry, lying 0.07-0.16 kJ/mol below a C2h saddle point structure, which, in turn, is predicted to lie energetically 0.4-0.5 kJ/mol below the lowest-energy D2d structure. This is in contrast with IR spectroscopic studies that infer an equilibrium D2d structure. It is proposed that the inclusion of vibrational zero-point motion gives an averaged structure of D2d symmetry.

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short-range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short-range charge penetration correction modifying the charge-charge, charge-dipole and charge-quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry-Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono- and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER-HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration-corrected polarizable force fields highlighting the mandatory need of non-spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short-range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio- or bioinorganic systems in periodic boundary conditions.

Interactions of Molecules with cis and trans Double Bonds: A Theoretical Study of cis- and trans-2-Butene

Noncovalent interactions of cis- and trans-2-butene, as the smallest model systems of molecules with cis and trans double bonds, were studied to find potential differences in interactions of these molecules. The study was performed using quantum chemical methods including very accurate CCSD(T)/CBS method. We studied parallel and displaced parallel interactions in 2-butene dimers, in butane dimers, and between 2-butene and saturated butane. The results show the trend that interactions of 2-butene with butane are the strongest, followed by interactions in butane dimers, whereas the interaction in 2-butene dimers are the weakest. The strongest calculated interaction energy is between trans-2-butene and butane, with a CCSD(T)/CBS energy of -2.80 kcal mol(-1) . Interactions in cis-2-butene dimers are stronger than interactions in trans-2-butene dimers. Interestingly, some of the interactions involving 2-butene are as strong as interactions in a benzene dimer. These insights into interactions of cis- and trans-2-butene can improve understanding of the properties and processes that involve molecules with cis and trans double bonds, such as fatty acids and polymers.

Rotational spectroscopy of the atmospheric photo-oxidation product o-toluic acid and its monohydrate

o-Toluic acid, a photo-oxidation product in the atmosphere, and its monohydrate were characterized in the gas phase by pure rotational spectroscopy. High-resolution spectra were measured in the range of 5-14 Hz using a cavity-based molecular beam Fourier-transform microwave spectrometer. Possible conformers were identified computationally, at the MP2/6-311++G(2df,2pd) level of theory. For both species, one conformer was identified experimentally, and no methyl internal rotation splittings were observed, indicative of relatively high barriers to rotation. In the monomer, rocking of the carboxylic acid group is a large amplitude motion, characterized by a symmetrical double-well potential. This and other low-lying out-of-plane vibrations contribute to a significant (methyl top-corrected) inertial defect (-1.09 amu Å(2)). In the monohydrate, wagging of the free hydrogen atom of water is a second large amplitude motion, so the average structure is planar. As a result, no c-type transitions were observed. Water tunneling splittings were not observed, because the water rotation coordinate is characterized by an asymmetrical double-well potential. Since the minima are not degenerate, tunneling is precluded. Furthermore, a concerted tunneling path involving simultaneous rotation of the water moiety and rocking of the carboxylic acid group is precluded, because the hilltop along this coordinate is a virtual, rather than a real, saddle-point. Inter- and intramolecular non-covalent bonding is discussed in terms of the quantum theory of atoms in molecules. The percentage of o-toluic acid hydrated in the atmosphere is estimated to be about 0.1% using statistical thermodynamics.

Wetting Camphor: Multi-Isotopic Substitution Identifies the Complementary Roles of Hydrogen Bonding and Dispersive Forces

Using broadband rotational spectroscopy, we report here on the delicate interplay between hydrogen bonds and dispersive forces when an unprecedentedly large organic molecule (camphor, C10H16O) is microsolvated with up to three molecules of water. Unambiguous assignment was achieved by performing multi H2(18)O isotopic substitution of clustered water molecules. The observation of all possible mono- and multi-H2(18)O insertions in the cluster structure yielded accurate structural information that is not otherwise achievable with single-substitution experiments. The observed clusters exhibit water chains starting with a strong hydrogen bond to the C═O group and terminated by a mainly van der Waals (dispersive) contact to one of the available sites at the monomer moiety. The effect of hydrogen bond cooperativity is noticeable, and the O···O distances between the clustered water subunits decrease with the number of attached water molecules. The results reported here will further contribute to reveal the hydrophobic and hydrophilic interactions in systems of increasing size.

σ Bond activation through tunneling: formation of the boron hydride cations BHn+ (n = 2, 4, 6)

The network of H₂ additions to B⁺ and subsequent insertion reactions serve as a tractable model for hydrogen storage in elementary boron-containing compounds.

Chemical Assignment of Symmetry-Adapted Perturbation Theory Interaction Energy Components: The Functional-Group SAPT Partition

Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex.

Benchmark Study of Density Cumulant Functional Theory: Thermochemistry and Kinetics

We present an extensive benchmark study of density cumulant functional theory (DCFT) for thermochemistry and kinetics of closed- and open-shell molecules. The performance of DCFT methods (DC-06, DC-12, ODC-06, and ODC-12) is compared to that of coupled-electron pair methods (CEPA0 and OCEPA0) and coupled-cluster theory (CCSD and CCSD(T)) for the description of noncovalent interactions (A24 database), barrier heights of hydrogen-transfer reactions (HTBH38), radical stabilization energies (RSE30), adiabatic ionization energies (AIE), and covalent bond stretching in diatomic molecules. Our results indicate that out of four DCFT methods the ODC-12 method is the most reliable and accurate DCFT formulation to date. Compared to CCSD, ODC-12 shows superior results for all benchmark tests employed in our study. With respect to coupled-pair theories, ODC-12 outperforms CEPA0 and shows similar accuracy to the orbital-optimized CEPA0 variant (OCEPA0) for systems at equilibrium geometries. For covalent bond stretching, ODC-12 is found to be more reliable than OCEPA0. For the RSE30 and AIE data sets, ODC-12 shows competitive performance with CCSD(T). In addition to benchmark results, we report new reference values for the RSE30 data set computed using coupled cluster theory with up to perturbative quadruple excitations.

London Dispersion Decisively Contributes to the Thermodynamic Stability of Bulky NHC-Coordinated Main Group Compounds

We evaluated the dispersion stabilization of a series of seemingly reactive main group compounds coordinated to bulky N-heterocyclic carbene ligands. We computed the thermochemistry of hypothetical isodesmic exchange reactions of these ligands with their unsubstituted parent systems employing the B3LYP/6-311G(d,p) level of theory with and without dispersion corrections. The energy difference between these two approaches gave dispersion corrections of 30 kcal mol(-1) and more. We therefore conclude that London dispersion contributes critically to the thermodynamic stabilities of these compounds. As such, these core-shell structures undergo reactions of the reactive core as long as the dispersion stabilization is conserved.

A theoretical investigation of the energetics and spectroscopic properties of the gas-phase linear proton-bound cation-molecule complexes, XCH(+)-N2 (X = O, S)

The structural features, spectroscopic properties, and interaction energies of the linear proton-bound complexes of OCH(+) and its sulfur analog SCH(+) with N2 were investigated using the high-level ab initio methods MP2 and CCSD(T) as well as density functional theory with the aug-cc-pVXZ (X = D, T) basis sets. The rotational constants along with the vibrational frequencies of the cation-molecule complexes are reported here. A comparison of the interaction energies of the OCH(+)-N2 and SCH(+)-N2 complexes with those of the OCH(+)-CO and OCH(+)-OC complexes was also performed. The energies of all the complexes were determined at the complete basis set (CBS) limit. CS shows higher proton affinity at the C site than CO does, so the complex OCH(+)-N2 is relatively strongly bound and has a higher interaction energy than the SCH(+)-N2 complex. Symmetry-adapted perturbation theory (SAPT) was used to decompose the total interaction energies of the complexes into the attractive electrostatic interaction energy (E elst), induction energy (E ind), dispersion energy (E disp), and repulsive exchange energy (E exch). We found that the ratio of E ind to E disp is large for these linear proton-bound complexes, meaning that inductive effects are favored in these complexes. The bonding characteristics of the linear complexes were elucidated using natural bond orbital (NBO) theory. NBO analysis showed that the attractive interaction is caused by NBO charge transfer from the lone pair on N to the σ*(C-H) antibonding orbital in XCH(+)-N2 (X = O, S). The quantum theory of atoms in molecules (QTAIM) was used to analyze the strengths of the various bonds within and between the cation and molecule in each of these proton-bound complexes in terms of the electron density at bond critical points (BCP). Graphical Abstract Linear proton-bound complexes of OCH(+)-N2 and SCH(+)-N2. In these complexes, inductive effect is favored over dispersive effect. The attractive interaction is the NBO charge transfer from N-lone pair of N2 to CH σ* antibonding orbital of XCH(+) (X = O, S).

Communication: Practical intramolecular symmetry adapted perturbation theory via Hartree-Fock embedding

We develop a simple methodology for the computation of symmetry-adapted perturbation theory (SAPT) interaction energy contributions for intramolecular noncovalent interactions. In this approach, the local occupied orbitals of the total Hartree-Fock (HF) wavefunction are used to partition the fully interacting system into three chemically identifiable units: the noncovalent fragments A and B and a covalent linker C. Once these units are identified, the noninteracting HF wavefunctions of the fragments A and B are separately optimized while embedded in the HF wavefunction of C, providing the dressed zeroth order wavefunctions for A and B in the presence of C. Standard two-body SAPT (particularly SAPT0) is then applied between the relaxed wavefunctions for A and B. This intramolecular SAPT procedure is found to be remarkably straightforward and efficient, as evidenced by example applications ranging from diols to hexaphenyl-ethane derivatives.

Competition Between π-π and C-H/π Interactions: A Comparison of the Structural and Electronic Properties of Alkoxy-Substituted 1,8-Bis((propyloxyphenyl)ethynyl)naphthalenes

The structural and electronic consequences of π-π and C-H/π interactions in two alkoxy-substituted 1,8-bis- ((propyloxyphenyl)ethynyl)naphthalenes are explored by using X-ray crystallography and electronic structure computations. The crystal structure of analogue 4, bearing an alkoxy side chain in the 4-position of each of the phenyl rings, adopts a π-stacked geometry, whereas analogue 8, bearing alkoxy groups at both the 2- and the 5-positions of each ring, has a geometry in which the rings are splayed away from a π-stacked arrangement. Symmetry-adapted perturbation theory analysis was performed on the two analogues to evaluate the interactions between the phenylethynyl arms in each molecule in terms of electrostatic, steric, polarization, and London dispersion components. The computations support the expectation that the π-stacked geometry of the alkoxyphenyl units in 4 is simply a consequence of maximizing π-π interactions. However, the splayed geometry of 8 results from a more subtle competition between different noncovalent interactions: this geometry provides a favorable anti-alignment of C-O bond dipoles, and two C-H/π interactions in which hydrogen atoms of the alkyl side chains interact favorably with the π electrons of the other phenyl ring. These favorable interactions overcome competing π-π interactions to give rise to a geometry in which the phenylethynyl substituents are in an offset, unstacked arrangement.