Charge transfer interaction using quasiatomic minimal-basis orbitals in the effective fragment potential method

A Merger of the Spin-Flip ORMAS Approach and the MC-PDFT Method

The SF-ORMAS-PDFT (spin-flip occupation restricted multiple active space-pair density functional theory) approach combines the SF-ORMAS-CI method with the MC-PDFT method to treat both static and dynamic correlation in multiconfigurational systems. The static correlation description is generated via the spin-flip approach, which uses a high-spin single reference determinant to treat excited states with multiconfigurational characters. The on-top pair density functional theory uses a translation scheme applied to GGA density functionals. The SF-ORMAS-PDFT scheme has also been combined with virtual valence orbitals (VVO), a well-defined subspace of the virtual molecular orbitals, giving rise to significant speedups relative to the use of the full virtual space. The accuracy of the SF-ORMAS-PDFT method is tested by calculating 65 vertical excitation energies of 12 small- and medium-sized organic molecules. The SF-ORMAS-PDFT vertical excitation energies calculated with VVOs are comparable to those calculated with the full virtual space. The SF-ORMAS-PDFT/6-31G(d) level of theory predicts the rotational barrier of ethylene to be 65.5 and 65.9 kcal/mol, with full virtual space and VVOs, respectively. These predicted barrier heights compare well with the experimental value of 65 kcal/mol.

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

Detangling Solvatochromic Effects by the Effective Fragment Potential Method

Understanding molecular interactions in complex systems opens avenues for the efficient design of new materials with target properties. Energy decomposition methods provide a means to obtain a detailed picture of intermolecular interactions. This work introduces a molecular modeling approach for decomposing the solvatochromic shifts of the electronic excited states into the contributions of the individual molecular fragments of the environment surrounding the chromophore. The developed approach is implemented for the QM/EFP (quantum mechanics/effective fragment potential) model that provides a rigorous first-principles-based description of the electronic states of the chromophores in complex polarizable environments. On the example of two model systems, water pentamer and hydrated uracil, we show how the decomposition of the solvatochromic shifts into the contributions of individual solvent water molecules provides a detailed picture of the intermolecular interactions in the ground and excited states of these systems. The analysis also demonstrates the nonadditivity of solute-solvent interactions and the significant contribution of solute polarization to the total values of solvatochromic shifts.

R-8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method

The anisotropic and isotropic R-8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang-Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole-octopole polarizability tensor and the quadrupole-quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. While the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang-Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

Intermolecular interactions in clusters of ethylammonium nitrate and 1-amino-1,2,3-triazole

The intermolecular interaction energies, including hydrogen bonds (H-bonds), of clusters of the ionic liquid ethylammonium nitrate (EAN) and 1-amino-1,2,3-triazole (1-AT) based deep eutectic propellants (DeEP) are examined. 1-AT is introduced as a neutral hydrogen bond donor (HBD) to EAN in order to form a eutectic mixture. The effective fragment potential (EFP) is used to examine the bonding interactions in the DeEP clusters. The resolution of the Identity (RI) approximated second order Møller-Plesset perturbation theory (RI-MP2) and coupled cluster theory (RI-CCSD(T)) are used to validate the EFP results. The EFP method predicts that there are significant polarization and charge transfer effects in the EAN:1-AT complexes, along with Coulombic, dispersion and exchange repulsion interactions. The EFP interaction energies are in good agreement with the RI-MP2 and RI-CCSD(T) results. The quasi-atomic orbital (QUAO) bonding and kinetic bond order (KBO) analyses are additionally used to develop a conceptual and semi-quantitative understanding of the H-bonding interactions as a function of the size of the system. The QUAO and KBO analyses suggest that the H-bonds in the examined clusters follow the characteristic hydrogen bonding three-center four electron interactions. The strongest H-bonding interactions between the (EAN)1:(1-AT)n and (EAN)2:(1-AT)n (n = 1-5) complexes are observed internally within EAN; that is, between the ethylammonium cation [EA]+ and the nitrate anion ([NO3]-). The weakest H-bonding interactions occur between [NO3]- and 1-AT. Consequently, the average strengths of the H-bonds within a given (EAN)x:(1-AT)n complex decrease as more 1-AT molecules are introduced into the EAN monomer and EAN dimer. The QUAO bonding analysis suggests that 1-AT in (EAN)x:(1-AT)n can act as both a HBD and a hydrogen bond acceptor simultaneously. It is observed that two 1-AT molecules can form H-bonds to each other. Although the KBOs that correspond to H-bonding interactions in [EA]+:1-AT, [NO3]-:1-AT and between two 1-AT molecules are weaker than the H-bonds in EAN, those weak H-bond networks with 1-AT could be important to form a stable DeEP.

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

Molecular interactions in diffusion-controlled aldol condensation with mesoporous silica nanoparticles

The aldol reaction of p-nitrobenzaldehyde in amino-catalyzed mesoporous silica nanoparticles (MSN) has revealed varying catalytic activity with the size of the pores of MSN. The pore size dependence related to the reactivity indicates that the diffusion process is important. A detailed molecular-level analysis for understanding diffusion requires assessment of the noncovalent interactions of the molecular species involved in the aldol reaction with each other, with the solvent, and with key functional groups on the pore surface. Such an analysis is presented here based upon the effective fragment potential (EFP). The EFP method can calculate the intermolecular interactions, decomposed into Coulomb, polarization, dispersion, exchange-repulsion, and charge-transfer interactions. In this study, the potential energy surfaces corresponding to each intermolecular interaction are analyzed for homo- and hetero-dimers with various configurations. The monomers that compose dimers are five molecules such as p-nitrobenzaldehyde, acetone, n-hexane, propylamine, and silanol. The results illustrate that the dispersion interaction is crucial in most dimers.

Ab initio effective one-electron potential operators: Applications for charge-transfer energy in effective fragment potentials

The concept of effective one-electron potentials (EOPs) has proven to be extremely useful in efficient description of electronic structure of chemical systems, especially extended molecular aggregates such as interacting molecules in condensed phases. Here, a general method for EOP-based elimination of electron repulsion integrals is presented, that is tuned toward the fragment-based calculation methodologies such as the second generation of the effective fragment potentials (EFP2) method. Two general types of the EOP operator matrix elements are distinguished and treated either via the distributed multipole expansion or the extended density fitting (DF) schemes developed in this work. The EOP technique is then applied to reduce the high computational costs of the effective fragment charge-transfer (CT) terms being the bottleneck of EFP2 potentials. The alternative EOP-based CT energy model is proposed, derived within the framework of intermolecular perturbation theory with Hartree-Fock noninteracting reference wavefunctions, compatible with the original EFP2 formulation. It is found that the computational cost of the EFP2 total interaction energy calculation can be reduced by up to 38 times when using the EOP-based formulation of CT energy, as compared to the original EFP2 scheme, without compromising the accuracy for a wide range of weakly interacting neutral and ionic molecular fragments. The proposed model can thus be used routinely within the EFP2 framework.

Quantum Mechanical Modeling of the Interactions between Noble Metal (Ag and Au) Nanoclusters and Water with the Effective Fragment Potential Method

Explicit solvent interactions can significantly alter the physical and chemical properties of noble metal (e.g., gold and silver) nanoclusters. In order to compute these solvent interactions at a reasonable computational cost, a quantum mechanical (QM)/molecular mechanics (MM) approach, where the metal nanocluster is treated with full QM and the water molecules are treated with a MM force field, can be used. However, classical MM force fields were typically parameterized using molecules containing main group elements as the reference. The accuracy of noble metal-solvent interactions obtained with these force fields therefore remains unpredictable. The effective fragment potential (EFP) force field, designed to model explicitly solvated systems, represents an attractive method to simulate solvated noble metal nanoclusters because it is derived from first principles and contains few or no fitted parameters, depending on implementation. At the density functional theory-optimized geometries, good correlation is obtained between the nanocluster-water interaction energies computed with EFP and those computed with the reference coupled cluster singles, doubles, and perturbative triples method. It is shown that the EFP method gives qualitatively accurate interaction energies at medium-large intermolecular distances for various molecular configurations. In order to achieve higher quantitative accuracy, the first solvation shell should be treated with full QM, if possible. EFP is therefore a promising method for the QM modeling of explicitly solvated silver and gold nanoclusters.

An Accurate Quantum-Based Approach to Explicit Solvent Effects: Interfacing the General Effective Fragment Potential Method with Ab Initio Electronic Structure Theory

An interface between ab initio quantum mechanics (QM) methods and the general effective fragment potential (EFP2) method, QM-EFP2, is implemented in which the intermolecular interactions between a QM molecule and EFP fragments consist of Coulomb, polarization, exchange repulsion (exrep), and dispersion components. In order to ensure accuracy in the QM-EFP2 exrep interaction energy, the EFP2-EFP2 spherical Gaussian overlap (SGO) approximation is abandoned and replaced with the exact electron repulsion integrals (ERI) that are evaluated with a direct method to reduce disk usage. A Gaussian damping function for the QM-EFP2 Coulomb component damps both the EFP nuclear and electronic charges. A new overlap damping function has been implemented for the QM-EFP2 dispersion component. The current QM-EFP2 implementation has been benchmarked with the S22 and S66 data sets and demonstrates excellent agreement with symmetry-adapted perturbation theory (SAPT) for component energies and with coupled cluster theory [CCSD(T)] for the total interaction energies. Water clusters of various sizes (up to 256 water molecules) have been tested; it is shown that the QM-EFP2 method has an accuracy that is comparable to that of EFP2-EFP2. It has been shown previously that the accuracy of EFP2-EFP2 intermolecular interactions is comparable to that of second-order perturbation theory (MP2) or better. The implementation of the distributed data interface (DDI) parallelization scheme significantly improves the efficiency of QM-EFP2 calculations. The time to form the QM-EFP2 Fock operator per SCF iteration for water clusters scales linearly with the number EFP basis functions.

Ionic liquids from a fragmented perspective

The efficacy of using fragmentation methods, such as the effective fragment potential, the fragment molecular orbital and the effective fragment molecular orbital methods is discussed. The advantages and current limitations of these methods are considered, potential improvements are suggested, and a prognosis for the future is provided.