Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Non-radiative decay and fragmentation in water molecules after 1a1 -14a1 excitation and core ionization studied by electron-energy-resolved electron-ion coincidence spectroscopy.

In this paper, we examine decay and fragmentation of core-excited and core-ionized water molecules combining quantum chemical calculations and electron-energy-resolved electron-ion coincidence spectroscopy. The experimental technique allows us to connect electronic decay from core-excited states, electronic transitions between ionic states, and dissociation of the molecular ion. To this end, we calculate the minimum energy dissociation path of the core-excited molecule and the potential energy surfaces of the molecular ion. Our measurements highlight the role of ultra-fast nuclear motion in the 1a1 -14a1 core-excited molecule in the production of fragment ions. OH+ fragments dominate for spectator Auger decay. Complete atomization after sequential fragmentation is also evident through detection of slow H+ fragments. Additional measurements of the non-resonant Auger decay of the core-ionized molecule (1a1 -1) to the lower-energy dication states show that the formation of the OH+ + H+ ion pair dominates, whereas sequential fragmentation OH+ + H+ → O + H+ + H+ is observed for transitions to higher dication states, supporting previous theoretical investigations.

A new QM/MM method oriented to the study of ionic liquids.

The interest on room temperature ionic liquids has grown in the last decades because of their use as all-purpose solvent and their low environmental impact. In the present work, a new theoretical procedure is developed to study pure ionic liquids within the framework of the quantum mechanics/molecular mechanics method. Each type of ion (cation or anion) is considered as an independent entity quantum mechanically described that follows a differentiated path in the liquid. The method permits, through an iterative procedure, the full coupling between the polarized charge distribution of the ions and the liquid structure around them. The procedure has been tested with 1-ethyl-3-methylimidazolium tetrafluoroborate. It was found that, similar to non-polar liquids and as a consequence of the low value of the reaction field, the cation and anion charge distributions are hardly polarized by the rest of molecules in the liquid. Their structure is characterized by an alternance between anion and cation shells as evidenced by the coincidence of the first maximum of the anion-anion and cation-cation radial distribution functions with the first minimum of the anion-cation. Some degree of stacking between the cations is also found.

Restricted-Variance Molecular Geometry Optimization Based on Gradient-Enhanced Kriging.

Machine learning techniques, specifically gradient-enhanced Kriging (GEK), have been implemented for molecular geometry optimization. GEK-based optimization has many advantages compared to conventional-step-restricted second-order truncated expansion-molecular optimization methods. In particular, the surrogate model given by GEK can have multiple stationary points, will smoothly converge to the exact model as the number of sample points increases, and contains an explicit expression for the expected error of the model function at an arbitrary point. Machine learning is, however, associated with abundance of data, contrary to the situation desired for efficient geometry optimizations. In this paper, we demonstrate how the GEK procedure can be utilized in a fashion such that in the presence of few data points, the surrogate surface will in a robust way guide the optimization to a minimum of a potential energy surface. In this respect, the GEK procedure will be used to mimic the behavior of a conventional second-order scheme but retaining the flexibility of the superior machine learning approach. Moreover, the expected error will be used in the optimizations to facilitate restricted-variance optimizations. A procedure which relates the eigenvalues of the approximate guessed Hessian with the individual characteristic lengths, used in the GEK model, reduces the number of empirical parameters to optimize to two: the value of the trend function and the maximum allowed variance. These parameters are determined using the extended Baker (e-Baker) and part of the Baker transition-state (Baker-TS) test suites as a training set. The so-created optimization procedure is tested using the e-Baker, full Baker-TS, and S22 test suites, at the density functional theory and second-order Møller-Plesset levels of approximation. The results show that the new method is generally of similar or better performance than a state-of-the-art conventional method, even for cases where no significant improvement was expected.

Solvent effects on internal conversions and intersystem crossings: the radiationless de-excitation of acrolein in water.

An extended version of the averaged solvent electrostatic potential from molecular dynamics data (ASEP/MD) method oriented to the study of the solvent effects on internal conversion and intersystem crossing processes is presented. The method allows for the location of crossing points between free energy surfaces both in equilibrium and in frozen solvent conditions. The ground and excited states of the solute molecule are described at the complete active space self-consistent field (CASSCF) level while the solvent structure is obtained from molecular dynamics simulations. As an application, we studied the nonradiative de-excitation of s-trans-acrolein 1(n --> pi*) in aqueous solution. We found that the solvent modifies the relative stability of the different crossing points but not enough as to alter the relative order of stability with respect to the in vacuo situation. The relaxation through an equilibrium path involves a strong solvent reorganization. On the contrary, the nonequilibrium path does not involve solvent motion and the de-excitation could proceed with the same speed as in vacuo.

A CASPT2//CASSCF study of vertical and adiabatic electron transitions of acrolein in water solution.

The 1(n --> pi*) excited-state of acrolein in liquid water was studied theoretically by using the averaged solvent electrostatic potential from molecular dynamics method (ASEP/MD). The model combines a multireference perturbational CASPT2//CASSCF treatment in the description of the solute molecule with NVT molecular dynamics simulations in the description of the solvent. In this paper, we present two alternative methods for calculating solvent shift on adiabatic transitions and their performance is analyzed. In the first method, the free energy change during an adiabatic transition is calculated classically by using the free energy perturbation method. In the second method, it is calculated from the quantum values of the vertical absorption and emission electron transition energies. The 1(n --> pi*) excitation is accompanied by a charge flux from the oxygen to the carbon skeleton, this charge flux decreases the dipole moment of the excited-state with respect to the ground state value and, consequently, the solute-solvent interaction energy. This effect destabilizes the excited-state with respect to the ground state and produces a blue shift in the absorption and emission bands. For the emission process, there also exists an additional destabilization due to a partial desolvation of the excited state. The effect of the solvent electron polarization, the inclusion of the solute electron correlation, and the use of relaxed geometries in solution on the calculated solvent shift of the absorption and emission spectra are also analyzed.

Solvent Effects on the Absorption Spectra of the para-Coumaric Acid Chromophore in Its Different Protonation Forms.

The effects of the solvent and protonation state on the electronic absorption spectrum of the para-coumaric acid (pCA), a model of the photoactive yellow protein (PYP), have been studied using the ASEP/MD (averaged solvent electrostatic potential from molecular dynamics) method. Even though, in the protein, the chromophore is assumed to be in its phenolate monoanionic form, when it is found in water solution pH control can favor neutral, monoanionic, and dianionic species. As the pCA has two hydrogens susceptible of deprotonation, both carboxylate and phenolate monoanions are possible. Their relative stabilities are strongly dependent on the medium. In gas phase, the most stable isomer is the phenolate while in aqueous solution it is the carboxylate, although the population of the phenolate form is not negligible. The s-cis, s-trans, syn, and anti conformers have also been included in the study. Electronic excited states of the chromophore have been characterized by SA-CAS(14,12)-PT2/cc-pVDZ level of theory. The bright state corresponds, in all the cases, to a π → π* transition involving a charge displacement in the system. The magnitude and direction of this displacement depends on the protonation state and on the environment (gas phase or solution). In the same way, the calculated solvatochromic shift of the absorption maximum depends on the studied form, being a red shift for the neutral, carboxylate monoanion, and dianionic chromophores and a blue shift for the phenolate monoanion. Finally, the contribution that the solvent electronic polarizability has on the solvent shift was analyzed. It represents a very important part of the total solvent shift in the neutral form, but its contribution is completly negligible in the mono- and dianionic forms.

Solvent Effects on the Radiative and Nonradiative Decay of a Model of the Rhodopsin Chromophore.

The radiative and nonradiative decay of a model with five double bonds of the 11-cis-retinal protonated Schiff base was studied both in vacuum and in methanol solution using an extended version of the averaged solvent electrostatic potential from molecular dynamics data (ASEP/MD) method that allows the location of crossing points between free energy surfaces both in equilibrium and in frozen solvent conditions. The multireference quantum method CASSCF was used for the description of the states of interest, while the solvent structure was obtained from molecular dynamics simulations. Electron dynamic correlation corrections to the energy were included at CASPT2 level. Unlike in gas phase, where only two states seem to be implicated, in methanol solution, three states are necessary to describe the photoisomerization process. At the Franck-Condon point the S1 and S2 states are almost degenerate; consequently, the S1 surface has a region with an ionic character ((1)Bu-like) and another one with a covalent character ((2)Ag-like). Emission from the ionic minima is responsible for the low-frequency part of the fluorescence band, while emission from the covalent minima originates the high-frequency part. The ionic minimum is separated from the conical intersection yielding the all-trans isomer by an energy barrier that was estimated in 0.7 kcal/mol. The geometry of the optimized conical intersection was found at a torsion angle of the central double bond close to 90° both in vacuum and in methanol solution. This large torsion in addition to the accompanying charge displacements forces a strong solvent reorganization during the de-excitation process which slows down the photoisomerization kinetics in methanol with respect to the gas phase. Solvent fluctuations modulate the minima depth and the barrier height and could explain the multiexponential relaxation time observed in the experiments.

Theoretical Study of the Dual Fluorescence of 4-(N,N-Dimethylamino)benzonitrile in Solution.

We have performed high-level quantum calculations of absorption and emission properties of 4-(N,N-dimethylamino)benzonitrile (DMABN) in gas phase and in polar solvents, including the solvent effects with an explicit mean field model. Two excited states of DMABN have been found and optimized, corresponding to the two excited states assumed by the generally accepted hypotheses for the dual fluorescence of this molecule: a locally excited (LE) state and a charge transfer (CT) state. The results show that, in the gas phase, the charge transfer state is severely distorted and higher in energy than the locally excited state, while in polar solvents, it becomes almost an ideal twisted intramolecular charge transfer state (TICT) and is stabilized with respect to the locally excited state and the Franck-Condon point. The relative free energies calculated for the two excited states in solution suggest that both states are accessible from initial Franck-Condon excitation, the charge transfer state being highly favored in aqueous solution and less so in tetrahydrofuran. The results support the validity of the TICT model in this system.

Improving the efficiency of the NEB reaction path finding algorithm.

The nudged elastic band (NEB) method is a successful optimization method for obtaining minimum energy reaction paths if only the initial and final structures are known. However, the original implementation of the method had some limitations, which has meant that there has been considerable interest in proposing alternative NEB formulations, which show improved convergence behavior. In this work, we present two modifications to the standard NEB procedure. The first involves the use of a second-order quasi-Newton optimization technique applied separately to each of the images that form the path. The second consists of the use of an interpolating spline to represent the path. This ensures that the images along the path are evenly spaced and means that the arbitrary spring forces employed in the standard NEB method are no longer necessary. We tested these modifications on a set of small, but relatively complex, chemical systems and found that the computation time was reduced by as much as 90% compared with the standard method.

Framework-based design of a new all-purpose molecular simulation application: the Adun simulator.

Here we present Adun, a new molecular simulator that represents a paradigm shift in the way scientific programs are developed. The traditional algorithm centric methods of scientific programming can lead to major maintainability and productivity problems when developing large complex programs. These problems have long been recognized by computer scientists; however, the ideas and techniques developed to deal with them have not achieved widespread adoption in the scientific community. Adun is the result of the application of these ideas, including pervasive polymorphism, evolutionary frameworks, and refactoring, to the molecular simulation domain. The simulator itself is underpinned by the Adun Framework, which separates the structure of the program from any underlying algorithms, thus giving a completely reusable design. The aims are twofold. The first is to provide a platform for rapid development and implementation of different simulation types and algorithms. The second is to decrease the learning barrier for new developers by providing a rigorous and well-defined structure. We present some examples on the use of Adun by performing simple free-energy simulations for the adiabatic charging of a single ion, using both free-energy perturbation and the Bennett's method. We also illustrate the power of the design by detailing the ease with which ASEP/MD, an elaborated mean field QM/MM method originally written in FORTRAN 90, was implemented into Adun.