Fragment Molecular Orbital Method Research Articles

The peptide bond: resonance increases bond order and complicates fragmentation.

The enhancement of the peptide bond order by a resonance in the lone pair of N and the π-bond of CO is analyzed. A decomposition of the bond order in terms of localized molecular orbitals is developed and applied to the peptide bond. A combination of two rotations of hybrid orbitals is proposed to improve the boundary treatment in the fragment molecular orbital method. The developed approach is applied to peptide bonds, and it is found crucial to retain the π orbital in the variational space of both fragments across the boundary. The interaction energies between conventional amino acid residues in Trp-cage (1L2Y) are discussed.

Leveraging the Fragment Molecular Orbital and MM-GBSA Methods in Virtual Screening for the Discovery of Novel Non-Covalent Inhibitors Targeting the TEAD Lipid Binding Pocket

Leveraging the Fragment Molecular Orbital and MM-GBSA Methods in Virtual Screening for the Discovery of Novel Non-Covalent Inhibitors Targeting the TEAD Lipid Binding Pocket

Discovery of a novel SHP2 allosteric inhibitor using virtual screening, FMO calculation, and molecular dynamic simulation.

SHP2 is a non-receptor protein tyrosine phosphatase to remove tyrosine phosphorylation. Functionally, SHP2 is an essential bridge to connect numerous oncogenic cell-signaling cascades including RAS-ERK, PI3K-AKT, JAK-STAT, and PD-1/PD-L1 pathways. This study aims to discover novel and potent SHP2 inhibitors using a hierarchical structure-based virtual screening strategy that combines molecular docking and the fragment molecular orbital method (FMO) for calculating binding affinity (referred to as the Dock-FMO protocol). For the SHP2 target, the FMO method prediction has a high correlation between the binding affinity of the protein-ligand interaction and experimental values (R2 = 0.55), demonstrating a significant advantage over the MM/PBSA (R2 = 0.02) and MM/GBSA (R2 = 0.15) methods. Therefore, we employed Dock-FMO virtual screening of ChemDiv database of ∼2,990,000 compounds to identify a novel SHP2 allosteric inhibitor bearing hydroxyimino acetamide scaffold. Experimental validation demonstrated that the new compound (E)-2-(hydroxyimino)-2-phenyl-N-(piperidin-4-ylmethyl)acetamide (7188-0011) effectively inhibited SHP2 in a dose-dependent manner. Molecular dynamics (MD) simulation analysis revealed the binding stability of compound 7188-0011 and the SHP2 protein, along with the key interacting residues in the allosteric binding site. Overall, our work has identified a novel and promising allosteric inhibitor that targets SHP2, providing a new starting point for further optimization to develop more potent inhibitors. All the molecular docking studies were employed to identify potential leads with Maestro v10.1. The protein-ligand binding affinities of potential leads were further predicted by FMO calculations at MP2/6-31G* level using GAMESS v2020 system. MD simulations were carried out with AmberTools18 by applying the FF14SB force field. MD trajectories were analyzed using VMD v1.9.3. MM/GB(PB)SA binding free energy analysis was carried out with the mmpbsa.py tool of AmberTools18. The docking and MD simulation results were visualized through PyMOL v2.5.0.

Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method.

An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

Computational study on the inhibition mechanism of cyclodextran against GTF-SI from Streptococcus mutans focusing on the glucan-binding domain

Glucosyltransferases (GTFs) from Streptococcus mutans (S. mutans) are enzymes that synthesize glucan, a polymer that forms a biofilm causing dental caries. Cyclodextran (CI), which contains a ring structure formed from D-glucose by α-1,6 glycoside linkage, has been reported to strongly inhibit GTFs. In contrast, cyclodextrin, formed by α-1,4 glycoside linkage, has almost no inhibitory activity. In this study, we examined the inhibition mechanism of CI through computational chemistry, focusing on the glucan-binding domain of GTF-SI, which is one of GTFs produced by S. mutans. Analysis using molecular dynamics simulation and fragment molecular orbital method demonstrated a clear difference in the molecular interaction mechanism between α-1,6- and α-1,4-linked oligosaccharides. The calculated affinity of α-1,6-linked oligosaccharides was higher than that of α-1,4-linked oligosaccharides. Additionally, geometry optimization based on density functional theory revealed that three amino acids—Q1282, K1284, and S1302—play an essential role in the binding with α-1,6-linked oligosaccharides. These results successfully explain the inhibition mechanism of CI.

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.

FMO-guided design of darunavir analogs as HIV-1 protease inhibitors

The prevalence of HIV-1 infection continues to pose a significant global public health issue, highlighting the need for antiretroviral drugs that target viral proteins to reduce viral replication. One such target is HIV-1 protease (PR), responsible for cleaving viral polyproteins, leading to the maturation of viral proteins. While darunavir (DRV) is a potent HIV-1 PR inhibitor, drug resistance can arise due to mutations in HIV-1 PR. To address this issue, we developed a novel approach using the fragment molecular orbital (FMO) method and structure-based drug design to create DRV analogs. Using combinatorial programming, we generated novel analogs freely accessible via an on-the-cloud mode implemented in Google Colab, Combined Analog generator Tool (CAT). The designed analogs underwent cascade screening through molecular docking with HIV-1 PR wild-type and major mutations at the active site. Molecular dynamics (MD) simulations confirmed the assess ligand binding and susceptibility of screened designed analogs. Our findings indicate that the three designed analogs guided by FMO, 19–0–14–3, 19–8–10–0, and 19–8–14–3, are superior to DRV and have the potential to serve as efficient PR inhibitors. These findings demonstrate the effectiveness of our approach and its potential to be used in further studies for developing new antiretroviral drugs.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization.

An excitonic coupling model is developed based on an equation-of-motion coupled cluster combined with the fragment molecular orbital method. The effects of polarization and excitonic coupling on the splitting of quasi-degenerate levels in systems containing multiple chromophores are elucidated on dimers of formaldehyde, water, formic acid, hydrogen fluoride, and carbon monoxide. It is shown that the level structure is mainly determined by the mutual polarization of chromophores and to a lesser extent by the excitonic coupling. The role of symmetry in excitonic coupling in dimers is discussed. The excitonic coupling between all residues in the photoactive yellow protein (PDB: 2PHY) is analyzed.

Binding Free Energy Calculation Based on the Fragment Molecular Orbital Method and Its Application in Designing Novel SHP-2 Allosteric Inhibitors.

The accurate prediction of binding free energy is a major challenge in structure-based drug design. Quantum mechanics (QM)-based approaches show promising potential in predicting ligand-protein binding affinity by accurately describing the behavior and structure of electrons. However, traditional QM calculations face computational limitations, hindering their practical application in drug design. Nevertheless, the fragment molecular orbital (FMO) method has gained widespread application in drug design due to its ability to reduce computational costs and achieve efficient ab initio QM calculations. Although the FMO method has demonstrated its reliability in calculating the gas phase potential energy, the binding of proteins and ligands also involves other contributing energy terms, such as solvent effects, the 'deformation energy' of a ligand's bioactive conformations, and entropy. Particularly in cases involving ionized fragments, the calculation of solvation free energy becomes particularly crucial. We conducted an evaluation of some previously reported implicit solvent methods on the same data set to assess their potential for improving the performance of the FMO method. Herein, we develop a new QM-based binding free energy calculation method called FMOScore, which enhances the performance of the FMO method. The FMOScore method incorporates linear fitting of various terms, including gas-phase potential energy, deformation energy, and solvation free energy. Compared to other widely used traditional prediction methods such as FEP+, MM/PBSA, MM/GBSA, and Autodock vina, FMOScore showed good performance in prediction accuracies. By constructing a retrospective case study, it was observed that incorporating calculations for solvation free energy and deformation energy can further enhance the precision of FMO predictions for binding affinity. Furthermore, using FMOScore-guided lead optimization against Src homology-2-containing protein tyrosine phosphatase 2 (SHP-2), we discovered a novel and potent allosteric SHP-2 inhibitor (compound 8).

Differential molecular mechanisms of substrate recognition by selenium methyltransferases, INMT and TPMT, in selenium detoxification and excretion

It is known that the recommended dietary allowance of selenium (Se) is dangerously close to its tolerable upper intake level. Se is detoxified and excreted in urine as trimethylselenonium ion (TMSe) when the amount ingested exceeds the nutritional level. Recently, we demonstrated that the production of TMSe requires two methyltransferases: thiopurine S-methyltransferase (TPMT) and indolethylamine N-methyltransferase (INMT). In this study, we investigated the substrate recognition mechanisms of INMT and TPMT in the Se-methylation reaction. Examination of the Se-methyltransferase activities of two paralogs of INMT, namely, nicotinamide N-methyltransferase (NNMT) and phenylethanolamine N-methyltransferase (PNMT), revealed that only INMT exhibited Se-methyltransferase activity. Consistently, molecular dynamics simulations demonstrated that dimethylselenide (DMSe) was preferentially associated with the active center of INMT. Using the fragment molecular orbital method, we identified hydrophobic residues involved in the binding of DMSe to the active center of INMT. The INMT-L164R mutation resulted in a deficiency in Se- and N-methyltransferase activities. Similarly, TPMT-R152, which occupies the same position as INMT-L164, played a crucial role in the Se-methyltransferase activity of TPMT. Our findings suggest that TPMT recognizes negatively charged substrates, whereas INMT recognizes electrically neutral substrates in the hydrophobic active center embedded within the protein. These observations explain the sequential requirement of the two methyltransferases in producing TMSe.

In Silico Design of Natural Inhibitors of ApoE4 from the Plant Moringa oleifera: Molecular Docking and Ab Initio Fragment Molecular Orbital Calculations.

Alzheimer's disease (AD) is a neurological disease, and its signs and symptoms appear slowly over time. Although current Alzheimer's disease treatments can alleviate symptoms, they cannot prevent the disease from progressing. To accurately diagnose and treat Alzheimer's disease, it is therefore necessary to establish effective methods for diagnosis. Apolipoprotein E4 (ApoE4), the most frequent genetic risk factor for AD, is expressed in more than half of patients with AD, making it an attractive target for AD therapy. We used molecular docking simulations, classical molecular mechanics optimizations, and ab initio fragment molecular orbital (FMO) calculations to investigate the specific interactions between ApoE4 and the naturally occurring compounds found in the plant Moringa Oleifera. According to the FMO calculations, quercetin had the highest binding affinity to ApoE4 among the sixteen compounds because its hydroxyl groups generated strong hydrogen bonds with the ApoE4 residues Trp11, Asp12, Arg15, and Asp130. As a result, we proposed various quercetin derivatives by introducing a hydroxyl group into quercetin and studied their ApoE4 binding properties. The FMO data clearly showed that adding a hydroxyl group to quercetin improved its binding capacity to ApoE4. Furthermore, ApoE4 Trp11, Asp12, Arg15, and Asp130 residues were discovered to be required for significant interactions between ApoE4 and quercetin derivatives. They had a higher ApoE4 binding affinity than our previously proposed epicatechin derivatives. Accordingly, the current results evaluated using the ab initio FMO method will be useful for designing potent ApoE4 inhibitors that can be used as a candidate agent for AD treatment.

Leveraging the Fragment Molecular Orbital Method to Explore the PLK1 Kinase Binding Site and Polo-Box Domain for Potent Small-Molecule Drug Design.

Polo-like kinase 1 (PLK1) plays a pivotal role in cell division regulation and emerges as a promising therapeutic target for cancer treatment. Consequently, the development of small-molecule inhibitors targeting PLK1 has become a focal point in contemporary research. The adenosine triphosphate (ATP)-binding site and the polo-box domain in PLK1 present crucial interaction sites for these inhibitors, aiming to disrupt the protein's function. However, designing potent and selective small-molecule inhibitors can be challenging, requiring a deep understanding of protein-ligand interaction mechanisms at these binding sites. In this context, our study leverages the fragment molecular orbital (FMO) method to explore these site-specific interactions in depth. Using the FMO approach, we used the FMO method to elucidate the molecular mechanisms of small-molecule drugs binding to these sites to design PLK1 inhibitors that are both potent and selective. Our investigation further entailed a comparative analysis of various PLK1 inhibitors, each characterized by distinct structural attributes, helping us gain a better understanding of the relationship between molecular structure and biological activity. The FMO method was particularly effective in identifying key binding features and predicting binding modes for small-molecule ligands. Our research also highlighted specific "hot spot" residues that played a critical role in the selective and robust binding of PLK1. These findings provide valuable insights that can be used to design new and effective PLK1 inhibitors, which can have significant implications for developing anticancer therapeutics.

Site-Specific Ionization Potentials and Electron Affinities in Large Molecular Systems at Coupled Cluster Level.

A many-body expansion of ionization potentials and electron affinities is developed based on a combination of the fragment molecular orbital method and equation-of-motion coupled-cluster (EOM-CC). In addition to site-specific values, obtained as one-body properties, pair and triple corrections are added to account for nonlocal EOM-CC contributions of the molecular environment of a chromophore. The developed method is applied to carboxylic acids, alkyl cations, a protein ubiquitin (Protein Data Bank ID 1UBQ), and a nano ribbon of white graphene elucidating the effect of environment on ionization potential and electron affinity.

The C-terminal tail of Rad17, iVERGE, binds the 9‒1‒1 complex independently of AAA+ ATPase domains to provide another clamp–loader interface

The ATR pathway plays a crucial role in maintaining genome integrity as the major DNA damage checkpoint. It also attracts attention as a therapeutic target in cancer treatment. The Rad17–RFC2–5 complex loads the Rad9–Hus1–Rad1 (9–1–1) DNA clamp complex onto damaged chromatin to activate the ATR pathway. We previously reported that phosphorylation of a polyanionic C-terminal tail of human Rad17, iVERGE, is essential for the interaction between Rad17 and the 9–1–1 complex. However, the molecular mechanism has remained unclear. Here, we show that iVERGE directly interacts with the Hus1 subunit of the 9–1–1 complex through Rad17-S667 phosphorylation independently of the AAA+ ATPase domains. An exogenous iVERGE peptide interacted with the 9–1–1 complex in vivo. The binding conformation of the iVERGE peptide was analyzed by de novo modeling with docking simulation, simulated annealing-molecular dynamics simulation, and the fragment molecular orbital method. The in silico analyses predicted the association of the iVERGE peptide with the hydrophobic and basic patches on the Hus1 protein, and the corresponding Hus1 mutants were deficient in the interaction with the iVERGE peptide in vivo. The iVERGE peptide occupied the same position as the C-terminus of Saccharomyces cerevisiae RAD24 on MEC3. The interaction energy calculation suggested that the Rad17 KYxxL motif and the iVERGE peptide are the primary and secondary interaction surfaces between the Rad17–RFC2–5 and 9–1–1 complexes. Our data reveal a novel molecular interface, iVERGE, between the Rad17–RFC2–5 and 9–1–1 complexes in vertebrates and implicate that Rad17 utilizes two distinct molecular interfaces to regulate the 9–1–1 complex.

Application of Model Core Potentials to Zn- and Mg-containing Metalloproteins in the Fragment Molecular Orbital Method

Application of Model Core Potentials to Zn- and Mg-containing Metalloproteins in the Fragment Molecular Orbital Method

Designing Potent α-Glucosidase Inhibitors: A Synthesis and QSAR Modeling Approach for Biscoumarin Derivatives.

Nineteen biscoumarins were synthesized, well-characterized, and evaluated against α-glucosidases in vitro. Of these, six compounds (10, 12, 16, and 17-19) were newly synthesized and not previously reported in the chemical literature. The majority of the synthesized derivatives demonstrated significant inhibitory activity. A quantitative structure-activity relationship (QSAR) model was developed, revealing a strong correlation between the anti-α-glucosidase activity and selected molecular descriptors. Based on this model, two new compounds (18 and 19) were designed, which exhibited the strongest inhibition with IC50 values of 0.62 and 1.21 μM, respectively, when compared to the positive control (acarbose) with an IC50 value of 93.63 μM. Enzyme kinetic studies of compounds 18 and 19 revealed their competitive inhibition with Ki values of 3.93 and 1.80 μM, respectively. Computational studies demonstrated that compound 18 could be inserted into the original binding site (OBS) of α-glucosidase MAL12 and form multiple hydrophobic interactions with nearby amino acids, with the bromo group playing an essential role in enhancing the binding strength and stability at the OBS of the enzyme based on the quantum mechanical calculations using the fragment molecular orbital method. These findings provide valuable insights into the design of potent α-glucosidase inhibitors, which may have potential therapeutic applications in the treatment of diabetes and related diseases.

Multi-level parallelization of quantum-chemical calculations.

Strategies for multiple-level parallelizations of quantum-mechanical calculations are discussed, with an emphasis on using groups of workers for performing parallel tasks. These parallel programming models can be used for a variety abinitio quantum chemistry approaches, including the fragment molecular orbital method and replica-exchange molecular dynamics. Strategies for efficient load balancing on problems of increasing granularity are introduced and discussed. A four-level parallelization is developed based on a multi-level hierarchical grouping, and a high parallel efficiency is achieved on the Theta supercomputer using 131072 OpenMP threads.

SophosQM: Accurate Binding Affinity Prediction in Compound Optimization.

The optimization of compounds' binding affinity for a biological target is a crucial aspect of the drug development process. Being able to accurately predict binding energies in advance of synthesizing compounds would have a massive impact on the speed of the drug discovery process. The ideal binding affinity prediction method should combine accuracy, reliability, and speed. In this paper, we present SophosQM, a quantum mechanics (QM)-based approach, which can accurately predict the binding affinities of compounds to proteins. The binding affinity predictive models generated by SophosQM are based on the fragment molecular orbital (FMO) method to estimate the enthalpic component of the binding free energy, and a macroscopic descriptor, clog P, is used as an approximation of the entropic component. The affinity prediction is performed using multilinear regression, fitting the experimental values against the FMO-computed enthalpic term and clog P. The quality of the prediction can be assessed in terms of the correlation coefficient between experimental and predicted values. In this work, the method's reliability and accuracy are exemplified by applying SophosQM to 70 compounds binding to six different targets of pharmaceutical relevance. Overall, the results show a very satisfactory performance with a global correlation coefficient in the order of 0.9. Our predictions also show a satisfactory performance compared to data based on free energy perturbation. Finally, SophosQM can also be applied in high-throughput mode by using semiempirical QM methods to evaluate large portions of chemical space, while retaining a good level of accuracy, but decreasing the computing time to just a few seconds per compound.

Fragment Molecular Orbital based affinity prediction toward pyruvate dehydrogenase kinases: Insights into the charge transfer in hydrogen bond networks.

The fragment molecular orbital (FMO) method is a fast quantum-mechanics method that divides systems into pieces of fragments and performs ab initio calculations. The method has been expected to improve the accuracy of describing protein-ligand interactions by incorporating electronic effects. In this article, FMO calculation with solvation methods were applied to the affinity prediction at the ATP-binding site of PDHK4. As the ionized aspartic acid lies at the center and is involved in the complex hydrogen bond networks, this system has turned out to be a difficult target to describe by traditional molecular-mechanics method. In the FMO calculation with the polarizable continuum model (PCM) solvation method, a considerable amount of charge (-0.27e) was transferred from the ionized aspartate to the surrounding residues. We found that using FMO with the PCM solvation method was important to increase the correlation, and by incorporating the ligand deformation energy, the correlation was improved to R = 0.81 for whole twelve compounds and R= 0.91 without one outlier compound.

Predicting Kinetics and Dynamics of Spin-Dependent Processes

ConspectusPredicting mechanisms and rates of nonadiabatic spin-dependent processes including photoinduced intersystem crossings, thermally activated spin-forbidden reactions, and spin crossovers in metal centers is a very active field of research. These processes play critical roles in transition-metal-based and metalloenzymatic catalysis, molecular magnets, light-harvesting materials, organic light-emitting diodes, photosensitizers for photodynamic therapy, and many other applications. Therefore, accurate modeling of spin-dependent processes in complex systems and on different time scales is important for many problems in chemistry, biochemistry, and materials sciences.Nonadiabatic statistical theory (NAST) and nonadiabatic molecular dynamics (NAMD) are two complementary approaches to modeling the kinetics and dynamics of spin-dependent processes. NAST predicts the probabilities and rate constants of nonradiative transitions between electronic states with different spin multiplicities using molecular properties at only few critical points on the potential energy surfaces (PESs), including the reactant minimum and the minimum energy crossing point (MECP) between two spin states. This makes it possible to obtain molecular properties for NAST calculations using accurate but often computationally expensive electronic structure methods, which is critical for predicting the rate constants of spin-dependent processes. Alternatively, NAST can be used to study spin-dependent processes in very large complex molecular systems using less computationally expensive electronic structure methods. The nuclear quantum effects, such as zero-point vibrational energy, tunneling, and interference between reaction paths can be easily incorporated. However, the statistical and local nature of NAST makes it more suitable for large systems and slow kinetics. In contrast, NAMD explores entire PESs of interacting electronic states, making it ideal for modeling fast barrierless spin-dependent processes. Because the knowledge of large portions of PESs is often needed, the simulations require a very large number of electronic structure calculations, which limits the NAMD applicability to relatively small molecular systems and ultrafast kinetics.In this Account, we discuss our contribution to the development of the NAST and NAMD approaches for predicting the rates and mechanism of spin-dependent processes. First, we briefly describe our NAST and NAMD implementations. The NAST implementation is an extension of the transition state theory to the processes involving two crossing potential energy surfaces of different spin multiplicities. The NAMD approach includes the trajectory surface hopping (TSH) and ab initio multiple spawning (AIMS) methods. Second, we discuss several applications of NAST and NAMD to model spin-dependent processes in different systems. The NAST applicability to large complex systems is demonstrated by the studies of the spin-forbidden isomerization of the active sites of metal-sulfur proteins. Our implementation of the MECP search algorithm within the fully ab initio fragment molecular orbital method allows applying NAST to systems with thousands of atoms, such as the solvated protein rubredoxin. Applications of NAMD to ultrafast spin-dependent processes are represented by the generalized AIMS simulations utilizing the fast GPU-based TeraChem electronic structure program to gain insight into the complex photoexcited state relaxation in 2-cyclopentenone.