Quantum Chemical Perspective Research Articles

Vibrational signatures of dynamic excess proton storage between primary amine and carboxylic acid groups.

Ammonium and carboxylic moieties play a central role in proton-mediated processes of molecular recognition, charge transfer or chemical change in (bio)materials. Whereas both chemical groups constitute acid-base pairs in organic salt-bridge structures, they may as well host excess protons in acidic environments. The binding of excess protons often precedes proton transfer reactions and it is therefore of fundamental interest, though challenging from a quantum chemical perspective. As a benchmark for this process, we investigate proton storage in the amphoteric compound 5-aminovaleric acid (AV), within an intramolecular proton bond shared by its primary amine and carboxylic acid terminal groups. Infrared ion spectroscopy is combined with abinitio Molecular Dynamics (AIMD) calculations to expose and rationalize the spectral signatures of protonated AV and its deuterated isotopologues. The dynamic character of the proton bond confers a fluxional structure to the molecular framework, leading to wide-ranging bands in the vibrational spectrum. These features are reproduced with remarkable accuracy by AIMD computations, which serves to lay out microscopic insights into the excess proton binding scenario.

Protection mechanism of β-carotene on the chlorophyll photostability through aggregation: a quantum chemical perspective

Protection mechanism of β-carotene on the chlorophyll photostability through aggregation: a quantum chemical perspective

(Invited) The Electric Double Layer Revisited from an Atomistic Perspective

At the interface between two conducting phases, an electric double layer (EDL) forms. In interfacial electrochemistry, such an EDL is present at the interface between the electrode and the electrolyte. The structure of the EDL can be crucial for all processes that occur at such interfaces, for example in electrochemical energy conversion and storage. Yet, it is fair to say that our understanding of the structure of the EDL is still limited and mainly based on concepts that are more than one hundred years old. In this contribution, I will focus on relatively simple interfaces between metallic electrodes and aqueous electrolytes [1] from a conceptual and from a quantum chemical atomistic perspective. I will discuss how elecrochemically control parameter such as the electrode potential and pH values can enter a first-principles description of electrochemical interfaces. Furthermore, I will present examples in which the explicit consideration of the electrochemical environment is not necessary in order to faithfully reproduce adsorbate structures on metal electrodes as a function of the electrochemical control parameters [2]. In addition, I will critically discuss the properties of electrochemical interfaces that correspond to observables from an atomistic perspective.[1] A. Groß and S. Sakong, Ab initio simulations of water/metal interfaces, Chem. Rev. 2022, 122, 10746.[2] A. Groß, Reversible vs. standard hydrogen electrode scale in interfacial electrochemistry from a theoretician's atomistic point of view, J. Phys. Chem. C 2022, 126, 11439.

It from bit: AI and the laws of nature

AbstractThe present rate of growth of powerful AI systems motivates an accurate comparison between the notion of computers and the workings of natural sciences. Statements such as “intelligence doesn't require flesh, blood or carbon atoms” or “it's computation all the way down” incite a substrate‐independent view, providing shortcuts for Darwinian evolution and the possible appearance of sentient machines. This view is discussed and contrasted from a quantum chemical perspective. The qualitative difference between the developed AI and the evolved HI is recognized and the importance of a material constituent, formulated in terms of energy‐temperature, conjugate to an immaterial ingredient, in the context of time‐entropy, is pointed out as a necessary feature. The popular dictum “it from bit” does not appear valid unless amended with its obverse “bit from it.”

Beyond Cavity Born-Oppenheimer: On Nonadiabatic Coupling and Effective Ground State Hamiltonians in Vibro-Polaritonic Chemistry.

The emerging field of vibro-polaritonic chemistry studies the impact of light-matter hybrid states known as vibrational polaritons on chemical reactivity and molecular properties. Here, we discuss vibro-polaritonic chemistry from a quantum chemical perspective beyond the cavity Born-Oppenheimer (CBO) approximation and examine the role of electron-photon correlation in effective ground state Hamiltonians. We first quantitatively review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz Hamiltonian in dipole approximation and a vibrational strong coupling (VSC) Born-Huang expansion. We then derive nonadiabatic coupling elements arising from both "slow" nuclei and cavity modes compared to "fast" electrons via the generalized Hellmann-Feynman theorem, discuss their properties, and reevaluate the CBO approximation. In the second part, we introduce a crude VSC Born-Huang expansion based on adiabatic electronic states, which provides a foundation for widely employed effective Pauli-Fierz Hamiltonians in ground state vibro-polaritonic chemistry. Those do not strictly respect the CBO approximation but an alternative scheme, which we name crude CBO approximation. We argue that the crude CBO ground state misses electron-photon correlation relative to the CBO ground state due to neglected cavity-induced nonadiabatic transition dipole couplings to excited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as a first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model with a focus on nonadiabatic coupling under VSC and electron-photon correlation effects on classical activation barriers. We finally discuss the potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime.

Tuning nonlinear optical properties of tetracyclopentatetraphenylnene by superhalogens doping: Quantum chemical perspective of novel NLO materials for modern optoelectronic applications

Fabrication of stable NLO materials is highly demanding because of their numerous applications in optoelectronic and optical devices. This research attempts to theoretically design superhalogens (LiF2, BeF3, MgF3, LiCl2, BeCl3, MgCl3) doped tetracyclopentatetraphenylnene (TCPTP) as potential NLO materials for cutting-edge NLO applications. Density functional theory (DFT) computations explore their geometric, thermodynamic, electrical, and nonlinear optical (NLO) properties. NCI analysis, DOS, FMO, MEP, TDM, and NBO analysis are performed to confirm the type of interaction, participation of various fragments, and charge transfer, respectively. The computational findings demonstratedthat the superhalogen-doped isomers of TCPTP have remarkablethermodynamic stabilities, with the highestbinding energy of −81.344 kcalmol−1. The HOMO–LUMO energy gap was significantly decreased from 1.5319 eV (TCPTP) to 1.2807––1.2269 eV by superhalogens doping. The TD-DFT analysis demonstrates that these proposed complexes have sufficient transparency in the UV region, which is necessary to add a high nonlinear optical response for valuable applications in optoelectronics. Magnification in the dipole moment (µ0), polarizability (α0), and hyperpolarizability (β0) values from 0.0 D, 325.00 a.u. and 0.0 a.u to 18.23 D, 463.92 a.u and 4.11 × 104 a.u respectively, is achieved upon superhalogens doping on TCPTP surface. These complexes also had considerably large initial hyperpolarizability (βo) from 1.57 × 103 to 4.11 × 104 au, which was particularly noteworthy. This research with promising initial hyperpolarizability (βo) value will provide new opportunities for experimental and theoretical researchers to develop innovative NLO materials.

A quantum chemical perspective on the potential application of Fe-decorated C24N24 porous fullerene for catalytic ethylene epoxidation

Density functional theory calculations are used to investigate the reaction mechanisms and activation barriers of ethylene (C2H4) epoxidation by molecular oxygen (O2) using Fe-decorated C24N24 porous fullerene. Calculated adsorption energies demonstrate that the decorated Fe atom has a greater propensity to adsorb O2 molecules than C2H4. The results, on the other hand, indicate that ethylene epoxidation by O2 proceed through the Langmuir Hinshelwood (LH) mechanism. The whole ethylene epoxidation reaction is exothermic, with activation energies ranging from 0.36 to 0.68 eV, showing that this process is both thermodynamically and kinetically favorable. The side reaction, i.e., formation of acetaldehyde, is almost impossible over the proposed catalyst due to its large activation energy.

On the Nature of the Partial Covalent Bond between Noble Gas Elements and Noble Metal Atoms

This article provides a discussion on the nature of bonding between noble gases (Ng) and noble metals (M) from a quantum chemical perspective by investigating compounds such as NgMY (Y=CN, O, NO3, SO4, CO3), [NgM-(bipy)]+, NgMCCH, and MCCNgH complexes, where M=Cu, Ag, Au and Ng=Kr-Rn, with some complexes containing the lighter noble gas atoms as well. Despite having very low chemical reactivity, noble gases have been observed to form weak bonds with noble metals such as copper, gold, and silver. In this study, we explore the factors that contribute to this unusual bonding behavior, including the electronic structure of the atoms involved and the geometric configuration of the concerned fragments. We also investigate the metastable nature of the resulting complexes by studying the energetics of their possible dissociation and internal isomerization channels. The noble gas-binding ability of the bare metal cyanides are higher than most of their bromide counterparts, with CuCN and AgCN showing higher affinity than their chloride analogues as well. In contrast, the oxides seem to have lower binding power than their corresponding halides. In the oxide and the bipyridyl complexes, the Ng-binding ability follows the order Au > Cu > Ag. The dissociation energies calculated, considering the zero-point energy correction for possible dissociation channels, increase as we move down the noble gas group. The bond between the noble gases and the noble metals in the complexes are found to have comparable weightage of orbital and electrostatic interactions, suggestive of a partial covalent nature. The same is validated from the topological analysis of electron density.

(Invited, Digital Presentation) Charge Transfer at Heterogeneous Functional Interfaces in Energy Conversion and Storage Devices: A Quantum Chemical Perspective

Energy conversion and storage devices are triggering the ecological transition toward a sustainable economic and social development. In these technological devices, several constituent materials and their interfaces undergo charge/mass transport processes over different time/space scales, from local fast electron transfer to long-range slow ionic diffusion.Often, experimental techniques cannot dissect such processes at the nanoscale, which hinders a rational design of new devices with better performances. Thus, the application of computational modeling tools with atomistic resolution represents an ongoing revolution in materials design and device development.In this context, this contribution will display how cutting edge DFT-based approaches allow to unveil the charge transfer mechanisms in several different electrochemical environments: (i) at hybrid interfaces considering promising Cu-based molecular redox couples in dye sensitized solar cell photoanodes [1,2], (ii) at heterogeneous interface in last generation perovskite solar cells [3] and (iii) ion-electrode interfaces in the context of nanostructured electrodes in sodium-ion batteries [4,5,6].The results will provide new insights on the structure-property-functional relationships of different functional materials/interfaces and will pave the basis of new design principles for further improvements of the corresponding devices.[1] AB Muñoz-García, I Benesperi , G. Boschloo, JJ Concepcion, JH Delcamp, EA Gibson, GJ Meyer, M Pavone, H Pettersson, A Hagfeldt, M Freitag Dy e-sensitized Solar Cells strike back 2021 Chemical Society Reviews 50, 12450-12550[2] I Benesperi, H Michaels, T Edvinsson, M Pavone, MR Probert, P Waddel, AB Muñoz-García*, M Freitag Dynamic dimer copper coordination redox shuttles 2022 Chem 8, 439-449 (Cover Article)[3] A Pecoraro, A De Maria, P Delli Veneri, M Pavone, AB Muñoz-García* Interfacial electronic features in methyl-ammonium lead iodide and p-type oxide heterostructures: new insights for inverted perovskite solar cells 2020 Physical Chemistry Chemical Physics 22, 28401-28413[4] A Massaro, AB Muñoz-García, PP Prosini, C Gerbaldi, M Pavone Unveiling Oxygen Redox Activity in P2-Type NaxNi0.25Mn0.68O2 High-Energy Cathode for Na-Ion Batteries 2021 ACS Energy Letters 6, 2470-2480[5] A Massaro, A. Langella, AB Muñoz-García, M Pavone First-principles insights on anion redox activity in NaxFe1/8Ni1/8Mn3/4O2: Towards efficient high-energy cathodes for Na-ion batteries 2022 Journal of American Ceramic Society https://doi.org/10.1111/jace.18494[6] A Massaro, AB Muñoz-García, P Maddalena, F Bella, G Meligrana, C Gerbaldi, M Pavone First-principles study of Na insertion at TiO2 anatase surfaces: new hints for Na-ion battery design 2020 Nanoscale Advances 2, 2745-2751

Photovoltaic properties and enhancement in near-infrared light absorption capabilities of acceptor materials for organic solar cell applications: A quantum chemical perspective via DFT

More than 22% power conversion efficiency (PCE) of organic solar cells (OSCs) has been reported with efficient narrow bandgap acceptor materials as the active layers. And end-capped modifications of such acceptor materials are an efficient approach for designing highly stable and efficient materials for organic solar cell applications. In this study, four new molecules (TOS1 to TOS4) are designed for the active layer of organic solar cells. Density functional theory and time-dependent functional theory have been employed for the computation of various geometric, photovoltaic, optoelectronic properties of newly designed molecules. Different analyses like frontier molecular orbitals, transition density matrix, open-circuit voltage, absorption maxima, excitation and binding energies have been performed and examined with great care. Further, reorganization energy of hole and electron of novel designed molecules has been calculated and results suggested that designed systems are effective contributors for future development of organic solar cells. Overall, the outcomes of this study urge the experimentalists for the future development of highly stable and near-infrared absorbing organic solar cells.

Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry.

The pharmaceutical success of atorvastatin (ATV), a widely employed drug against the “bad” cholesterol (LDL) and cardiovascular diseases, traces back to its ability to scavenge free radicals. Unfortunately, information on its antioxidant properties is missing or unreliable. Here, we report detailed quantum chemical results for ATV and its ortho- and para-hydroxy metabolites (o-ATV, p-ATV) in the methanolic phase. They comprise global reactivity indices, bond order indices, and spin densities as well as all relevant enthalpies of reaction (bond dissociation BDE, ionization IP and electron attachment EA, proton detachment PDE and proton affinity PA, and electron transfer ETE). With these properties in hand, we can provide the first theoretical explanation of the experimental finding that, due to their free radical scavenging activity, ATV hydroxy metabolites rather than the parent ATV, have substantial inhibitory effect on LDL and the like. Surprisingly (because it is contrary to the most cases currently known), we unambiguously found that HAT (direct hydrogen atom transfer) rather than SPLET (sequential proton loss electron transfer) or SET-PT (stepwise electron transfer proton transfer) is the thermodynamically preferred pathway by which o-ATV and p-ATV in methanolic phase can scavenge DPPH (1,1-diphenyl-2-picrylhydrazyl) radicals. From a quantum chemical perspective, the ATV’s species investigated are surprising because of the nontrivial correlations between bond dissociation energies, bond lengths, bond order indices and pertaining stretching frequencies, which do not fit the framework of naive chemical intuition.

Strength and nature of host–guest interactions in metal–organic frameworks from a quantum chemical perspective

Strength and nature of host–guest interactions in metal–organic frameworks from a quantum chemical perspective

Density functional theory-based analyses on selective gas separation by β-PVDF-supported ionic liquid membranes

Finding proper candidates for polymer-supported ionic liquid (IL)-based gas separating membranes is a challenge. The current article elucidates the quantum chemical perspective of the selective gas adsorption efficiency, from a mixture of CO2, CO, CH4, and H2, of α- and β-polyvinylidene fluoride (PVDF)-supported imidazolium- and pyridinium-based six ionic liquid membranes. Although IL-based membrane efficiency mainly depends on the gas solubility of ILs, IL/support binding and gas adsorption on the support material are also studied to describe the overall gas adsorption properties of the PVDF/IL complexes. β-PVDF exhibits better binding with the ILs, and better gas affinity, thus, qualified as a more suitable membrane component as compared to α-PVDF. Dispersion-corrected density functional calculations are performed to provide a detailed insight into the energetic interactions, nonbonding intermolecular interactions based on symmetry adapted perturbation theory (SAPT), natural bond orbitals (NBO), Bader's quantum theory of atoms in molecules (QTAIM), reduced density gradient (RDG), frontier orbital interactions, density of states (DOS), and thermochemical analyses of the gas-adsorbed systems. Gas molecules interact with the membrane components through weak hydrogen bonds and exhibit low interaction energies, indicating physisorption of the gases. Gas adsorption energies are more negative than the mutual interaction energies of the gas molecules, ensuring effective gas adsorption by the membrane components. All the β-PVDF/IL systems have shown the highest and lowest affinity for CO2 and H2, respectively, leading to effective separation of CO2 and H2 from the other gases.

Discovery of potential inhibitors against New Delhi metallo-\u03b2-lactamase-1 from natural compounds: in silico-based methods

New Delhi metallo-β-lactamase variants and different types of metallo-β-lactamases have attracted enormous consideration for hydrolyzing almost all β-lactam antibiotics, which leads to multi drug resistance bacteria. Metallo-β-lactamases genes have disseminated in hospitals and all parts of the world and became a public health concern. There is no inhibitor for New Delhi metallo-β-lactamase-1 and other metallo-β-lactamases classes, so metallo-β-lactamases inhibitor drugs became an urgent need. In this study, multi-steps virtual screening was done over the NPASS database with 35,032 natural compounds. At first Captopril was extracted from 4EXS PDB code and use as a template for the first structural screening and 500 compounds obtained as hit compounds by molecular docking. Then the best ligand, i.e. NPC120633 was used as templet and 800 similar compounds were obtained. As a final point, ten compounds i.e. NPC171932, NPC100251, NPC18185, NPC98583, NPC112380, NPC471403, NPC471404, NPC472454, NPC473010 and NPC300657 had proper docking scores, and a 50 ns molecular dynamics simulation was performed for calculation binding free energy of each compound with New Delhi metallo-β-lactamase. Protein sequence alignment, 3D conformational alignment, pharmacophore modeling on all New Delhi metallo-β-lactamase variants and all types of metallo-β-lactamases were done. Quantum chemical perspective based on the fragment molecular orbital (FMO) method was performed to discover conserved and crucial residues in the catalytic activity of metallo-β-lactamases. These residues had similar 3D coordinates of spatial location in the 3D conformational alignment. So it is posibble that all types of metallo-β-lactamases can inhibit by these ten compounds. Therefore, these compounds were proper to mostly inhibit all metallo-β-lactamases in experimental studies.

Polaritonic Chemistry: Collective Strong Coupling Implies Strong Local Modification of Chemical Properties.

A fundamental question in the field of polaritonic chemistry is whether collective coupling implies local modifications of chemical properties scaling with the ensemble size. Here we demonstrate from first-principles that an impurity present in a collectively coupled chemical ensemble features such locally scaling modifications. In particular, we find the formation of a novel dark state for a nitrogen dimer chain of variable size, whose local chemical properties are altered considerably at the impurity due to its embedding in the collectively coupled environment. Our simulations unify theoretical predictions from quantum optical models (e.g., collective dark states and bright polaritonic branches) with the single molecule quantum chemical perspective, which relies on the (quantized) redistribution of charges leading to a local hybridization of light and matter. Moreover, our findings suggest that recently developed ab initio methods for strong light-matter coupling are suitable to access these local polaritonic effects and provide a detailed understanding of photon-modified chemistry.

Rising trend on the halogen and non-halogen derivatives (Br, Cl, CF3, F, CH3 and NH2) in ruminal β-d-Xylopyranose – a quantum chemical perspective

The utmost aim of the current study is to find significance of the binding affinity in the halogen and non-halogen derivatives: Br, Cl, CF3, F, CH3 and NH2 of β-d-Xylopyranose with the hinge region amino acids of ruminant-β-glycosidase. The interaction energy analysis was carried out in detail through various density functional studies as M062X/def2-QZVP, M062X/LANL2DZ, B3LYP/LANL2DZ and M06HF/LANL2DZ level of theories. The total interaction energy of halogen derivatives: Br, Cl, F and CF3 are −618.21, −599.00, −720.45 and −553.08 kcal/mol respectively, and non-halogen derivative: amine group (NH2) is −87.96 kcal/mol at M062X/def2-QZVP level of theory, which exist with strong binding affinity. Ligand properties: dipole moment, polarizability, volume, molecular mass, electrostatic potential map was evaluated to understand its electrostatic and structural behavior. The nature of the bonds was inferred from the electrostatic potential map for all the halogen and non-halogen derivatives ligand. The stabilization energy from NBO analysis reveals the stability of single hydrogen and halogen bonds (N–H…Br, C–Br…O, N–H…Cl, C–Cl…O, O–H…F, C–H…F, N–H…F, C–F…O, N–H…O, O–H…O, N–H…N, O–H…N) in β-d-Xylopyranose and its derivatives. Overall, this study paves way for scientist and medicinal chemist in modelling new drugs. Further, it suggests mutations that increase the binding and may enhance the catalytic action and strengthen the complex diet in animals and hence recommended for experimental synthesis. Communicated by Ramaswamy H. Sarma

Intermolecular interaction among Remdesivir, RNA and RNA-dependent RNA polymerase of SARS-CoV-2 analyzed by fragment molecular orbital calculation

COVID-19, a disease caused by a new strain of coronavirus (SARS-CoV-2) originating from Wuhan, China, has now spread around the world, triggering a global pandemic, leaving the public eagerly awaiting the development of a specific medicine and vaccine. In response, aggressive efforts are underway around the world to overcome COVID-19. In this study, referencing the data published on the Protein Data Bank (PDB ID: 7BV2) on April 22, we conducted a detailed analysis of the interaction between the complex structures of the RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2 and Remdesivir, an antiviral drug, from the quantum chemical perspective based on the fragment molecular orbital (FMO) method. In addition to the hydrogen bonding and intra-strand stacking between complementary strands as seen in normal base pairs, Remdesivir bound to the terminus of an primer-RNA strand was further stabilized by diagonal π-π stacking with the -1A’ base of the complementary strand and an additional hydrogen bond with an intra-strand base, due to the effect of chemically modified functional group. Moreover, stable OH/π interaction is also formed with Thr687 of the RdRp. We quantitatively revealed the exhaustive interaction within the complex among Remdesivir, template-primer-RNA, RdRp and co-factors, and published the results in the FMODB database.

What is the driving force behind molecular triangles and their guests? A quantum chemical perspective about host-guest interactions.

The physical nature of host-guest (HG) interactions occurring between molecular triangles and linear anions was explored using density functional theory (DFT) calculations combined with energy decomposition analyses (EDA), nuclear independent chemical shift (NICS), and non-covalent interaction index (NCI). We demonstrate that: (i) in addition to the host being significantly rigid, the strain energies are not negligible, especially for host 2; (ii) halogen anions interact mainly by electrostatic forces (ΔEelst > ΔE > ΔEdisp), meanwhile; (iii) trihalogen anions interact mostly by dispersion forces (ΔEdisp > ΔEelst≈ΔE). The NICS and NCI calculations corroborate the idea that HG interactions are considerably mediated through dispersion terms, and also indicate an antiaromatic character inside the host walls.

A quantum chemical perspective on the potency of electron donors and acceptors in pnicogen bonds (AS...N, P...N, N...N).

A quantum chemical perspective of 31 structures contains electron acceptors: ASCl3 (arsenic trichloride), PCl3 (phosphorous trichloride) and NCl3 (nitrogen trichloride); forming non-covalent bond with various nitrogen-based electron donors that resulted in pnicogen bonds, AS...N, P...N and N...N were calculated at M062X/def2-QZVP level of theory. Besides the above method, MP2/def2-QZVP and CCSD(T)/def2-QZVP level of theories have also been analysed to have in depth knowledge about the bonds formed. The nature of the bonds was assumed from the electrostatic potential evaluated for all the monomers, where σ hole is positive for all the monomers. The strongest pnicogen bonds are ASCl3-NF2H, PCl3-NCH3CH3CH3 and NCl3-NCH3CH3CH3 having interaction energies as -4.15, -11.58 and -3.25 kcal/mol, respectively, at MP2/def2-QZVP level of theory. Further at CCSD(T)/def2-QZVP level of theory, ASCl3-NF2H and NCl3-NCH3CH3CH3 are found to be the most stable with interaction energies as -3.53 and -2.45 kcal/mol, respectively. The potential energy surface scan was performed for all the stable complexes in order to confirm the existences of energies are true minima. Moreover to confirm the halogen and pnicogen bonds, AIM analysis was carried out. The results from the above factors of pnicogen bond will help crystal growth, material science and engineering community to explore novel materials, which abide for modernization. Graphical abstract PCl3-NCH3CH3CH3 complex with 2.61 Å and pnicogen angle of 178.54° is strong, and interaction energy is -11.58 kcal/mol. Electron donors - ASCl3, PCl3 and NCl3 and electron acceptors -NCH3CH3CH3, NH3C2 and NHCO have strong electrostatic contribution. High and low values of (ρ) ∇2(ρ) reveal the strong and weak pnicogen bond. Schematic representation of acceptors surrounded by its donors and Electrostatic Potential map.

Factors Stabilizing β-Sheets in Protein Structures from a Quantum-Chemical Perspective.

Protein folds are determined by the interplay between various (de)stabilizing forces, which can be broadly divided into a local strain of the protein chain and intramolecular interactions. In contrast to the α-helix, the β-sheet secondary protein structure is significantly stabilized by long-range interactions between the individual β-strands. It has been observed that quite diverse amino acid sequences can form a very similar small β-sheet fold, such as in the three-β-strand WW domain. Employing "calibrated" quantum-chemical methods, we show herein on two sequentially diverse examples of the WW domain that the internal strain energy is higher in the β-strands and lower in the loops, while the interaction energy has an opposite trend. Low strain energy computed for peptide sequences in the loop 1 correlates with its postulated early formation in the folding process. The relatively high strain energy within the β-strands (up to 8 kcal mol-1 per amino acid residue) is compensated by even higher intramolecular interaction energy (up to 15 kcal mol-1 per residue). It is shown in a quantitative way that the most conserved residues across the structural family of WW domains have the highest contributions to the intramolecular interaction energy. On the other hand, the residues in the regions with the lowest strain are not conserved. We conclude that the internal interaction energy is the physical quantity tuned by evolution to define the β-sheet protein fold.