Regions Of Potential Energy Surface Research Articles

Assessment of advanced xDH@B3LYP methods in describing various potential energy curves driven by π-π, CH/π, and SH/π non-bonded interactions

Accurate description of potential energy curves driven by non-bonded interactions remains a great challenge for pure density functional approximations (DFAs). It is because the R−6 decay behavior of dispersion cannot be intrinsically captured by the (semi)-local ingredients and the exact-exchange used in the popular hybrid DFAs. Overemphasizing the accuracy on the equilibrium region for the functional construction would likely deteriorate the overall performance on the other regions of potential energy surfaces. In consequence, the empirical dispersion correction becomes the standard component in DFAs to treat the non-bonded interactions. In this Letter, we demonstrate that without the use of empirical dispersion correction, doubly hybrid approximations, in particular two recently proposed revXYG3 and XYG7 functionals, hold the promise to have a balanced description of non-bonded interactions on the whole potential energy curves for several prototypes of π-π, CH/π, and SH/π interactions. The error of revXYG3 and XYG7 for non-bonded interactions is around 0.1 kcal/mol, and their potential energy curves almost coincide with the accurate CCSD(T)/CBS curves.

SpectrumSDT: A program for parallel calculation of coupled rotational-vibrational energies and lifetimes of bound states and scattering resonances in triatomic systems

We present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities. Program summaryProgram title: SpectrumSDTCPC Library link to program files:https://doi.org/10.17632/9gftxjs4yk.1Developer's repository link:https://github.com/IgorGayday/SpectrumSDTLicensing provisions: GNU General Public License 3 (GPL)Programming language: FortranNature of problem: Calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems.Solution method: A Hamiltonian matrix is built in APH coordinates using an optimal 2D basis set, adjusted for a given problem. A complex absorbing potential (CAP) is added to define a boundary condition for calculation of scattering resonances above the dissociation threshold. The eigenstates of the Hamiltonain matrix are found using a state-of-the-art iterative eigensolver.Restrictions: The present version is restricted to ABA-molecules and wave functions that do not extend into linear and equilateral triangle configurations.Additional comments including restriction and unusual features: Probabilities and lifetimes of the wave functions can be calculated in user-defined regions on the PES, which allows to analyze their localization properties (i.e. automatic isotopomer assignment) and obtain channel-specific lifetimes for scattering resonances.

Calculation of Chemical Reaction Barrier Heights by Multiconfiguration Pair-Density Functional Theory with Correlated Participating Orbitals.

The accurate description of reaction barrier heights is challenging for quantum mechanical methods due to the need for a balanced treatment of dynamic and static correlation energies because their importance varies during the course of a chemical reaction. While some regions of potential energy surfaces are well-described by a single-reference wave function or by Kohn-Sham density functional theory, in other cases a multireference treatment is needed. For systems with many active electrons, most accurate multireference methods have prohibitive computational scalings with system size. Multiconfiguration pair-density functional theory, MC-PDFT, is a more affordable multireference approach that computes the total electron correlation energy in a single step by using the multiconfiguration kinetic energy, density, and on-top pair density and an on-top density functional. In this work, we apply MC-PDFT to a benchmark database (DBH24/18) of 24 diverse reaction barrier heights. We explore the role of active space and basis set selection on the performance of MC-PDFT. We find that MC-PDFT is able to calculate reaction barrier heights with a similar accuracy to complete active space second order perturbation theory, CASPT2, but at a lower computational cost, and we find that MC-PDFT is less dependent on basis set selection than CASPT2.

Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions.

We present two sampling measures to gauge critical regions of potential energy surfaces. These sampling measures employ (a) the instantaneous quantum wavepacket density, an approximation to the (b) potential surface, its (c) gradients, and (d) a Shannon information theory based expression that estimates the local entropy associated with the quantum wavepacket. These four criteria together enable a directed sampling of potential surfaces that appears to correctly describe the local oscillation frequencies, or the local Nyquist frequency, of a potential surface. The sampling functions are then utilized to derive a tessellation scheme that discretizes the multidimensional space to enable efficient sampling of potential surfaces. The sampled potential surface is then combined with four different interpolation procedures, namely, (a) local Hermite curve interpolation, (b) low-pass filtered Lagrange interpolation, (c) the monomial symmetrization approximation (MSA) developed by Bowman and co-workers, and (d) a modified Shepard algorithm. The sampling procedure and the fitting schemes are used to compute (a) potential surfaces in highly anharmonic hydrogen-bonded systems and (b) study hydrogen-transfer reactions in biogenic volatile organic compounds (isoprene) where the transferring hydrogen atom is found to demonstrate critical quantum nuclear effects. In the case of isoprene, the algorithm discussed here is used to derive multidimensional potential surfaces along a hydrogen-transfer reaction path to gauge the effect of quantum-nuclear degrees of freedom on the hydrogen-transfer process. Based on the decreased computational effort, facilitated by the optimal sampling of the potential surfaces through the use of sampling functions discussed here, and the accuracy of the associated potential surfaces, we believe the method will find great utility in the study of quantum nuclear dynamics problems, of which application to hydrogen-transfer reactions and hydrogen-bonded systems is demonstrated here.

Configuration interaction singles natural orbitals: an orbital basis for an efficient and size intensive multireference description of electronic excited states.

Multireference quantum chemical methods, such as the complete active space self-consistent field (CASSCF) method, have long been the state of the art for computing regions of potential energy surfaces (PESs) where complex, multiconfigurational wavefunctions are required, such as near conical intersections. Herein, we present a computationally efficient alternative to the widely used CASSCF method based on a complete active space configuration interaction (CASCI) expansion built from the state-averaged natural orbitals of configuration interaction singles calculations (CISNOs). This CISNO-CASCI approach is shown to predict vertical excitation energies of molecules with closed-shell ground states similar to those predicted by state averaged (SA)-CASSCF in many cases and to provide an excellent reference for a perturbative treatment of dynamic electron correlation. Absolute energies computed at the CISNO-CASCI level are found to be variationally superior, on average, to other CASCI methods. Unlike SA-CASSCF, CISNO-CASCI provides vertical excitation energies which are both size intensive and size consistent, thus suggesting that CISNO-CASCI would be preferable to SA-CASSCF for the study of systems with multiple excitable centers. The fact that SA-CASSCF and some other CASCI methods do not provide a size intensive/consistent description of excited states is attributed to changes in the orbitals that occur upon introduction of non-interacting subsystems. Finally, CISNO-CASCI is found to provide a suitable description of the PES surrounding a biradicaloid conical intersection in ethylene.

Quantum localization/delocalization of muonium in the glycine–K+ complex

Previous electronic structure studies have revealed that the glycine–K+ complex has a low-barrier intramolecular proton-transfer pathway between zwitterionic and neutral forms. We have theoretically calculated quantum molecular structures of this complex including the proton-transfer process using a path-integral molecular dynamics technique on an interpolated potential energy surface developed at the B3LYP level of theory. When the transferring proton is substituted by muon, it was found that the muonium atom showed a broad distribution around the proton(muon)-transfer transition state region between the neutral and zwitterionic structures due to extreme nuclear quantum effects of a very light particle although the distribution peak is slightly deviated from the transition state. The present study demonstrates that Mu can be employed to probe transition-state regions of potential energy surfaces of proton-transfer chemical reactions.

Potential energy surface studies via a single root multireference coupled cluster theory

We have employed complete active space based single root multireference coupled cluster method (the resulting method is referred to by the acronym sr-MRCC) to compute the potential energy surfaces (PESs) of some well studied "protypical model" systems for which a highly accurate and reliable database is available for comparison. As that of state-specific theory, the sr-MRCC approach focuses and correlates one state while using a multiconfigurational reference and thus it naturally avoids intruder states. The present method is structurally different from the well known state specific multireference coupled cluster (SS-MRCC) method introduced by Mahapatra et al. [Mol. Phys. 94, 157 (1998)]. As that of the SS-MRCC theory, the present method is also based on the Jeziorski-Monkhorst ansatz where a different exponential cluster operator exp(T(mu)) acts on its corresponding model function phi(mu). The final cluster finding equations contain coupling between the cluster operators for all the mu, which are mainly responsible to prove the extensivity of both the cluster amplitudes and the energy. The present sr-MRCC theory is size-extensive and size-consistent when localized orbitals are used. The systems considered here exhibit varying degrees of degeneracy at different regions of PES. The treatment of these systems via traditional effective Hamiltonian based methods suffers from divergence problems in the iterative solution of the CC equations (the issue termed as "intruder state"). The sr-MRCC results lie closer to the ones obtained by the SS-MRCC method for these systems. To judge the efficacy of the present method, we have compared our results with other previously published theoretical estimations, which clearly indicate that the present method is reliable in studying the dissociation PES of states plagued by electronic degeneracy as well as notorious intruder effects. The highly satisfactory performance of the sr-MRCC method, vis-a-vis the other sophisticated methods, in describing the lowest and the first excited singlet states of BeH(2) at points of high degeneracy is noticeable.

Combining two-body density functionals with multiconfigurational wavefunctions: diatomic molecules

The MCSCF method provides a correct zero-order wavefunction for all regions of molecular potential energy surfaces. To obtain quantitative accuracy a proper treatment of the dynamic correlation problem must be implemented. Traditionally this has been achieved through multireference variants of perturbation theory, configuration interaction and coupled cluster theory. The computational cost of such techniques makes them prohibitive for all but the smallest molecular problems. Reported here is an investigation into the efficacy of two-body density functionals in providing the dynamic correlation energy for MCSCF reference states. Tests were made on the two-body density functionals of Colle and Salvetti (CS), Moscardó and San-Fabán (MSF), and Moscardó and Pérez-Jiménez (MPJS) in predicting the equilibrium bond lengths, harmonic frequencies and dissociation eneries of fifteen diatomic molecules (3B2, 3BN, 2BS, 1C2, 2CN, 1CO, 1F2, 1FC1, 1N2, 3NCl, 3O2, 1PN, 3Si2, 1SiO, 3SO) using full valence-shell CASSCF reference wavefunctions. Also studied were modifications of these functionals recently suggested by Miehlich, Stoll and Savin (MSS) and Gráfenstein and Cremer (GC). The results obtained show accuracy comparable with and typically superior to the popular Kohn-Sham BLW and B3LW methods. However, the latter methods are not applicable in all regions of a potential energy surface, and even predict incorrect ground states for some systems. The use of two-body density functionals with MCSCF reference states does not share this shortcoming.

New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory

A new implementation of the trajectory surface hopping (TSH) method is proposed to treat multidimensional nonadiabatic dynamics by incorporating the analytical Zhu–Nakamura semiclassical theory of nonadiabatic transition. The problem of classically forbidden hops in the TSH method can now be solved and dealt with just as easily as the classically allowed hops by introducing nonvertical hopping techniques. This is made possible, because the theory can treat both classically allowed and forbidden hops accurately in a unified way. The Zhu–Nakamura theory also enables us to predetermine important regions of potential energy surface before carrying out any dynamics calculations, and thus to save a lot of computational efforts. The charge transfer processes in the collinear H3+ system are studied numerically to test the new TSH method. Comparing the new and old versions of TSH with exact quantum calculations, the new method shows much better agreement with the exact calculations. It also works well when all trasitions are classically forbidden and the old method fails completely.

Theoretical Study on Bis(imino)pyridyl−Fe(II) Olefin Poly- and Oligomerization Catalysts. Dominance of Different Spin States in Propagation and β-Hydride Transfer Pathways

Mechanisms of chain propagation and β-hydride transfer (BHT) chain termination stages of poly- and oligomerization of ethylene by catalysts of general formula [2,6-(CR1N((2-R2)(4-R4)(6-R3)C6H2)2C5H3N]FeCl2 were studied theoretically. Density functional (B3LYP) and integrated molecular orbitals + molecular mechanics (IMOMM) methods were applied respectively to a model (“low steric bulk”, LSB) system, [2,6-(CHNH)2C5H3N]FeCH3+, and one of the catalytic (“high steric bulk”, HSB) systems studied experimentally, [2,6-(CMeN(2,6-iPr2C6H3))2C5H3N]FeCH3+. We find that two axial ligands are required in order for the dz2 orbital (with the trichelating ligand defining the equatorial xy plane) to be destabilized and for the singlet to be the ground state and that this is realized in BHT chain termination related species. In contrast, in the chain propagation region of potential energy surface (PES) only one axial ligand is present, where, consequently, the dz2 orbital is singly occupied and the singlet becomes a low lying excited state. Our calculations on the LSB system place the lowest (singlet) BHT transition state (TS) 5.7 kcal/mol lower than the lowest (quintet and singlet) chain propagation TSs. Inclusion of both zero point energy and entropy corrections, namely, the Gibbs free energy, notably favors higher spin states, in which metal−ligand antibonding orbitals are occupied. This effect should be of general character for highly coordinated open shell transition metal complexes. On the Gibbs free energy surface of the LSB system, the lowest singlet BHT TS is only 1.0 kcal/mol lower than the lowest quintet chain propagation TS. In the HSB system, the axial positions are sterically destabilized. The main effect of increasing the steric bulk in axial position is the differentiation of the two ways of “saturating” the dz2 orbital, one by destabilizing it, as in singlet species, and the other by populating it with Fe's d electron, in favor of the latter. On the PES of the HSB system, the lowest BHT TS lies 17.6 kcal/mol higher than the lowest chain propagation TS. This is in agreement with the experimentally observed suppression of BHT chain termination upon increase in steric bulk.

Methane-to-Methanol Conversion by First-Row Transition-Metal Oxide Ions: ScO+, TiO+, VO+, CrO+, MnO+, FeO+, CoO+, NiO+, and CuO+

The reaction pathway and energetics for methane-to-methanol conversion by first-row transition-metal oxide ions (MO+s) are discussed from density functional theory (DFT) B3LYP calculations, where M is Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. The methane-to-methanol conversion by these MO+ complexes is proposed to proceed in a two-step manner via two transition states: MO+ + CH4 → OM+(CH4) → [TS] → OH−M+−CH3 → [TS] → M+(CH3OH) → M+ + CH3OH. Both high-spin and low-spin potential energy surfaces are characterized in detail. A crossing between the high-spin and the low-spin potential energy surfaces occurs once near the exit channel for ScO+, TiO+, VO+, CrO+, and MnO+, but it occurs twice in the entrance and exit channels for FeO+, CoO+, and NiO+. Our calculations strongly suggest that spin inversion can occur near a crossing region of potential energy surfaces and that it can play a significant role in decreasing the barrier heights of these transition states. The reaction pathway from methane to methanol is ...

Effects of electron correlation and spin projection on rotational barriers of trithiocarbenium ion [C(SH)3]+ and Radical Dication [C(SH)3]?,2+

Theoretical level dependencies are discussed of relative isomer stabilities and rotational barriers of trithiomethyl cation [C(SH)3]+ (a) and of radical dication [C(SH3)]⋅,2+ (b). Spin polarization and dynamic electron correlation are very important for the radical dictation. Removal of an electron from one of the degenerate π-HOMOs of C3h symmetric [C(SH)3]+ stabilizes the remaining π electron to such an extent that the unpaired electron is not in the HOMO of the dictation. The radial π MO's “diving below the Fermi level” facilitates strong spin polarization because of its energetic proximity to σ MOs. Projection of the first three higher spin states eliminates spin contaminations, and the terms E(PUHF(s+3))-E(UHF) and E(PMP4(s+3))-E(MP4) are discussed. The combination of annihilation of spin contamination and electron correlation is essential for the determination of relative energies and rotational barriers of the radical dication. The results obtained at this level match the results of high level QCISD(T) calculations in a near-quantitative fashion. Perturbation theory alone does not correct for spin contamination even if it is carried to full fourth order and includes triple excitations; the E(PMP4(s+3))-E(MP4) values are all negative and can exceed 5 kcal/mol in magnitude. Previous studies showed that annihilation of spin contaminations is important in regions of potential energy surfaces where σ bonds are broken (homolytic dissociation), formed (radical addition), or both (H abstraction by radical). Our findings stress that the annihilation of spin contaminations can be just as important for any process that greatly alters spin polarization and even if that process proceeds without breaking or forming of σ bonds. For comparison, density functional theory also was employed in the potential energy surface analyses. The results obtained with the B3LYP formalism were found to be less susceptible to spin contamination and resulted in rather good agreement with the best pertubation and configuration interaction results. © 1997 John Wiley & Sons, Inc. J Comput Chem 18:1023–1035, 1997

Effects of electron correlation and spin projection on rotational barriers of trithiocarbenium ion [C(SH)3] and Radical Dication [C(SH)3],2

Theoretical level dependencies are discussed of relative isomer stabilities and rotational barriers of trithiomethyl cation [C(SH)3]+ (a) and of radical dication [C(SH3)]⋅,2+ (b). Spin polarization and dynamic electron correlation are very important for the radical dictation. Removal of an electron from one of the degenerate π-HOMOs of C3h symmetric [C(SH)3]+ stabilizes the remaining π electron to such an extent that the unpaired electron is not in the HOMO of the dictation. The radial π MO's “diving below the Fermi level” facilitates strong spin polarization because of its energetic proximity to σ MOs. Projection of the first three higher spin states eliminates spin contaminations, and the terms E(PUHF(s+3))-E(UHF) and E(PMP4(s+3))-E(MP4) are discussed. The combination of annihilation of spin contamination and electron correlation is essential for the determination of relative energies and rotational barriers of the radical dication. The results obtained at this level match the results of high level QCISD(T) calculations in a near-quantitative fashion. Perturbation theory alone does not correct for spin contamination even if it is carried to full fourth order and includes triple excitations; the E(PMP4(s+3))-E(MP4) values are all negative and can exceed 5 kcal/mol in magnitude. Previous studies showed that annihilation of spin contaminations is important in regions of potential energy surfaces where σ bonds are broken (homolytic dissociation), formed (radical addition), or both (H abstraction by radical). Our findings stress that the annihilation of spin contaminations can be just as important for any process that greatly alters spin polarization and even if that process proceeds without breaking or forming of σ bonds. For comparison, density functional theory also was employed in the potential energy surface analyses. The results obtained with the B3LYP formalism were found to be less susceptible to spin contamination and resulted in rather good agreement with the best pertubation and configuration interaction results. © 1997 John Wiley & Sons, Inc. J Comput Chem 18:1023–1035, 1997

Helical region of the potential energy surface of α‐aminoisobutyric acid: A theoretical study

AbstractThe helical region of the potential energy surface of blocked α‐aminoisobutyric acid (Aib) dipeptide has been studied by using ab initio and semiempirical quantum mechanical methods, as well as force‐field‐derived methods. Depending on the method, an α‐helix or a 310‐helix is found to be the energy minimum. The conformations obtained from computations performed at the ab initio quantum mechanical level, as well as by using the AMBER force field, are in excellent agreement with X‐ray data. Semiempirical results display some important differences with regard to experimental data. On the other hand, the CVFF force field predicts no energy minimum in the helical region of the Aib potential energy surface. © 1993 John Wiley & Sons, Inc.