Analytical Potential Energy Function Research Articles

Quantum chemical study on the structure and the analytic potential energy function of PS2 (X2A1)

The equilibrium geometry of the ground electronic state of PS2 are calculated using B3LYP, B3P86, CCSD(T), and QCISD(T) methods with 6-311G** and cc-pVTZ basis sets. Compared with the experimental values and other available theoretical results, B3P86/cc-pVTZ method can give best energy calculations for PS2 molecule. Based on the principle of atomic and molecular reaction statics, the possible electronic states and their reasonable dissociation limits of PS2 molecule are determined. Then the contour potential lines of PS2 molecule is first derived in many-body expansion method form. The potential curves correctly reproduce the configurations and the dissociation energy for the PS2 molecule.

Accurate potential energy curve and spectroscopic properties of S2(b1∑g+) via extrapolation to the complete basis set limit

The potential energy curves (PECs) of the state of have been calculated using a multi-reference configuration interaction method with the Davidson correction and a series of Dunning’s correlation-consistent basis sets: aug-c.c.-pVXZ and aug-c.c.-pV(X + d)Z (X = Q, 5 and 6). The calculated PECs are subsequently extrapolated to the complete basis set limit. Such PECs are then used to deduce the analytical potential energy functions (APEFs), which show small root mean square derivations. Based on the APEFs, we have calculated the spectroscopic parameters and compared them with the experimental data available at present. By solving the Schrödinger equation numerically, we also obtain the complete set of vibrational levels, classical turning points and rotation and centrifugal distortion constants when The present results can serve as a useful reference for future experimental and dynamics studies.

Dissociation energies and potential energy functions for the ground X (1)Σ(+) and "avoided-crossing" A (1)Σ(+) states of NaH.

A direct-potential-fit analysis of all accessible data for the A (1)Σ(+) - X (1)Σ(+) system of NaH and NaD is used to determine analytic potential energy functions incorporating the correct theoretically predicted long-range behaviour. These potentials represent all of the data (on average) within the experimental uncertainties and yield an improved estimate for the ground-state NaH well depth of 𝔇e = 15797.4 (±4.3) cm(-1), which is ∼20 cm(-1) smaller than the best previous estimate. The present analysis also yields the first empirical determination of centrifugal (non-adiabatic) and potential-energy (adiabatic) Born-Oppenheimer breakdown correction functions for this system, with the latter showing that the A-state electronic isotope shift is -1.1(±0.6) cm(-1) going from NaH to NaD.

Accurate ab initio-based analytical potential energy function for S2 (ã1Δg) via extrapolation to the complete basis set limit**Project supported by the National Natural Science Foundation of China (Grant Nos. 11304185 and 11074151).

The potential energy curves (PECs) of the first electronic excited state of S2(ã1Δg) are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlation-consistent basis sets from Dunning: aug-cc-pVXZ (X = T, Q, 5, 6). In order to obtain PECs with high accuracy, PECs calculated with aug-cc-pV(Q, 5)Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function (APEF) using the extended Hartree-Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schrödinger equation numerically with the APEFs obtained at the AV6Z and the extrapolated AV(Q, 5)Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.

Analytical potential energy functions for some interhalogen diatomic electronic states

The studies of vibrational energies and analytical potential energy functions (APEFs) have been carried out for four interhalogen diatomic electronic states B(3 Π 0 +) and A(3 Π 1) of ClF, A′(3 Π 2u ) of Cl2, and the ground state X 1 Σ + of Br2 by using an improved variational algebraic energy-consistent method (VAECM(4)). The full vibrational energies, the vibrational spectroscopic constants, the force constants f n , and the expansion coefficients a n of the ECM (energy-consistent method) potential are tabulated. The VAECM(4) APEF with adjustable variational parameter λ for each electronic state is determined, and is shown to be in excellent agreement with available experimental data and has no any artificial barrier in all the calculation ranges that may appear in some other analytical potentials.

Structure and potential energy function of PuNO molecules

Density functional (B3LPY) method has been utilized to optimize the possible structures of PuN, PuO, NO and PuNO molecules using the contracted valence basis set (LANL2 DZ) for Pu atom, and the AUG-cc-pVTZ basis set for N and O atoms. It is shown that the ground state of the PuNO molecules has Cv (Pu-N-O) symmetry and the ground electronic state is 6-. The equilibrium nuclear distances for Pu-N and N-O bonds in the PuNO molecules are RPuN=0.22951 nm and RNO=0.12257 nm, and the dissociation energy is De=8.10537 eV. Furthermore, the other two metastable states of the PuNO molecules are also obtained, and the electronic states of the two configurations are 6- and A with Cv (Pu-O-N) and Cs (O-Pu-N) symmetry, respectively. Then the Murrell-Sorbie potential energy functions of the PuN, PuO and NO molecules have been simulated and the analytical potential energy function of the PuNO molecules has been derived using the many-body expansion theory. The contours of the potential energy functions reproduce exactly the most stable equilibrium structures, the two metastable state structures as well as the dissociation energy of the PuNO molecules. The molecular static reaction pathway, based on the potential energy function, is also discussed.

Molecular structure and analytical potential energy function of SeCO

The density functional method (B3P86/6-311G) is used for calculating the possible structures of SeC, SeO, and SeCO molecules. The result shows that the ground state of the SeC molecule is 1Σ, the equilibrium nuclear distance is RSeC = 0.1699 nm, and the dissociation energy is De = 8.7246 eV. The ground state of the SeO molecule is 3Σ, with equilibrium nuclear distance RSeO = 0.1707 nm and dissociation energy De = 7.0917 eV. There are two structures for the ground state of the SeCO molecule: Se=C=O and Se=O=C. The linear Se=C=O is 1Σ. Its equilibrium nuclear distances and dissociation energy are RSeC = 0.1715 nm, RCO = 0.1176 nm and 18.8492 eV, respectively. The other structure Se=O=C is 1Σ. Its equilibrium nuclear distances and dissociation energy are RCO = 0.1168 nm, RSeO = 0.1963 nm and 15.5275 eV, respectively. The possible dissociative limit of the SeCO molecule is analyzed. The potential energy function for the SeCO molecule has been obtained from the many-body expansion theory. The contour of the potential energy curve describes the structure characters of the SeCO molecule. Furthermore, contours of the molecular stretching vibration based on this potential energy function are discussed.

Rapid evaluation of individual hydrogen bonding energies in linear water chains

A model is proposed to rapidly evaluate the individual hydrogen bonding energies in linear water chains. We regarded the two O-H bonds of a water molecule as two dipoles. The magnitude of the O-H bond dipole moment can be varied due to the other water molecules’ presence. An analytic potential energy function, which explicitly contains the permanent dipole-dipole interactions, the polarization interactions, the van der Waals interactions and the covalent interactions, was therefore established. The individual hydrogen bonding energies in a series of linear water chains were evaluated via the analytic potential energy function and compared with those obtained from the CP-corrected MP2/aug-cc-pVTZ calculations. The results show that the analytic potential energy function not only can produce the individual hydrogen bonding energies as accurately as the CP-corrected MP2/aug-cc-pVTZ method, but is very efficient as well, demonstrating the model proposed is reasonable and useful. Based on the individual hydrogen bonding energies obtained, the hydrogen bonding cooperativity in the linear water chains was explored and the natures of the hydrogen bonding in these water chains were discussed.

Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates.

Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantum mechanical fragment methods share with combined quantum mechanical/molecular mechanical (QM/MM) methods the need to treat a quantum mechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantum mechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantum mechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate.

Potential energy curves and spectroscopic properties of X2Σ+ and A2Π states of 13C14N

The potential energy curves (PECs) of X2Σ+ and A2Π states of the CN molecule have been calculated with the multi-reference configuration interaction method and the aug-cc-pwCV5Z basis set. Based on the PECs, all of the vibrational and rotational levels of the 13C14N molecule are obtained by solving the Schrödinger equation of the molecular nuclear motion. The spectroscopic parameters are determined by fitting the Dunham coefficients with the levels. Both the levels and the spectroscopic parameters are in good qualitative agreement with the experimental data available. The analytical potential energy functions are also deduced from the calculated PECs. The present results can provide a helpful reference for future spectroscopy experiments or dynamical calculations of the molecule.

On the accuracy of analytical potentials: comment on ‘Accurate ab initio calculation of the Ar–CF4 intermolecular potential energy surface’

In a recent study of the Ar–CF4 intermolecular interaction potential [Shen C-C, Chang R-Y. Accurate ab initio calculation of the Ar–CF4 intermolecular potential energy surface. Mol Sim. 2010;36:1111–1122], Shen and Chang (SC) illustrated how the use of bond functions can improve the accuracy and basis-set saturation of electronic structure calculations employing perturbation and coupled-cluster theory. SC then used these ab initio data to derive analytic potential energy functions for use in chemical dynamics simulations. We critically examine these analytic potentials and comment on their usage in such simulations. Our analysis highlights the need for care and global validation when deriving analytic potential energy functions.

Intermolecular potential for binding of protonated peptide ions with perfluorinated hydrocarbon surfaces.

An analytic potential energy function was developed to model both short-range and long-range interactions between protonated peptide ions and perfluorinated hydrocarbon chains. The potential function is defined as a sum of two-body potentials of the Buckingham form. The parameters of the two-body potentials were obtained by fits to intermolecular potential energy curves (IPECs) calculated for CF4, which represents the F and C atoms of a perfluoroalkane chain, interacting with small molecules chosen as representatives of the main functional groups and atoms present in protonated peptide ions: specifically, CH4, NH3, NH4(+), and HCOOH. The IPECs were calculated at the MP2/aug-cc-pVTZ level of theory, with basis set superposition error (BSSE) corrections. Good fits were obtained for an energy range extending up to about 400 kcal/mol. It is shown that the pair potentials derived from the NH3/CF4 and HCOOH/CF4 fits reproduce acceptably well the intermolecular interactions in HCONH2/CF4, which indicates that the parameters obtained for the amine and carbonyl atoms may be transferable to the corresponding atoms of the amide group. The derived potential energy function may be used in chemical dynamics simulations of collisions of peptide-H(+) ions with perfluorinated hydrocarbon surfaces.

Ab initio study on the ground and low-lying states of BAlk (Alk = Li, Na, K) molecules.

The potential energy curves (PECs) and dipole moment functions of (1)Π, (3)Π, (1)Σ(+), and (3)Σ(+) states of BAlk (Alk = Li, Na, K) are calculated using multireference configuration interaction method and large all-electron basis sets. The effects of inner-shell correlation electron for BAlk are considered. The ro-vibrational energy levels are obtained by solving the Schrödinger equation of nuclear motion based on the ab initio PECs. The spectroscopic parameters are determined from the ro-vibrational levels with Dunham expansion. The PECs are fitted into analytical potential energy functions using the Morse long-range potential function. The dipole moment functions for the states of BAlk are presented. The transition dipole moments for (1)Σ(+) → (1)Π and (3)Σ(+) → (3)Π states of BAlk are obtained. The interactions between the outermost electron of Alk and B 2p electrons for (1)Π, (3)Π, (1)Σ(+), and (3)Σ(+) states are also analyzed, respectively.

Analytical potential energy functions for the ground and some excited states of N2

The analytical potential energy functions have been calculated for the ground state X1Σ+g and four excited electronic states a1Πg, A3Σ+u, B′3Σ−u and B3Πg of N2 molecule using the algebraic and energy-consistent methods (AM-ECM). Based on our previously published full AM vibrational energies and spectroscopic constants, the low-lying force constants fn, the expansion coefficients an and the variational parameters λ in the AM–ECM potentials are determined for these states. The computed AM–ECM potential energy curve of each state is in excellent agreement with the experimental data and better than other analytical potentials.

Direct-potential-fit analyses yield improved empirical potentials for the ground $X\,^1\Sigma _g^+$XΣg+1 state of Be2

We have performed new direct-potential-fit (DPF) analyses of the rotationally resolved A (1)Π(u)(ν'=2,3;J' =1,2)→X(1)Σ(+)(g) (ν" ∈[0,11];J" ∈[0,3]) stimulated emission pumping spectra of Be2 [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] using two quite different analytical potential energy functions that incorporate the correct theoretically known long-range behaviour in different ways. These functions are: the damped Morse/long-range potential [R. J. Le Roy, C. C. Haugen, J. Tao, and H. Li, Mol. Phys. 109, 435 (2011)], and the Chebyshev polynomial expansion potential [L. Busevica, I. Klincare, O. Nikolayeva, M. Tamanis, R. Ferber, V. V. Meshkov, E. A. Pazyuk, and A. V. Stolyarov, J. Chem. Phys. 134, 104307 (2011)]. In contrast with the expanded Morse oscillator potential determined in the original DPF analysis of Merritt et al. [Science 324, 1548 (2009)], both of these functions unambiguously support the existence of the v″ = 11 last vibrational levels which is bound by only ∼0.5 cm(-1), and they give equivalent, essentially exact predictions for this level when using the original data set which ended at v″ = 10. These empirical potentials predict an equilibrium distance of re = 2.445(5) Å and a well depth of D(e) = 934.9(0.4) cm(-1), values which agree (within the uncertainties) with the best ab initio estimates of 2.444(10) Å and 935(10) cm(-1), respectively [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)].

Molecular dynamics simulation of nanoindentation of Fe3C and Fe4C

Study of nanomechanical response of iron carbides is important because presence of iron carbides greatly influences the performance and longevity of steel components. This work contributes to the literature by exploring nanoindentation of Fe3C and tetrahedral-Fe4C using molecular dynamics simulation. The chemical interactions of iron and carbon were described through an analytical bond order inter-atomic potential (ABOP) energy function. The indentations were performed at an indentation speed of 50m/s and a repeat trial was performed at 5m/s. Load–displacement (P–h) curve for both these carbides showed residual indentation depth and maximum indentation depth (hf/hmax) ratio to be higher than 0.7 i.e. a circumstance where Oliver and Pharr method was not appropriate to be applied to evaluate the material properties. Alternate evaluation revealed Fe3C to be much harder than Fe4C. Gibbs free energy of formation and radial distribution function, coupled with state of the average local temperature and von Mises stresses indicate the formation of a new phase of iron-carbide. Formation of this newer phase was found to be due to deviatoric strain rather than the high temperature induced in the substrate during nanoindentation.

Coupled-cluster single-double theory study on the analytic potential energy function of the SeN2 radicals

The coupled-cluster single-double (CCSD) theory in combination with the quadruple correlation-consistent basis set (cc-pVQZ) of Dunning and co-workers is employed to estimate the equilibrium geometry, dissociation energy and vibrational frequencies of the SeN2 radical. The computational results show that the ground state of SeN2 has C2v symmetry and its ground electronic state is X1A1. The equilibrium parameters of the structure are RSe-N=0.1691 nm, RN-N=0.1970 nm, αN-Se-N =71.289°, and the dissociation energy is De=4.78 eV. The vibrational frequencies are ν1=326.9288 cm-1, ν2=808.0161 cm-1, and ν3=948.3430 cm-1, respectively. The whole potential curves for the ground electronic states of SeN and N2 are further scanned using the above method, the potential energy functions and relevant spectroscopic constants are then obtained by least square fitting to the Murrell-Sorbie function. Compared with other theoretical results and the experimental values, our computational results are very accurate. Then the analytic potential energy function of SeN2 is derived by many-body expansion theory. The potential curves correctly describe the configurations and the dissociation energy for the SeN2 radical.

Spin polarization and potential energy function of FeH2

Among the three methods (B3LYP, BP86 and B3LYP*) in density functional theory (DFT), the best tools for predicting the ground state of metal hydride, the B3LYP method for predicting the harmonic frequencies and geometric parameters of the ground state of FeH2 gives result in good accordance with the experimental data; so it is employed to optimize the structure of molecules FeH and FeH2 in possible geometries and multiplicities based on 6-311++g(d,p) level in searching of the structure with the lowest energy. Results show that their electronic states in the ground states are FeH(4Δ) and FeH2(5A1), supposing that the two molecules have three and four unpaired electrons respectively, with spin polarization effect, and they are paramagnetic substances, and the stable structure of molecule FeH2 is of C2v symmetry. The Murrell-Sorbie potential energy function-the sufficient analytical potential function form for biatomic molecules-with 4 parameters in molecule FeH is derived via the least square method. Their spectra data and force constants are deduced according to the results. The analytical potential energy function of FeH2 is also obtained from the many-body expansion theory, which gives the analytical potential function of triatom molecules of the single-value potential surface consisting of three parts with single body terms, two body terms, and three body terms. The deduced analytical functions for FeH2 in this paper predict successfully a global minimum stable structure of quintet FeH2 with a 4.68 eV depth potential trap, and other higher energy stable and saddle structures. This potential function predicts the balanced ground structure and the second derivative force constants of this molecule. According to the potential function of FeH2(C2v), when it is formed from H and FeH, a potential trap with its depth being 4.68 eV is excited and the complex molecule of H–Fe–H is easily formed. The reaction of Fe+H2 → HFeH is exothermic with ΔH=-0.08305 eV.

Potential energy curve study on the 3Π electronic states of GaX (X = F, Cl, and Br) molecules

The potential energy curves (PECs) of the 3Π states of GaX (X = F, Cl, and Br) molecules are calculated using the multireference configuration interaction method with a large contracted basis set aug-cc-pV5Z. The PECs are accurately fitted to analytical potential energy functions (APEFs) using the Murrell—Sorbie potential function. The spectroscopic parameters for the states are determined using the obtained APEFs, and compared with the theoretical and experimental data available presently in the literature.

Comparison of Cluster, Slab, and Analytic Potential Models for the Dimethyl Methylphosphonate (DMMP)/TiO2(110) Intermolecular Interaction

In a previous study (J. Phys. Chem. C 2011, 115, 12403), cluster models for the TiO2 rutile(110) surface and MP2 calculations were used to develop an analytic potential energy function for dimethyl methylphosphonate (DMMP) interacting with this surface. In the work presented here, this analytic potential and MP2 cluster models are compared to DFT “slab” calculations for DMMP interacting with the TiO2(110) surface and with DFT cluster models for the TiO2(110) surface. The DFT slab calculations were performed with the PW91 and PBE functionals. The analytic potential gives DMMP/TiO2(110) potential energy curves in excellent agreement with those obtained from the slab calculations. The cluster models for the TiO2(110) surface, used for the MP2 calculations, were extended to DFT calculations with the B3LYP, PW91, and PBE functionals. These DFT calculations do not give DMMP/TiO2(110) interaction energies that agree with those from the DFT slab calculations. Analyses of the wave functions for these cluster models show that they do not accurately represent the HOMO and LUMO for the surface, which should be 2p and 3d orbitals, respectively, and the models also do not give an accurate band gap. The MP2 cluster models do not accurately represent the LUMO, and that they give accurate DMMP/TiO2(110) interaction energies is apparently fortuitous, arising from their highly inaccurate band gaps. To address this issue, accurate cluster models, consisting of 7, 10, and 15 Ti-atoms and that have the correct HOMO and LUMO properties, are proposed. The Ti7-cluster model gives a DMMP + TiO2 rutile(110) potential energy curve, determined with DFT, which is consistent with those for the MP2 cluster and DFT slab calculations and with the analytic potential energy function. DFT-D calculations, with a dispersion correction, give DMMP + TiO2 rutile(110) binding energies ∼10–15 kcal/mol stronger than those obtained from pure DFT. The DMMP + TiO2 rutile(110) binding energy is found to depend on the size of the model used to represent the TiO2(110) surface. The work presented here illustrates that care must be taken in “constructing” cluster models that accurately model surfaces.