Complete Potential Energy Curves Research Articles

High Accuracy Ab Initio Potential Energy Curves and Dipole Moment Functions for the X1Σ+ and a3Π Spin States of the CF+ Diatomic Molecule.

Potential energy curves and dipole moment functions constructed using high-accuracy ab initio methods allow for an in-depth examination of the electronic structure of diatomic molecules. Ab initio computations serve as a valuable complement to experimental data, offering insights into the nature of short-lived molecules such as those encountered within the interstellar medium (ISM). While laboratory experiments provide critical groundwork, the ISM's conditions often permit longer lifetimes for lower stability molecules, enabling unique observations. The CF+ diatomic molecule is one such molecule that has been observed spectroscopically in the ISM. Previous experimental and theoretical work have examined different spectroscopic aspects of the CF+ molecule, but the development of newer, more complete potential energy curves and dipole moment functions allows for even greater insight. We constructed both potential energy curves and dipole moment functions for the ground X1Σ+ and first excited a3Π states of CF+ for both the 12C and 13C isotopologues. The potential energy curves were constructed using coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set limit with corrections from full triple, quadruple, quintuple, and hextuple excitations within a finite-basis coupled cluster wave function as well as corrections from full configuration interaction and relativistic effects. Rovibrational wave functions were calculated using a vibrational Hamiltonian matrix, which moves beyond the harmonic oscillator approximation. The equilibrium bond length, vibrational constant, and rotational constant were reproduced to within 0.00013 Å, 0.28 cm-1, and 0.00045 cm-1, respectively, of experimental values. Experimental transition energies from rovibrational spectra were reproduced with an error of no larger than 0.63 cm-1. The triplet excited state (a3Π) was found to have a longer equilibrium bond length at 1.21069 Å, a vibrational constant of 1611.29 cm-1, and a rotational constant of 1.56376 cm-1. Rovibrational line lists for the 12C and 13C isotopologues for both the X1Σ+ and the excited a3Π states were generated.

Parametrisation of the optimised effective potential method based on the Coulson–Fischer wave function for excited states

ABSTRACT This article further develops the Coulson–Fischer formalism in conjunction with the optimised effective potential method [V.N. Glushkov and S. Wilson, Molec. Phys. 110, 149 (2012)] to incorporate both exchange and static correlation effects for excited states having the same symmetry as the ground state. By using this formalism, we compute complete potential energy curves for the ground and first excited states of the molecule and the isoelectronic heteronuclear ion. Effective potentials are generated in according to a novel density functional theory [A.K. Theophilou, J. Chem. Phys. 149, 074104 (2018)] in which the Kohn–Sham (KS) like potential has spherical symmetry around each nucleus. In this way, the inconsistencies of standard density functional theory concerning the asymmetry of the KS potential are remedied. In our implementation, an effective potential which satisfies this requirement is expressed as a direct mapping of the external potential. Different approximations for the effective potentials are investigated. It is shown that applications of the proposed formalism support good agreement with the exact Coulson–Fischer theory for both the ground and first excited state potential energy curves and thus a qualitatively correct description of dissociation.

Ab initio Potential Energy Curve for the Ground State of Beryllium Dimer.

This work concerns ab initio calculations of the complete potential energy curve and spectroscopic constants for the ground state X1Σ g+ of the beryllium dimer, Be2. High accuracy and reliability of the results is one of the primary goals of the paper. To this end, we apply large basis sets of Slater-type orbitals combined with high-level electronic structure methods including triple and quadruple excitations. The effects of the relativity are also fully accounted for in the theoretical description. For the first time the leading-order quantum electrodynamics effects are fully incorporated for a many-electron molecule. Influence of the finite nuclear mass corrections (post-Born-Oppenheimer effects) turns out to be completely negligible for this system. The predicted well-depth ( De = 934.6 ± 2.5 cm-1) and the dissociation energy ( D0 = 807.7 cm-1) are in a very good agreement with the most recent experimental data. We confirm the existence of the weakly bound twelfth vibrational level [Patkowski et al. Science 2009, 326, 1382] that it lies just below the onset of the continuum.

Low-Lying Electronic States of AlZn Calculated by MRCI+Q Method

Some low-lying electronic states of AlZn have been studied by the ab initio calculation method of multireference configuration interaction (MRCI). The complete potential energy curves (PECs) of the...

The Coulson–Fischer wave functions for the ground and excited states of H2 and HeH+: parametrisation using distributed Gaussian basis sets

Coulson–Fischer wave functions are used to determine complete potential energy curves for the X1Σ+g ground state of the H2 molecule and for the first excited state (EF1Σ+g) having the same symmetry. The Coulson–Fischer orbitals are parametrised by expansion in distributed Gaussian basis sets of s-type functions. The exponents of the Gaussian functions are generated by using an even-tempered prescription. An anharmonic model is used to locate the basis functions along the internuclear axis. Sequences of basis sets are used to reduce the basis set truncation error to the sub-μhartree level. Equations are derived to determine the generalised Coulson–Fischer orbitals for the excited state which ensure that orthogonality conditions with respect to the ground state are satisfied. Potential energy curves are also calculated using smaller basis sets for which both exponents and basis function positions are determined by invoking the variation principle. The results of calculations for the isoelectronic heteronuclear HeH+ ion are also reported. The potential energy curves obtained in the present study are compared with literature values for both H2 and HeH+.

First principles exploration of NiO and its ions NiO+ and NiO−

We present a high level ab initio study of NiO and its ions, NiO(+) and NiO(-). Employing variational multireference configuration interaction (MRCI) and single reference coupled-cluster methods combined with basis sets of quintuple quality, 54, 20, and 10 bound states of NiO, NiO(+), and NiO(-) have been studied. For all these states, complete potential energy curves have been constructed at the MRCI level of theory; in addition, for the ground states of the three species core subvalence (3s(2)3p(6)∕(Ni)) and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The agreement with experiment is in the case of NiO good, but certain discrepancies that need further investigation have arisen in the case of the anion whose ground state remains computationally a tantalizing matter. The cation is experimentally almost entirely unexplored, therefore, the study of many states shall prove valuable to further investigators. The ground state symmetry, bond distances, and binding energies of NiO and NiO(+) are (existing experimental values in parenthesis), X(3)Σ(-)(X(3)Σ(-)), r(e) = 1.606 (1.62712) Å, D(0) = 88.5 (89.2 ± 0.7) kcal/mol, and X(4)Σ(-)(?), r(e) = 1.60(?) Å, D(0) = 55 (62.4 ± 2.4) kcal/mol, respectively. The ground state of NiO(-) is (4)Σ(-) (but (2)Π experimentally) with D(0) = 85-87 (89.2 ± 0.7) kcal/mol.

Electronic Structure and Bonding of Cobalt Monoxide, CoO, and Its Ions CoO+ and CoO–: An Ab Initio Study

We present a systematic and high-level ab initio study of CoO and its ions, CoO(+) and CoO(-). Employing variational multireference (MRCI) and single-reference coupled-cluster methods combined with basis sets of quintuple quality, we have calculated 50, 31, and 7 bound states for CoO, CoO(+), and CoO(-), respectively. For all these states, complete potential energy curves have been constructed at the MRCI level of theory, whereas for a few low-lying states core subvalence and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The ground states of CoO, CoO(+), and CoO(-) are X(4)Δ, X(5)Δ, and X(5)Δ, respectively, the latter established for the first time. The CoO is quite ionic with a Co to O Mulliken charge transfer of ~0.6 electrons and a dipole moment μ(X(4)Δ) = 4.5 ± 0.1 D. The overall agreement between theory and experiment is good, but there are also important deviations. Despite the seeming simplicity of these diatomic species, reliable results can only be obtained at a high level of theory.

First principles study of the ground and excited states of FeO, FeO+, and FeO−

Through a variety of highly correlated methods combined with large basis sets we have studied the electronic structure of FeO, FeO(+), and FeO(-). In particular, we have constructed complete potential energy curves for 48, 24, and 4 states for the FeO, FeO(+), and FeO(-) species, respectively, at the multireference level of theory. For all states examined we report energetics, common spectroscopic parameters, and dipole moments. Overall our results are in good agreement with experiment, but we have encountered as well interesting differences between experiment and theory deserving further investigation.

Electronic Structure and Bonding of the Early 3d-Transition Metal Diatomic Oxides and Their Ions: ScO0,±, TiO0,±, CrO0,±, and MnO0,±†

The diatomic neutral oxides and their ions, MO(0,+/-), M = Sc, Ti, Cr, and Mn, have been studied through multireference configuration interaction and coupled-cluster methods. With the purpose to paint a more comprehensive and detailed picture on these not so easily tamed systems, we have constructed complete potential energy curves for a large number of states of all MO(0,+/-)'s reporting structural and spectroscopic properties. Our overall results are in very good agreement with the, in general limited, experimental data. The always difficult to be pinpointed "nature of the chemical bond" becomes more recondite for these highly open ionic-covalent species. We have tried to give some answers as to the bonding interactions using simple valence-bond-Lewis diagrams in conjunction with Mulliken populations and the symmetry of the in situ atoms. It is our belief that, particularly for this kind of molecule, molecular orbital concepts are of limited help for a consistent rationalization of the bond formation.

Molecular electric dipole moments using the GVVPT2 variant of multireference perturbation theory

A Lagrangian approach for electric dipoles within second order Generalized Van Vleck Perturbation Theory (GVVPT2) is presented. The Lagrangian approach for this response property requires that only one, perturbation-independent, set of simultaneous equations needs to be solved. The presented formulation is demonstrated numerically on several well studied molecules at their equilibrium bond lengths and on the complete potential energy curves of the ground and first excited states of LiH. Numerical corroboration of the expected continuity for molecular properties for the GVVPT2 method is observed. It is seen that the GVVPT2 electric dipoles are in good agreement with experiment and with other high accuracy theoretical methods.

The Coulson–Fischer wave function: parametrisation using distributed Gaussian basis sets

A ‘generalised’ Coulson–Fischer wave function, in which the orbitals are approximated by means of a linear expansion in distributed Gaussian s-type basis functions, is used to determine a complete potential energy curve for the ground state of the hydrogen molecule by ab initio methods. A distributed basis set is developed in which both the positions and the exponents of Gaussian s-type functions are determined by invoking the variation principle. This basis set supports a sub-μhartree level of accuracy and provides a reference with respect to which calculations can be assessed, where the exponents are generated using an even-tempered prescription and an anharmonic model is employed to distribute the basis functions along the internuclear axis. This basis set also supports energy expectation values of a sub-μhartree level of accuracy.

An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H2S

Large, correlation-consistent basis sets have been used to very closely approximate the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set potential energy curves of several prototype nonbonded complexes, the sandwich, T-shaped, and parallel-displaced benzene dimers, the methane-benzene complex, the H2S-benzene complex, and the methane dimer. These benchmark potential energy curves are used to assess the performance of several methods for nonbonded interactions, including various spin-component-scaled second-order perturbation theory (SCS-MP2) methods, the spin-component-scaled coupled-cluster singles and doubles method (SCS-CCSD), density functional theory empirically corrected for dispersion (DFT-D), and the meta-generalized-gradient approximation functionals M05-2X and M06-2X. These approaches generally provide good results for the test set, with the SCS methods being somewhat more robust. M05-2X underbinds for the test cases considered, while the performances of DFT-D and M06-2X are similar. Density fitting, dual basis, and local correlation approximations all introduce only small errors in the interaction energies but can speed up the computations significantly, particulary when used in combination.

Benzene Dimer: Dynamic Structure and Thermodynamics Derived from On-the-Fly ab initio DFT-D Molecular Dynamic Simulations.

The dynamic nature of the benzene dimer was explored by on-the-fly molecular dynamics simulations based on the DFT-D method covering the dispersion energy. An all-electron DFT was performed at the BLYP/TZVP level. The parameters in the dispersion correction term were fitted to mimic the benchmark CCSD(T)/complete basis set limit potential energy curves for both the parallel-displaced (PD) and T-shaped (TS) structures of the dimer exactly. A dynamic description is important at temperatures above 10 K, where interconversion between the TS and PD structures is possible and a mixture of these two species exists. The higher the temperature, the more dominant the TS structure because of a favorable entropic contribution to the free energy. An analysis of the TS structures revealed that the symmetric c2v structure, a low-lying transition state, is practically not populated and that the tilted cs TS structure is prevalent. This finding is in perfect agreement with infrared spectroscopy.

Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C(2) molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.

Analytical Potential Energy Function, SpectroscopicConstants and Vibrational Levels for A1Σ+u State ofDimer 7Li2

The symmetry-adapted-cluster configuration-interaction method isused to investigate the spectroscopic properties of 7Li2(A1Σ+u) over the internuclear distance ranging from 2.4a0 to37a0. The complete potential energy curves are calculated at numbers ofbasis sets. All the ab initio calculated points are fitted to theanalytic Murrell–Sorbie function and then employed to compute thespectroscopic constants. By comparison, the spectroscopic constants reproducedby the potential attained at D95(3df,3pd) are found to be very close to theexperiments, and the values (Te, De, Re, ωe,ωeχe, αe and Be) are of 1.732 93 eV,1.161 36 eV, 0.313 27 nm, 251.95 cm−1, 1.623 cm−1,0.005 35 cm−1, and 0.490 cm−1, respectively. With the potentialobtained at D95(3df,3pd), the totally 75vibrational states are found when J = 0. The vibrational levels, the classicalturning points and the inertial rotation constants of the first 68vibrational states are calculated for the first time and compared with theavailable measurements. Good agreement is obtained. The centrifugaldistortion constants of the first 32 vibrational states are also reportedfor the first time. The reasonable dissociation limit for7Li2(A1Σ+u) is deduced using thecalculated results at present.

Ab initiocalculations on thea3Σ+ustate properties of dimer7Li2

The comparison between single-point energy scanning (SPES) and geometry optimization (OPT) in determining the equilibrium geometry of the a3Σ+u state for 7Li2 is made at numerous basis sets such as 6-311++G(2df), cc-PVTZ, 6-311++G(2df,p), 6-311G(3df,3pd), 6-311++G(2df,2pd), D95(3df,3pd), 6-311++G, DGDZVP, 6-311++G(3df,2pd), 6-311G(2df,2pd), D95V++, CEP-121G, 6-311++G(d,p), 6-311++G(2df,pd) and 6-311++G(3df,3pd) in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction (SAC/SAC-CI) method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at these sets over a wide internuclear distance range from about 3.0a0 to 37.0a0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at cc-PVTZ, the spectroscopic data (Te, De, D0, ωe,ωeχe, and Be) are computed and they are 1.006 eV, 338.71 cm−1, 307.12 cm−1, 64.88 cm−1, 3.41 cm−1, 0.0187 cm−1 and 0.279 cm−1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant (Bv) and six centrifugal distortion constants (Dv Hv, Lv, Mv, Nv and Ov) are calculated. The scattering length is calculated to be −27.138a0, which is in good accord with the experimental data.

A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr

We present the initial implementation of a determinant-based general-order coupled cluster method which fully accounts for relativistic effects within the four-component framework. The method opens the way for the treatment of multi-reference problems through a state-selective expansion of the model space. The evaluation of the coupled cluster vector function is carried out via relativistic configuration interaction expansions. The implementation is based on a large-scale configuration interaction technique, which may efficiently treat long determinant expansions of more than 108 terms. We demonstrate the capabilities of the new method in calculations of complete potential energy curves of the HBr molecule. The inclusion of spin–orbit interaction and higher excitations than coupled cluster double excitations, either by multi-reference model spaces or the inclusion of full iterative triple excitations, lead to highly accurate results for spectral constants of HBr.

Accurate Analytic Potential Energy Function andSpectroscopic Study for G1Πg State of Dimer 7Li2

The reasonable dissociation limit for theG1Πg state of dimer 7Li2 is determined.The equilibrium internuclear distance,dissociation energy, harmonic frequency, vibrationalzero energy, and adiabatic excitation energy are calculated usinga symmetry-adapted-cluster configuration-interaction method incomplete active space in Gaussian03 program package at such numerousbasis sets as 6-311++G, 6-311++G(2df,2pd), 6-311++G(2df,p), cc-PVTZ,6-311++G(3df,3pd), CEP-121G, 6-311++G(2df,pd), 6-311++G(d,p),6-311G(3df,3pd),D95(3df,3pd), 6-311++G(3df,2p), 6-311++G(2df), 6-311++G(df,pd)D95V++, and DGDZVP. The complete potential energy curves are obtainedat these sets over a wide internuclear distance range and haveleast squares fitted to Murrell–Sorbie function. The conclusionshows that the basis set 6-311++G(2df,p) is a most suitable onefor the G1Πg state. At this basis set,the calculated spectroscopic constants Te, De, E0,Re, ωe, ωeχe, αe,and Be are of 3.9523 eV, 0.813 06 eV, 113.56 cm−1,0.320 15 nm, 227.96 cm−1, 1.6928 cm−1,0.004 436 cm−1, and 0.4689 cm−1,respectively, which are in good agreementwith measurements whenever available. Thetotal 50 vibrational levels and corresponding inertial rotationconstants are for the first time calculated and compared withavailable RKR data. And good agreement with measurements is obtained.

Spin‐Orbit Ab Initio Investigation of the Ultraviolet Photolysis of Diiodomethane

The UV photodissociation (<5 eV) of diiodomethane (CH(2)I(2)) is investigated by spin-orbit ab initio calculations. The experimentally observed photodissociation channels in the gas and condensed phases are clearly assigned by multi-state second-order multiconfigurational perturbation theory in conjunction with spin-orbit interaction through complete active space-state interaction potential energy curves. The calculated results indicate that the fast dissociations of the first two singlet states of CH(2)I(2) and CH(2)I--I lead to geminate-radical products, CH(2)I (.)+I((2)P(3/2)) or CH(2)I (.)+ I*((2)P(1/2)). The recombination process from CH(2)I--I to CH(2)I(2) is explained by an isomerization process and a secondary photodissociation reaction of CH(2)I--I. Finally, the study reveals that spin-orbits effects are significant in the quantitative analysis of the electronic spectrum of the CH(2)I--I species.

Investigation of analytic potential energy function, harmonic frequency and vibrational levels for the 23Σ+g state of spin-aligned dimer 7Li2

Using the symmetry adapted cluster/symmetry adapted cluster-configuration interaction(SAC/SAC-CI) method in Gaussian03 program package, the equilibrium geometry of the 23Σ+g state of spin-aligned dimer 7Li2 is calculated at a number of basis sets. At the same time, the single-point energy scanning calculation is also made at each basis set near the equilibrium internuclear separation obtained by the geometry optimization so as to attain the more accurate result. A disagreement between the result obtained by the geometry optimization and that obtained by the single-point energy scanning calculation is found. Our analysis shows that the result obtained by the single-point energy scanning calculation should be more reasonable. We drew the conclusion that the basis sets 6-311++G(3df,3pd), 6-311++G(2df,2pd) and 6-311++G(2df,pd) are the most suitable ones for the 23Σ+g state calculation. The complete potential energy curve is further scanned at SAC-CI/6-311++G(3df,3pd) level of theory for the state over the internuclear separation range from 2.5a0 to 37a0, then a least squares fit to the Murrell-Sorbie function is made, at last the harmonic frequency is calculated, which is in good agreement with other theoretical results. At the same time, the same calculations are made for the ground state for comparison. In addition, we have also calculated the vibrational levels and the classical turning points.