Energy Functions For Diatomic Molecules Research Articles

Extended improved multiparameter exponential‐type potential energy function for diatomic molecules

AbstractBased on the improved multiparameter exponential‐type potential (IMPET), an extended IMPET (EIMPET) potential has been suggested to reduce the discrepancy between the calculated and experimental values, improving the accuracy near the equilibrium and in the asymptotic region. The average fitting deviation δav and Root‐Mean‐Square (RMS) error is used to evaluate the performance of the potential which generates potential energy curves (PECs) and vibrational energy levels for ClF‐A(3Π1), CP‐X2Σ+, ICl‐X1Σ+, IBr‐X1Σ+, CO‐X1Σ+, and 6Li2‐X1Σ+ molecules that agree better with the Rydberg‐Klein‐Rees (RKR) data than Morse, Huxley‐Murrell (HM) and IMPET potentials. This work provides a reference for the construction and improvement of potential energy functions for diatomic molecules.

A variationally improved Hulburt-Hirschfelder analytical potential energy function for diatomic molecules

In this paper, a variationally improved Hulburt-Hirschfelder (VIHH) analytical potential energy function (APEF) is presented and tested. The VIHH potential is composed of the remedy function and the improved Hulburt-Hirschfelder (IHH) APEF which possesses the same explicit parameters () with VIHH potential. Potential energy curves (PECs) for the ground electronic states of HI, HBr and KLi molecules have been modeled by the VIHH analytical potential, and it suggests that the VIHH potential is in good agreement of Rydberg-Klein-Rees (RKR) potential points and is superior to the original Hulburt-Hirschfelder (HH) potential, IHH potential and Morse potential, especially in the dissociation and the long-range region. The vibrational energy levels for the ground electronic state of the HI, HBr, and KLi molecules are obtained by numerically solving the radial Schrödinger equation using the LEVEL program for the case of the Morse potential, HH potential, IHH potential and the VIHH potential functions. The comparison for both vibrational energy levels and VIHH potential functions shows better agreement with the experimental data than the other potential functions. Comparing with IHH potential, the VIHH potential which included the remedy function has better physical behavior in the long-range region and the is effective for vanishing the invalid barrier.

A new modified Morse potential energy function for diatomic molecules

A new modified Morse potential is introduced to describe the vibrational motion of diatomic molecules. The vibrational energy eigenvalues for the ground state of the H2 and N2 molecules are obtained by numerically solving the time-independent Schrödinger equation using a Python program and the Matrix Numerov method for the case of the Morse potential, Hulbert-Hirschfelder potential, and the modified Morse potential functions. The comparison of the vibrational energy eigenvalues and the anharmonicity constant obtained for the modified Morse potential function reveals better agreement with the experimental data than the other potential functions. Also, the proposed modified Morse potential function fits the RKR potential energy curve more closely than the Morse potential function and Hulbert-Hirschfelder potential function, especially in the region where the potential extends to near the dissociation limit.

On the equivalence of the Badawi–Bessis–Bessis, Wei and Tietz potential energy functions for diatomic molecules

It is found that the general potential energy expression introduced by Badawi et al for several empirical potential energy functions that is conventionally defined in terms of five parameters, actually only has four independent parameters. It is demonstrated exactly that the Badawi–Bessis–Bessis potential is equivalent to the well-known Tietz potential model for diatomic molecules. When parameter a in the Badawi–Bessis–Bessis potential function has the values 0, +1 and −1, the Badawi–Bessis–Bessis potential becomes the standard Morse, Rosen–Morse and Manning–Rosen potentials, respectively.

Equivalence of the three empirical potential energy models for diatomic molecules

It is found that the Manning–Rosen potential, Schiöberg potential and Deng–Fan potential are the same solvable empirical potential energy function for diatomic molecules. We calculate the anharmonicity ωexe and vibrational rotational coupling parameter αe for 16 molecules by choosing the experimental values of the dissociation energy De, equilibrium bond length re and vibrational frequency ωe as inputs. The results show that the Manning–Rosen potential, Deng–Fan potential and Schiöberg potential are not better than the traditional Morse potential.

An extended Lennard-Jones potential energy function for diatomic molecules: Application to ground electronic states

A new simple analytical diatomic potential energy function that can be considered an extension of the prototypical Lennard-Jones model is proposed and tested. Five- and six-parameter models are considered and these can be easily constructed from widely available low-order vibrational–rotational constants and the dissociation energy. Accuracy tests are carried out on the ground electronic states of sixteen diatomic molecules. The proposed six-parameter function is found to be more accurate than other available few-parameter analytical models for the diatomic potential energy, and has accuracy comparable to that of modern high-level ab initio functions.

Determination of [formula omitted] and [formula omitted] from potential energy functions for diatomic molecules

For comparing three-parameter potential energy functions near the potential minimum, r e , k e and ω e x e have been used to determine the potential parameters and thence to calculate α e and ω e y e of homonuclear diatomic molecules. Detailed results are presented for α e and ω e y e for the Morse, Rydberg and Varshni potentials. Possible errors in certain spectroscopic constants of some molecules are pointed out.

New empirical potential energy function for diatomic molecules

A new empirical potential energy function for diatomic molecules, which has the simple form of V(r)=(arb+m)/(1−enr) is introduced, where a,b,m and n are variational parameters of the function. To obtain the parameters of this function, it was fitted to the points, which were obtained previously from the RKR calculations for a wide range of diatomic molecules in both their ground and excited states. The reliability of the proposed function was checked by calculation of some spectroscopic constants such as bond length (Re), dissociation energy (De), force constant (Ke), rotational constant (Be), vibrational frequency (ωe), anharmonicity constant (ωexe) and vibration–rotation coupling constant (αe) for these molecules. For ωexe and αe the results were compared with those of the Morse, Rosen–Morse, Rydberg, Pöschl–Teller, Linnett, Frost–Muslin, Varshni, Lippincott and Rafi functions. Our results are consistent with or have less error than those of the above-mentioned functions.

New empirical potential energy function for diatomic molecules

A new empirical potential energy function for diatomic molecules, which has the simple form of V( r)=( ar b + m)/(1−e nr ) is introduced, where a, b, m and n are variational parameters of the function. To obtain the parameters of this function, it was fitted to the points, which were obtained previously from the RKR calculations for a wide range of diatomic molecules in both their ground and excited states. The reliability of the proposed function was checked by calculation of some spectroscopic constants such as bond length ( R e), dissociation energy ( D e), force constant ( K e), rotational constant ( B e), vibrational frequency ( ω e), anharmonicity constant ( ω e x e) and vibration–rotation coupling constant ( α e) for these molecules. For ω e x e and α e the results were compared with those of the Morse, Rosen–Morse, Rydberg, Pöschl–Teller, Linnett, Frost–Muslin, Varshni, Lippincott and Rafi functions. Our results are consistent with or have less error than those of the above-mentioned functions.

Long-range properties of the generalized potential energy function for diatomic molecules. Application to the ground state of SiF +

The properties of the long-range part of the previously suggested generalized potential energy function and Coulomb-subtracted generalized potential energy function have been investigated. It is demonstrated that these empirical functions can correctly reproduce the long-range part of the diatomic potential, if certain relationships connecting the parameters of the functions are realized. The ground-state potential of SiF + with correct long-range behavior has been calculated with the help of derived relationships. The generalized potential energy function obtained for SiF + contains eleven parameters, yields the experimental value of the dissociation energy, reproduces the dispersion coefficient C 4 and the set of molecular constants R e, B e, ω e and a i ( i = 1, …, 5).

The generalized potential energy function for diatomic molecules

A new generalized potential energy function is suggested for diatomic molecules. The Dunham, Simons—Parr—Finlan, Thakkar and Ogilvie potentials are shown to be particular cases of the generalized potential energy function. It is also shown that the function suggested may reproduce the path of the potential curve with sufficient accuracy even for the cases of small expansion length.

A general potential energy function for diatomic molecules

A new and flexible function that is a valid representation of the potential energy of diatomic molecules within the entire range of accessible internuclear separations is proposed. This function is shown to be a member of a family of functions that includes previous polynomial functions having more restricted validity. Methods of generating the coefficients (parameters) of the new function are described, and tables of these parameters for a selection of molecules, including some ground and some excited electronic states,are presented.

Use of the virial theorem in construction of potential energy functions for diatomic molecules. 3. Improved potentials from the normalized kinetic field functions

Use of the virial theorem in construction of potential energy functions for diatomic molecules. 3. Improved potentials from the normalized kinetic field functions

Use of the virial theorem in construction of potential energy functions for diatomic molecules

The nth-order diatomic potential energy functions W(T)n and W(V)n are constructed, by the integration of the virial theorem −W−R[dW/dR]=T and 2W+R[dW/dR]=V, respectively, using the nth-order truncations of the perturbational λ=1−(Re/R) power series expansions of the kinetic (T) and potential (V) parts of the vibrational potential. The resulting W(T)n potential is a linear combination of terms R−1, R−2,⋅⋅⋅,R−n, and (lnR)/R; the W(V)n potential is a linear combination of terms R−1, R−2,⋅⋅⋅,R−n, and (lnR)/R2. For n=2, predictions of W(T)2, W(V)2, and also the generalized two-logarithmic second-order potential W(T,V)2 [including both the (lnR)/R and (lnR)/R2 terms] are compared with experiment and the results obtained from the Morse and Clinton potentials. Second-order logarithmic potentials for the ground states of H2, CO, and HF are given and compared with the Kol/os and Wolniewicz potential for H2 and the RKR classical turning points for CO and HF. Convergence properties of the W(T)n and W(V)n potentials are tested using the ground state of H2 as an example.

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n2:X1gS g + ,B3πg,A3 gSu,C3u,B′3 gSu.a1 πg, a′gS u − ,Ω1δuN 2 + :X2 gS g gS +A2 π,C2 gS u + ,B2 gS u + CO:X1gS+,a3 π, a′3 gSu,e3 gS−,d3gD1,A1π CO+:X2gS+,A2 π,B2gS+ O2:X3gS g − ,B3 gSu,c1 gS u − ,b1gS g s ,a1 δg,c3 δu O 2 + :X2πg,A2 πg, a1 πg,b4 gS g − A program for numerically integrating the radial Schrodinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.

A study of some potential energy functions for diatomic molecules

AbstractA detailed study of the performance of the Morse, the Hulburt‐‐Hirschfelder and the Lippincott potential energy functions has been carried out by comparing them with the Rydberg–Klein–Rees potential energy curves for a number of electronic states of various diatomic molecules. Further, by employing the above potential energy functions, the radial Schrödinger equation has been solved for the vibrational energy levels, G(v), and the vibrational wave functions, ψv. The latter have been employed to determine the rotational constants, Bv, for the individual vibrational energy levels. Then the molecular constants, we, wexe, weye, Be, αe and γe for the various electronic states, have been computed by using the values of G(v) and Bv. A comparison of the molecular constants derived in this manner with the experimental ones reveals better agreement, in most cases, than that reported by previous workers.

The frequencies, anharmonicities, and apparent dissociation energies of some (C–H) bonds

The vibrational frequencies of the fundamentals and of the first and second overtones of fifteen molecules each containing one (C–H) bond have been measured for liquid and solution (CCl4) states in the infrared region. Consideration is given to the medium effect on the frequencies in deducing the vibrational anharmonicity. Dissociation energies are deduced for the various (C–H) bonds on the basis of potential functions due to Morse and to Lippincott: these are compared with the thermochemical values and the data discussed. Individual (C–H) bonds do not generally conform well to the simple energy functions for diatomic molecules.

Rydberg Potential Energy Function for Diatomic Molecules as Extended to Polyatomic Species and Activated Complex

Rydberg Potential Energy Function for Diatomic Molecules as Extended to Polyatomic Species and Activated Complex

A New Potential Energy Function for Diatomic Molecules

A new potential energy function for diatomic molecules U ( r )= D e + D e {( a + b ) e -2α r - b e -α r }(1+ c e -α r ) -2 , is proposed. This function has the advantage that the Schrodinger equation can be solved exactly. The parameters a , b , c and α can be determined so as to fit calculated values of D e , k e , r e and β e to the observed ones. As to ω e x e , agreement with the observation is not bad, whereas the Morse curve does not give satisfactory result for several molecules.

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