The calculation of London coefficients by the variation-perturbation method

The London coefficients for the dispersion interaction between LiLi, BeBe and LiBe are calculated by the variation-perturbation method using the whole atomic hamiltonian as H₀ and the Hartree-Fock approximation for the upper turbed wavefunction ?₀. A single excited valence configuration with optimized orbital exponents gives accurate results for Li, whereas comparable accuracy for Be is obtained when part of the valence correlation energy in the ground as well as in the excited state is accounted for through a limited configuration interaction.     

Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited ¹S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.     

The structure and energetics of TPD ground and excited states

We analyse the optimized geometric structure and energies of N,N′-diphenyl-N,N′-bis(3-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TPD) neutral molecule in ground and excited states. Ab initio calculations are performed at the Hartree–Fock (HF) or single-excitation (CIS) level with 6-31G basis set using Gaussian 98 program. We got a good qualitative agreement with the results for the neutral molecule in the ground state obtained by density functional theory methods, which were previously reported in the literature. TPD in the ground state has a pronounced twisted geometry, with both central and peripheral dihedral angles of about 40°. On the other hand, the structure of excited state is more planar, as the central dihedral angle becomes smaller. We estimated the reorganization energies associated with the optical transitions, corresponding transition dipole moments, as well as HOMO and LUMO. On the basis of ab initio calculations, we developed a semi-empirical model for the observed absorption and photoluminescence and interpreted the large Stokes shift of about 0.4 eV.     

Excitation energies,oscillator strengths,and frequency dependent polarizabilities of Be: Comparison of TDHF,EOM (second order), and MCTDHF

Low-lying excitation energies from the ground state of Be were calculated using a basis set of 61 Cartesian Gaussian functions. Three approximations were employed: the time-dependent Hartree–Fock (TDHF ), second-order equations-of-motion (EOM ), and multiconfigurational time-dependent Hartree–Fock (MCTDHF ). The TDHF excitation energies are 0.5–1.1 eV lower than experiment, and the EOM values are 0.3–1.2 eV lower than experiment, whereas the MCTDHF excitation energies deviate on the absolute average from experiment by only 0.03 eV. We found that in an MCTDHF calculation, any proper MCSCF stationary point is a good reference (i.e., initial) state, not just the ground state. Experimental values for oscillator strength are accurately known only for the 2s²X¹S → 2s2p¹P⁰ transition. The TDHF value and the MCTDHF value agree with experiment, but the EOM value does not. The agreement of the TDHF value with experiment seems to be coincidental, because for higher lying transitions the TDHF values differ by approximately a factor of two or more from the more accurate MCTDHF . Frequency independent polarizabilities, α(0), were also calculated with the TDHF , HRPA , and MCTDHF and frequency dependent polarizabilities, β(ω), were calculated with the MCTDHF . No experimental data for Be polarizabilities exist, but we expect the MCTDHF values to be among the most accurate calculations available.     

Optimization of basis sets for isoelectronic series of closed-shell atoms in Hartree-Fock-Roothaan calculations

Optimization of the nonlinear parameters (orbital exponents) of basis functions in Hartree-Fock-Roothaan calculations may be canied out with a high degree of accuracy. A scheme using second-order methods is suggested for optimization of the orbital exponents of Slater type basis functions defining the ground state of closed-shell atoms. An exact fomula is derived for calculating the partial second derivatives of energy with respect to nonlinear parameters in temis of the density matrix. In bases of isoelectronic series, the orbital exponents are shown to be the linear functions of the charge of the ion nucleus. Optimization calculations are reported for He, Be, Ne, and Mg atoms and their isoelectronic series. Translated fromZhumal Struktumoi Khimii, Vol. 41, No. 2, pp. 217–228, March–April, 2000     

Perturbation calculation of atomic correlation energies for the first transition period

Results are presented for calculations of Hartree—Fock and correlation energies for the 3dⁿ 4s² and 3dⁿ⁺¹ 4s ground and excited states of the first transition series atoms using second-order Møller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.     

Excited state properties from the equations of motion method. Application of the MCTDHF-MCRPA to the dipole moments and oscillator strengths of the A 1Π, a′3Π, a′3Σ+ and d3Δ low-lying valence states of CO

By examining the exact operator O_λ⁺ which is the solution of the equations of motion-Green's function method, we rederive expressions for non-reference (usually excited) state properties. Hence, additional useful information such as state expectation values, oscillator strengths, and frequency dependent and independent polarizabilities may be easily obtained from an equation of motion-Green's function calculation. With the multiconfigurational random phase approximation (MCRPA), which is equivalent to the multiconfigurational time dependent Hartree-Fock (MCTDHF), excitation energies, oscillator strengths, and excitation operators from the ground states are obtained for the low-lying valence (under 10 eV above the ground state) states of CO at the experimental ground state equilibrium geometry. We apply these techniques to obtain the excited state dipole moments for and oscillator strengths between the A ¹Π, a ³Π, a′ ³Σ⁺, and d ³Δ states of CO and compare our results to other calculations and experiments.     

Local pair natural orbitals for excited states

We explore how in response calculations for excitation energies with wavefunction based (e.g., coupled cluster) methods the number of double excitation amplitudes can be reduced by means of truncated pair natural orbital (PNO) expansions and localized occupied orbitals. Using the CIS(D) approximation as a test model, we find that the number of double excitation amplitudes can be reduced dramatically with minor impact on the accuracy if the excited state wavefunction is expanded in state-specific PNOs generated from an approximate first-order guess wavefunction. As for ground states, the PNO truncation error can also for excitation energies be controlled by a single threshold related to generalized natural occupation numbers. The best performance is found with occupied orbitals which are localized by the Pipek-Mezey localization. For a large test set of excited states we find with this localization that already a PNO threshold of 10(-8)-10(-7), corresponding to an average of only 40-80 PNOs per pair, is sufficient to keep the PNO truncation error for vertical excitation energies below 0.01 eV. This is a significantly more rapid convergence with the number doubles amplitudes than in domain-based local response approaches. We demonstrate that the number of significant excited state PNOs scales asymptotically linearly with the system size in the worst case of completely delocalized excitations and sub-linearly whenever the chromophore does not increase with the system size. Moreover, we observe that the flexibility of state-specific PNOs to adapt to the character of an excitation allows for an almost unbiased treatment of local, delocalized and charge transfer excited states.     

Molecular orbital studies of dinitrogen tetroxide and related molecules

Hartree-Fock LCAO MO calculations for N₂O₄ have been performed in a basis of symmetry orbitals formed from a minimal Slater basis set. Effects of rounding and truncation errors were minimized by the use of the symmetry basis, which also allowed the order or tilling of molecular orbitals to be specified independently of orbital energies. Convergence difficulties were overcome by combined use of the conjugate gradients method and Roothaan's iterative procedure; the method of steepest descents was less effective than either of these. Multicentre ‘non-NDDO’ two-electron integrals were evaluated by the gaussian expansion technique. The wavefunction obtained for the lowest state is NN antibonding, largely as a result of the filling of the 6b_1u antibonding sigma orbital in preference to the 6a_g bonding sigma orbital. There is only a small amount of NN pi-bonding. A bond energy analysis shows that the lowest state is markedly stabilized by NNO three-centre interactions.     

On ab-initio calculations of singly excited states of atoms with augmented fuess-type basis functions

It is suggested that by simply augmenting a given optimized basis set for the ground state wavefunction of an atom by Fuess-type functions, quality wavefunctions of the singly excited states of the atom could be obtained. The non-linear parameters of the Fuess-type functions are determined from the known quantum defect data. As an illustrative example we present the results for the singly excited ¹S and ¹P states of He. The calculated energies are within 0.2% of the experimental values. The dipole oscillator strengths are also calculated from both the length and the velocity formulas. The results compare well with the experimental values; the velocity form giving generally slightly closer agreement with observations.     

Approximate relativistic Hartree-Fock equations and their solution within a minimum basis set of slater-type functions

Relativistic closed-shell atoms are treated by the use of a specific approximation for the small component of the one-electron Dirac spinors. It is assumed that the large and the small component are interconnected by a parameter-dependent relation which is formally analogous to that of the one-electron system. Subject to this constraint, the total energy is varied with respect to the large components. The resulting eigenvalue equations for the large components contain only regular potential terms and reduce to the familiar Hartree-Fock equations in the limit of infinite velocity of light. Analytical solution of these approximate relativistic Hartree-Fock equations is achieved using a minimum basis set of Slater-type functions for the expansion of the radial part of the large components. Total relativistic energies, orbital energies, orbital exponents and mean radii are calculated for the ground states of He, Be, Ne, Mg, Ar, Kr Xe and Cu⁺. Dedicated to Prof. O. E. Polansky on occasion of his 60th birthday.     

Pseudodiagonalization-based wavefunction optimization with contracted planewave basis functions

Electronic structure calculations representing the molecular orbitals (MOs) with contracted planewave basis functions (CPWBFs) have been reported recently. CPWBFs are Fourier-series representations of atom-centered basis functions. The mathematical features of CPWBFs permit the construction of matrix–vector products, FC _o , involving the application of the Fock matrix, F , to the set of occupied MOs, C _o , without the explicit evaluation of F . This approach offers a theoretical speed-up of M/n over F -based methods, where M and n are the number of basis functions and occupied MOs, respectively. The present study reports methodological advances that permit FC _o -based optimization of wavefunction formed from CPWBFs. In particular, a technique is reported for optimizing wavefunctions by combining pseudodiagonalization techniques based on an exact representation of FC _o , approximate information regarding the virtual orbital energies, and direct inversion of the iterative subspace optimization schemes to guide the wavefunction to a converged solution. This method is found to speed-up wavefunction optimizations by factors of up to ~6 − 8 over F -based optimization methods while providing identical results. Further, the computational cost of this technique is relatively insensitive to basis set size, thus providing further benefits in calculations using large CPWBF basis sets. The results of density functional theory calculations show that this method permits the use of hybrid exchange-correlation (XC) functionals with a small increase in effort over analogous calculations using generalized gradient approximation XC functionals. © 2019 Wiley Periodicals, Inc.     

Limited GSMO CI and ESMO CI study of electronic transitions in FNO

Limited CI calculations of vertical excitation energies and oscillator strengths have been performed in the ground state molecular orbital basis set (GSMO) and the excited state ones (ESMO). The absorption and emission spectrum of FNO is rediscussed on the basis of these calculations. The relaxation energy of excited states and the convergence of the CI expansion in the GSMO and ESMO basis sets is discussed.     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

A theoretical study of biphenylene in its ground and excited states

Molecular orbital studies of biphenylene in its geometrically optimized ground and triplet states have been performed at the INDO level. These calculations, together with CNDO/S, specially parameterized CNDO and calculations involving empirical force constants, are used to estimate the relative energies and geometries of the T₁ and S₁ excited states of biphenylene. The relation of these geometry changes on excitation to the unusual photophysical properties of biphenylene are discussed.     

The calculation of ionization energies by perturbation,configuration interaction and approximate coupled pair techniques and comparisons with green's function methods for Ne,H2O and N2

The vertical valence ionization potentials of Ne, H₂O and N₂ have been calculated by Rayleigh-Schrödinger perturbation and configuration interaction methods. The calculations were carried out in the space of a single determinant reference state and its single and double excitations, using both the N and N - 1 electron Hartree-Fock orbitals as hole/particle bases. The perturbation series for the ion state were generally found to converge fairly slowly in the N electron Hartree-Fock (frozen) orbital basis, but considerably faster in the appropriate N - 1 electron RHF (relaxed) orbital basis. In certain cases, however, due to near-degeneracy effects, partial, and even complete, breakdown of the (non-degenerate) perturbation treatment was observed. The effects of higher excitations on the ionization potentials were estimated by the approximate coupled pair techniques CPA′ and CPA″ as well as by a Davidson type correction formula. The final, fully converged CPA″ results are generally in good agreement with those from PNO-CEPA and Green's function calculations as well as experiment.     

Beryllium Atom Mediated Dinitrogen Activation via Coupling with Carbon Monoxide

The reactions of laser‐ablated beryllium atoms with dinitrogen and carbon monoxide mixtures form the end‐on bonded NNBeCO and side‐on bonded (η²‐N₂)BeCO isomers in solid argon, which are predicted by quantum chemical calculations to be almost isoenergetic. The end‐on bonded complex has a triplet ground state while the side‐on bonded isomer has a singlet electronic ground state. The complexes rearrange to the energetically lowest lying NBeNCO isomer upon visible light excitation, which is characterized to be an isocyanate complex of a nitrene derivative with a triplet electronic ground state. A bonding analysis using a charge‐ and energy decomposition procedure reveals that the electronic reference state of Be in the NNBeCO isomers has an 2s⁰2p² excited configuration and that the metal‐ligand bonds can be described in terms of N₂→Be←CO σ donation and concomitant N₂←Be→CO π backdonation. The results demonstrate that the activation of N₂ with the N?N bond being completely cleaved can be achieved via coupling with carbon monoxide mediated by a main group atom.     

Theoretical calculation about the valence and Rydberg excited states of hydrogen cyanide

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.     

Molecular calculations for HeH<Superscript>+</Superscript> with two-center correlated orbitals

A two-center correlated orbital approach was used to calculate the electronic ground state energy for the HeH⁺ molecular ion. The wavefunctions were constructed from the exact solution of the Schrödinger equation for the HeH⁺⁺ problem in prolate-spheroidal coordinates taken together with a Hylleraas type correlation factor. With a simple single term wavefunction, we obtained ground state energy of ?2.95308691 hartree without any variational parameters in the calculation. When a two-configuration-state wavefunction was used and effective charges were allowed to be adjusted, we found an energy of ?2.97384868 hartree, which is to be compared with ?2.97869074 hartree obtained by an 83 term configuration interaction wavefunction or ?2.97364338 hartree by an ab initio calculation (at the MP4(SDQ)/6-311++G(3df, 3dp) level) using the well-known “canned” code.