Atomic Configuration Interaction Research Articles

Deep-Learning Approach for the Atomic Configuration Interaction Problem on Large Basis Sets.

High-precision atomic structure calculations require accurate modeling of electronic correlations typically addressed via the configuration interaction (CI) problem on a multiconfiguration wave function expansion. The latter can easily become challenging or infeasibly large even for advanced supercomputers. Here, we develop a deep-learning approach which allows us to preselect the most relevant configurations out of large CI basis sets until the targeted energy precision is achieved. The large CI computation is thereby replaced by a series of smaller ones performed on an iteratively expanding basis subset managed by a neural network. While dense architectures as used in quantum chemistry fail, we show that a convolutional neural network naturally accounts for the physical structure of the basis set and allows for robust and accurate CI calculations. The method was benchmarked on basis sets of moderate size allowing for the direct CI calculation, and further demonstrated on prohibitively large sets where the direct computation is not possible.

Use of truncated taylor series for r-112 in electronic structure calculations

A new framework to carry out atomic configuration interaction calculations whereby the r–1ij electron repulsion terms of the Hamiltonian are replaced by truncated Taylor series has been formulated. Crucial for this development is a general reduction of atomic two-body integrals to an integration over three coordinates including cos θ12. Energy level calculations of light atoms show that, within a family of truncated Taylor series, the angular convergence may be adjusted to obtain accurate energies with basis sets containing only a small number of one-electron harmonics.

Analytic variationally optimized internally orthogonalized modified Laguerre orbitals in accurate atomic configuration interaction calculation

An analytic configuration interaction method based on variationally optimized internally orthogonalized modified Laguerre orbitals is presented. We have developed the corresponding computer code. For application, we study the 1s2s 1S isoelectronic sequence from helium to neon and compare with other methods. By taking into account the Eckart upper-bound theorem, we obtained more accurate and more intuitively understandable results than Hartree–Fock and multi-configuration Hartree–Fock reported results.

Analytic atomic wave functions of NMCSCF quality: Applications

AbstractConcise analytic, nonorthogonal but selectively orthogonalizable, modified Laguerre type atomic orbitals are developed, providing conciseness, clear physical interpretation, and near‐equivalent accuracy with numerical multi‐configuration self‐consistent field, to atomic configuration interaction calculations. By analyzing the general Eckart theorem, which introduces an energy augmentation to the variational criterion for excited states, securing against variational collapse, we use them to calculate several excited atomic states known to be in danger of suffering from variational collapse. We also use them to calculate highly excited states, applied to computation of recently measured VUV spectra of He states near the second ionization threshold. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Atomic configuration interaction and studies of He, Li, Be, and Ne ground states

The atomic configuration interaction (CI) is reconsidered. We compare the algebraic and geometric approaches to the construction of the CI matrix and point out advantages of the latter. One-electron basis sets of quality comparable to numerical multiconfigurational Hartree-Fock are readily obtained. The generation of large CI lists of symmetry eigenfunctions is monitored by a prescription establishing an {ital a priori} identification of relevant contributions to the wave function. Systematic and well-defined truncations to multireference CI{close_quote}s are examined. A formula for energy contributions of six-excited unlinked clusters is derived and shown to give reasonable estimates. Ensuing nonrelativistic CI calculations on He, Li, Be, and Ne ground states yield the lowest upper bounds in the literature, capturing 99.978, 99.923, 99.919, and 99.59{percent} of the accepted correlation energies, respectively. {copyright} {ital 1997} {ital The American Physical Society}

General contraction of Gaussian basis sets. II. Atomic natural orbitals and the calculation of atomic and molecular properties

Our recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.

NON- RELATIVISTIC AND RELATIVISTIC ATOMIC CONFIGURATION INTERACTION THEORY EXCITATION ENERGY AND RADIATIVE TRANSITION PROBABILITY

We have established the non-relativistic and relativistic atomic configuration interaction methods to calculate excitation energies of low excited states as well as radiative transition probabilities for allowed and forbidden transitions. In order to check our computer codes, we have calculated the excitation energies for N=2 states and the corresponding radiative transition rates for the atomic helium. The results of our non-relativistic and relativistic calculations agree with each other. The excitation energies are accurate within a few thousandths, the corresponding radiative transition probabilities within a few percents. Our methods can be readily applied to other atoms as well as ionized atoms.

Accurate basis sets for atomic configuration interaction calculations

A Hartree-Fock-Slater program and a compatible box potential program are developed to generate complete basis sets for configuration interaction calculations using many-body perturbation theory. Several problems in previous methods are remedied. Examples are given for Pr 3+ and Np 3+ ions. Good orthogonality between basis functions is obtained even for large values of n and l.

Symmetry eigenfunctions suitable for many‐electron theories and calculations. I. Mainly atoms

AbstractAn interpretation of degenerate symmetry spaces associated with a given atomic or molecular configuration is presented, and the theory necessary for atomic applications is discussed in detail. Löwdin's symmetric projection operator for spin and orbital angular momentum is applied on a well‐defined sequence of Slater determinants. In this way a degenerate LS space is divided into orthogonal invariant subspaces which can be classified according to internal couplings of angular momentum. A procedure is found which permits expression of each of these LS eigenfunctions as the smallest possible number of successively orthogonalized projected Slater determinants. In particular, minimum size Hartree‐Fock interacting spaces (important in rapidly convergent correlation energy calculations) are obtained in their most compact form. An optimum partition of degenerate spaces of three and four excited (atomic or molecular) configurations is obtained in general. Interpretations, simplifications, and systematizations in atomic configuration interaction calculations are discussed in light of present results.

A new approach in atomic configuration interaction calculations

A new type of potential function is derived from the atomic Hartree-Fock self- consistent potential which has almost identical occupied orbitals, but an adjustable set of unoccupied bound orbitals. Comparisons are made between the properties of this potential and the Hartree-Fock potential for trivalent praesodymium. It is shown that the use of the new potential introduces considerable simplifications into atomic configuration interaction calculations.

Electronic Wavefunctions for Atoms. III. Partition of Degenerate Spaces and Ground State of C

The atomic configuration-interaction (CI) expansion is expressed in terms of constituents which are invariant under linear transformations of the radial one-electron basis. For open-shell states, the degenerate LS spaces are partitioned into maximal Hartree–Fock (HF) noninteracting spaces and minimal HF interacting spaces. This particular partition is shown to improve considerably the convergence of the atomic CI expansion, and it may be applied to molecular CI expansions in terms of symmetry orbitals. An exhaustive calculation of the ground state of C is carried out. A well-defined linear transformation of the radial one-electron basis is made in order to improve further the convergence of the CI series. The final 234-term CI expansion (formed from a determinantal space of dimension 4836) obtained with an optimized 7s6p4d3f basis, gives an energy E = −37.83378 a.u. (C), accounting for more than 93% of the correlation energy. The C wavefunction is believed to be expressed in its most rapidly convergent form. The advantages of the present approach to atomic CI calculations are discussed.